diff --git a/.project b/.project new file mode 100644 index 0000000..acdb27f --- /dev/null +++ b/.project @@ -0,0 +1,11 @@ + + + tps + + + + + + + + diff --git a/Introduction.tex b/Introduction.tex new file mode 100644 index 0000000..5c8d840 --- /dev/null +++ b/Introduction.tex @@ -0,0 +1,3 @@ +This is a qualitative study.\\ +Its analytic lens is phenomenography.\\ +The research question is what are the conceptions of proof we find in the population of students of computer science (and engineering). \ No newline at end of file diff --git a/QlistCSE2500.tex b/QlistCSE2500.tex new file mode 100644 index 0000000..9922be5 --- /dev/null +++ b/QlistCSE2500.tex @@ -0,0 +1,315 @@ +Product: +an assessment list of questions for incoming to discrete math + +%\begin{enumerate} + +%\item Matching symbolic representations (i.e., equations in figures) with algorithms in pseudocode: + +%Stick breaking:\\ +%Start with a unit length.\\ % stick.\\ +%This unit serves as "what is in stock".\\ +%Every time a fractional part is required, a random fraction of the remaining %stock is taken.// %the stick is broken, one piece will be provided as output of the process, and the remainder will be held for future breaking.\\ +%When it is desired to have $p$ fractions, adding to length 1, $p-1$ iterations will satisfy this.\\ + + +\begin{figure}[ht] +\centering +\includegraphics[width=0.7 +\linewidth]{./pic8} +\caption{Equation (1)} +\end{figure} + +\begin{figure}[ht]\centering +\[ + \sum_{i=0}^k \frac{1}{2^i} +\] +\caption{Equation (2)} +\end{figure} + + +% \begin{algorithm}[H] +% factorization(n)\; +% \KwData{an integer $\geq 2$, which becomes bound to the variable n} +% \KwResult{a prime factorization of n} +% \eIf{$prime(n)$}{ +% return n +% }{ +% (factor1, factor2) = getFactors(n)\; +% return factorization(factor1) $\times$ factorization(factor2) +% } +% \caption{pseudocode for obtaining factorization } +% \end{algorithm} + + +\begin{multicols}{2} +\begin{algorithm}[H] +\caption{ } +\begin{algorithmic}[1] +%\IF{$A \rightarrow false$} +%\STATE $A = false$\\ +%\ENDIF +\STATE num = rand()*10;\\ +\STATE stock = 1;\\ +\STATE amount = 0;\\ +\STATE frac = 1/2;\\ +getRandomFraction() +\WHILE{num $>0$} +\STATE{stock = stock*frac; +\STATE amount = stock+amount;\\ +\STATE num = num-1;\\ +} \ENDWHILE + +return amount;\\ +\} +\end{algorithmic} + +\end{algorithm} + +\columnbreak + +\begin{algorithm}[H] +\caption{ } +\begin{algorithmic}[1] +%\IF{$A \rightarrow false$} +%\STATE $A = false$\\ +%\ENDIF +\STATE num = rand()*10;\\ +\STATE stock = 1;\\ +\STATE amount = 0;\\ +\STATE frac = 1/2;\\ +getRandomFraction() +\STATE frac=rand(); \\ +\STATE amount = stock*frac;\\ +\STATE stock = stock - amount;\\ +return amount; +\end{algorithmic} +\end{algorithm} + +\end{multicols} +Circle your choice:\\ +Equation 1 goes with Algorithm 1? Yes, No\\ +Equation 1 goes with Algorithm 2? Yes, No\\ +Equation 2 goes with Algorithm 1? Yes, No\\ +Equation 2 goes with Algorithm 2? Yes, No\\ + +\newpage +%\item Matching figures/diagrams with symbolic representations\\ +Show which equation goes with which diagram, if they can be matched. +\begin{enumerate} + + +\item \begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./pic2GNUPaint} +\caption{} +\label{fig:pic2} +\end{figure} + +\item \begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./pic4} +\caption{} +\label{fig:pic4} +\end{figure} +\end{enumerate} + +\begin{enumerate} +\item $b^2 + ab = (b+a/2)^2 - (a/2)^2$ +\item $(a+b)^2 + (a-b)^2 = 2(a^2 + b^2)$ +\end{enumerate} +Circle your choice:\\ +Equation (a) goes with Figure 3? Yes, No\\ +Equation (b) goes with Figure 3? Yes, No\\ +Equation (a) goes with Figure 4? Yes, No\\ +Equation (b) goes with Figure 4? Yes, No\\ + +\newpage +%\item Matching figures/diagrams with pseudocode +%\begin{enumerate} + +\begin{figure} +\centering +\includegraphics[width=0.6\linewidth]{./pic9} +\caption{First} +\label{fig:pic9} +\end{figure} + + + +\begin{figure} +\centering +\includegraphics[width=0.6\linewidth]{./pic10GNU} +\caption{Second} +\label{fig:pic10} +\end{figure} + + + + +\begin{multicols}{2} +\begin{algorithm}[H] +\caption{ } +\begin{algorithmic}[1] +\STATE amount = 1;\\ +getAmount(n)\{\\ +\STATE amount = 0; +\FOR{$i=0$ to $n$} +\STATE \FOR{$j=0$ to $i$} +\STATE amount = amount +j; +\ENDFOR +\ENDFOR\\ +return amount;\} +\end{algorithmic} +\end{algorithm} +\columnbreak + +\begin{algorithm}[H] +\caption{ } +\begin{algorithmic}[1] +\STATE amount = 1;\\ +getAmount(n)\{\\ +\IF{$n=0$} + \STATE return (1) + + \ELSE + \STATE return(2*getAmount(n-1)+1) + \ENDIF\\ +\} +\end{algorithmic} + +\end{algorithm} + +\end{multicols} +\newpage +Circle your choice:\\ +Figure 5 goes with Algorithm 3? Yes, No\\ +Figure 5 goes with Algorithm 4? Yes, No\\ +Figure 6 goes with Algorithm 3? Yes, No\\ +Figure 6 goes with Algorithm 4? Yes, No\\ + + +%\item + +%\item + + +%\end{enumerate} +%\newpage +%\item Comprehending figures\\ + +%Explain why the figure matches the equation $\frac{a+b}{2} \geq \sqrt{ab}$ with equality if and only if $a=b$ + +%\begin{figure} +%\centering +%\includegraphics[width=0.7\linewidth]{./pic5} +%\caption{} +%\label{fig:pic5} +%\end{figure} + +\newpage +%\item Comprehending symbolic representation\\ + +Describe in text what this symbolic statement means:\\ +\[ +\sum_{ k \in \mathbb{N}}^{\infty} (2k+1) +\] +\newpage +%\item Comprehending pseudocode + +Describe in text, what this process is doing:\\ +Challenge question: What is the significance of the process described by this pseudocode? + +\begin{algorithm}[H] +\caption{ } +\begin{algorithmic}[1] +\STATE done = false;\\ +\STATE a = 0;\\ +\STATE b = 0;\\ +\STATE c=0;\\ +\STATE n = 2;\\ +\WHILE{!done} +\STATE{ \WHILE{$a>0$} +\STATE{ a=a+1; +\WHILE{$b>0$} +\STATE{ b=b+1; +\WHILE{$c>0$} +\STATE{ c=c+1;\\ +\WHILE{$n>0$} +\STATE{ n=n+1;\\ +\IF{$a^n +b^n = c^n$} + \STATE done = true; + \ENDIF\\ + +} \ENDWHILE +} \ENDWHILE\\ +} \ENDWHILE\\ +} \ENDWHILE + +} \ENDWHILE + +\end{algorithmic} + +\end{algorithm} + +\newpage + Applying symbolic representation to figure + +Label these figures mathematical symbols:\\ +Challenge question: What is the significance of these figures taken together? + +\vspace{1cm} +\begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./pic1} +\caption{} +\label{fig:pic1} +\end{figure} + + +\newpage + Applying figure to symbolic representation + +Draw a figure that expresses:\\ +Through any three points that are not collinear, two can be used to identify a line, and the third can be used, combined with that line, to identify a line parallel to the first line. + +\newpage + Applying pseudocode to figure + +Write pseudocode (e.g., as has been seen earlier in these questions) to count the little squares, according to the method suggested by the shading in the figure: \\ +Hint: the bottom row could be row 1.\\ +$n$ and $k$ could be parameters.%(p. 93)\\ + +\begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./p93} + +\label{fig:p93} +\end{figure} + + +\newpage + Applying pseudocode to symbolic representation + +Write pseudocode for the calculation below:\\ +Hint: ${ n \choose k} $ means, from a set of size $n$ choose (without replacement) $k$ elements.\\ +For example, from a list of friends of size $n$, choose a list of party guests of size $k$. (Without replacement means, you do not send two invitations to the same friend.) + +Please say whether the concrete example (friends, guest list) aided your thinking. + +${ n \choose k} = {n-1 \choose k-1}+ {n-1 \choose k}$ +\newpage + Synthesis: word problems to figures + +Draw a figure for this word problem:\\ +Pick an angle between 0 and $\pi/2$ radians, call it $\theta$.\\ +A right triangle can be drawn, the height of which is 1 plus the tangent of $\theta$, the base of which is 1 plus the cotangent of $\theta$. The angle $\theta$ is adjacent to the base. It will be the case that the hypotenuse of this triangle is the cosecant of $\theta$ plus the secant of $\theta$. +\newpage +Synthesis: word problems to symbolic representation\\ + +Express in symbols this word problem:\\ +The number of moves in a game of size n is given by twice the number of moves in a game of size (n-1), plus one more move. +\newpage + Synthesis: word problems to pseudocode + +Write pseudocode for this word problem:\\ +Two trains, initially 40 miles apart on the same track, going opposite directions, are getting closer to each other at the rate of 40 miles per hour. An insect flies from one train to the other and back, at a constant speed of $v$, repeatedly. How far does the insect fly, before the trains collide? diff --git a/TODOs.tex b/TODOs.tex new file mode 100644 index 0000000..704aeed --- /dev/null +++ b/TODOs.tex @@ -0,0 +1,19 @@ +\newpage + +TODOs +read more on van Hiele levels and their theory + +Professor McC asks should this include communication? Is he talking about proofs being communicative, or is he talking about proving that communication occurs among algorithms? + +explanations of things : +DONE phenomenography, +DONE variation theory, +DONE constructivism/Piaget +DONE social constructivism + +how much detail on the description of the population of students in CS, or, interviewed students? + +details on data analysis: describing how analysis was done in detail really important. How do you do phenomenography? +Is "this" (my description of thematic analysis) the way everything was analyzed. + +details of semi-structured interview protocols for any interviews \ No newline at end of file diff --git a/abstract.tex b/abstract.tex new file mode 100644 index 0000000..abfd094 --- /dev/null +++ b/abstract.tex @@ -0,0 +1,9 @@ +Guided by constructivism, which posits that students assimilate new knowledge into what has made sense to them previously, we researched student conceptualizations of proof. +We used the qualitative research methods of thematic +analysis and phenomenography to learn and categorize student conceptualizations +of proof, and of mathematization more generally. Our published +work exhibited an explanatory connection between publications of others in +the mathematics education community and the computer science education +community. We used these phenomenographic categories to intuit ideas whose +emphasis might be helpful for students’ development of deeper understanding +of proof. \ No newline at end of file diff --git a/acknowledgments.tex b/acknowledgments.tex new file mode 100644 index 0000000..f94a2c1 --- /dev/null +++ b/acknowledgments.tex @@ -0,0 +1 @@ +Thank you to all of the members of the department, each of whom has helped me to some degree. Your daily example means a great deal. Scholarship, graciousness, patience and compassion are a few of the qualities with which you inspire us, the students. Thank you to Professor Donald Sheehy for his helpful suggestions and exemplary teaching. Thank you to Professors Shvartsman, Gokhale, and Ammar for support and kindness. Thank you to Professors Russell and Michel for inspiration. Thank you to Debra Mielczarek, Joy Billion and Rebecca Randazzo for exemplary competence and unfailing assistance. Thank you to Professor McCartney for support, example, and astonishing patience. Thank you to Jack, \textit{semper providente prospectu}. \ No newline at end of file diff --git a/algorithm.sty b/algorithm.sty new file mode 100644 index 0000000..58cef6c --- /dev/null +++ b/algorithm.sty @@ -0,0 +1,95 @@ +% ALGORITHM STYLE -- Released 8 April 1996 +% for LaTeX-2e +% Copyright -- 1994 Peter Williams +% +% E-mail pwil3058@bigpond.net.au +% +% This style file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public +% License as published by the Free Software Foundation; either +% version 2 of the License, or (at your option) any later version. +% +% This style file is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public +% License along with this style file; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithm} +\typeout{Document Style `algorithm' - floating environment} + +\RequirePackage{float} +\RequirePackage{ifthen} +\newcommand{\ALG@within}{nothing} +\newboolean{ALG@within} +\setboolean{ALG@within}{false} +\newcommand{\ALG@floatstyle}{ruled} +\newcommand{\ALG@name}{Algorithm} +\newcommand{\listalgorithmname}{List of \ALG@name s} + +% Declare Options +% first appearance +\DeclareOption{plain}{ + \renewcommand{\ALG@floatstyle}{plain} +} +\DeclareOption{ruled}{ + \renewcommand{\ALG@floatstyle}{ruled} +} +\DeclareOption{boxed}{ + \renewcommand{\ALG@floatstyle}{boxed} +} +% then numbering convention +\DeclareOption{part}{ + \renewcommand{\ALG@within}{part} + \setboolean{ALG@within}{true} +} +\DeclareOption{chapter}{ + \renewcommand{\ALG@within}{chapter} + \setboolean{ALG@within}{true} +} +\DeclareOption{section}{ + \renewcommand{\ALG@within}{section} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsection}{ + \renewcommand{\ALG@within}{subsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{subsubsection}{ + \renewcommand{\ALG@within}{subsubsection} + \setboolean{ALG@within}{true} +} +\DeclareOption{nothing}{ + \renewcommand{\ALG@within}{nothing} + \setboolean{ALG@within}{true} +} +\DeclareOption*{\edef\ALG@name{\CurrentOption}} + +% ALGORITHM +% +\ProcessOptions +\floatstyle{\ALG@floatstyle} +\ifthenelse{\boolean{ALG@within}}{ + \ifthenelse{\equal{\ALG@within}{part}} + {\newfloat{algorithm}{htbp}{loa}[part]}{} + \ifthenelse{\equal{\ALG@within}{chapter}} + {\newfloat{algorithm}{htbp}{loa}[chapter]}{} + \ifthenelse{\equal{\ALG@within}{section}} + {\newfloat{algorithm}{htbp}{loa}[section]}{} + \ifthenelse{\equal{\ALG@within}{subsection}} + {\newfloat{algorithm}{htbp}{loa}[subsection]}{} + \ifthenelse{\equal{\ALG@within}{subsubsection}} + {\newfloat{algorithm}{htbp}{loa}[subsubsection]}{} + \ifthenelse{\equal{\ALG@within}{nothing}} + {\newfloat{algorithm}{htbp}{loa}}{} +}{ + \newfloat{algorithm}{htbp}{loa} +} +\floatname{algorithm}{\ALG@name} + +\newcommand{\listofalgorithms}{\listof{algorithm}{\listalgorithmname}} diff --git a/algorithm2e.sty b/algorithm2e.sty new file mode 100644 index 0000000..d674a29 --- /dev/null +++ b/algorithm2e.sty @@ -0,0 +1,1259 @@ +%% algorithm2e.sty --- style file for algorithms +%% Copyright 1996-2003 Christophe Fiorio +% +% This program may be distributed and/or modified under the +% conditions of the LaTeX Project Public License, either version 1.2 +% of this license or (at your option) any later version. +% The latest version of this license is in +% http://www.latex-project.org/lppl.txt +% and version 1.2 or later is part of all distributions of LaTeX +% version 1999/12/01 or later. +% +% This program consists of the files algorithm2e.sty and algorithm2e.tex +% +% Report bugs and comments to: +% fiorio@lirmm.fr +% +% $Id: algorithm2e.sty,v 2.51 2003/10/27 16:56:05 fiorio Exp $ +% +% PACKAGES REQUIRED: +% +% - float (in contrib/supported/float) +% - ifthen (in base) +% - xspace (in packages/tools) +% +%%%%%%%%%%%%%%% Release 2.51 +% +% History: +% +% - October 27 2003 - revision 2.51 - Revision submitted to CTAN archive +% * correction of a minor which make caption in procedure +% and function to be blanck with pdfscreen package +% (thanks to Joel Gossens for the notification) +% * add two internal definition to avoid some errors when +% used with Hyperref package (Hyperref package need to +% define new counter macro from existing ones, and +% don't do it for algorithm2e package, so we do it) +% +% - October 17 2003 - revision 2.50 - first revision for CTAN archive +% +% * add \AlFnt and \SetAlFnt{font} macros: +% \AlFnt is used at the beginning of the caption and the +% body of algorithm in order to define the fonts used +% for typesetting algorithms. You can use it elsewhere +% you want to typeset text as algorithm. For example +% you can do \SetAlFnt{\small\sf} to have algorithms +% typeset in small sf font. Default is nothing so +% algorithm is typeset as the text of the document. +% * add \AlTitleFnt{text} and \SetAlTitleFnt{font} macros: +% The {Algorithm: } in the caption is typeset with +% \AlTitleFnt{Algorithm:}. You can use it to have text +% typeset as {Algorithm:} of captions. Default is +% textbf. +% Default can be redefined by \SetAlTitleFnt{font}. +% * add CommentSty typo for text comment. +% * add some compatibility with hyperref package (still +% an error on multiply defined refs but pdf correctly +% generated) +% * flush text to left in order to have correct +% indentation even with class as amsart which center +% all figures +% * add german, portugues and czech options for title of +% algorithms and typo. +% * add portuguese translation of predefined keywords +% * add czech translation of some predefined keywords +% +% - December 23 2002 - revision 2.40 +% * add some french keyword missing +% * add function* and procedure* environment like +% algorithme* environment: print in one column even +% if twocolumn option is specified for the document. +% * add a new macro \SetKwComment to define macro which +% writes comments in the text. First argument is the +% name of the macro, second is the text put before the +% comment, third is the text put at the end of the +% comment.Default are \tcc and \tcp +% * add new options to change the way algo are numbered: +% [algopart] algo are numbered within part (counter must exist) +% [algochapter] algo are numbered within chapter +% [algosection] algo are numbered within section +% +% - March 27 2002 - revision 2.39 +% Gilles Geeraerts: added the \SetKwIfElseIf to manage +% if (c) +% i; +% else if (c) +% i; +% ... +% else +% i; +% end +% Also added \gIf \gElsIf \gElse. +% +% - January 02 2001 - revision 2.38 +% bugs related to the caption in procedure and function +% environment are corrected. +% bug related to option noend (extra vertical space added +% after block command as If or For) is corrected. +% czech option language added (thanks to Libor Bus: l.bus@sh.cvut.cz). +% +% - October 16 2000 - revision 2.37 +% option algo2e added: change the name of environment +% algorithm into algorithm2e. So allow to use the package +% with some journal style which already define an algorithm +% environment. +% +% - September 13 2000 - revision 2.36 +% option slide added: require package color +% Hack for slide class in order to have correct +% margins +% +% - November 25 1999 - revision 2.35 +% revision number match RCS number +% Thanks to David A. Bader, a new option is added: +% noend: no end keywords are printed. +% +% - November 19 1999 - revision 2.32 +% minor bug on longend option corrected. +% +% - August 26 1999 - revision 2.31 +% add an option : figure +% this option treats algorithms as figure and so are numbered +% as figures and putted in the \listoffigures +% +% - January 21 1999 - revision 2.3 beta +% add 2 new environments: procedure and function. +% These environments works like algorithm environment but: +% - the ruled (or algoruled) style is imperative. +% - the caption now writes Procedure name.... +% - the syntax of the \caption command is restricted as +% follow: you MUST put a name followed by 2 braces like +% this ``()''. You can put arguments inside the braces and +% text after. If no argument is given, the braces will be +% removed in the title. +% - label now puts the name (the text before the braces in the +% caption) of the procedure or function as reference (not +% the number like a classic algorithm environment). +% There are also two new styles : ProcNameSty and +% ProcArgSty. These style are by default the same as FuncSty +% and ArgSty but are used in the caption of a procedure or a +% function. +% +% - November 28 1996 - revision 2.22 +% add a new macro \SetKwInParam{arg1}{arg2}{arg3}: +% it defines a macro \arg1{name}{arg} which prints name in keyword +% style followed byt arg surrounded by arg2 and arg3. The main +% application is to a function working as \SetKwInput to be used +% in the head of the algorithm. For example +% \SetKwInParam{Func}{(}{)} allows +% \Func{functionname}{list of arguments} which prints: +% \KwSty{functioname(}list of arguments\KwSty{)} +% +% +% - November 27 1996 - revision 2.21 : +% minor bug in length of InOut boxes fixed. +% add algorithm* environment. +% +% - July 12 1996 - revision 2.2 : \SetArg and \SetKwArg macros removed. +% +% \SetArg has been removed since it never has been +% documented. +% \SetKwArg has been removed since \SetKw can now +% take an argument in order to be consistent with +% \SetKwData and \SetKwFunction macros. +% +% - July 04 1996 - revision 2.1 : still more LaTeX2e! Minor compatibility break +% +% Macros use now \newcommand instead of \def, use of \setlength, +% \newsavebox, ... and other LaTeX2e specific stuff. +% The compatibility break: +% - \SetData becomes \SetKwData to be more consistent. So the old +% \SetKwData becomes \SetKwInput +% - old macros \titleofalgo, \Freetitleofalgo and \freetitleofalgo +% from LaTeX209 version which did print a warning message and call +% \Titleofalgo in version 2.0 are now removed! +% +% - March 13 1996 - revision 2.0: first official major revision. +% +% +%%%%%%%%%%%%%% +% +% Known bugs: +% ----------- +% - [H] option of algorithm environment doesn't work with * environments +% (ie. algorithm*). This is due to floats defined with float package (as +% algorithms are) and so can't be +% adressed here. +% - [figure] option is not compatible with floatflt package, in fact +% \texttt{caption} of floatingfigure are not compatible. \Optfigure restyle +% algo as figure, so caption of figure uses \texttt{float} package +% caption. \texttt{floatflt} package is declare as a figure but doesn't call +% some \texttt{figure} macro as in the original and so some stuffs are not +% defined correctly which makes a bug. If someone find a solution to this +% problem, I will be glad to include its contribution and thanks him. +% +%%%%%%%%%%%%%% +% +% Package options: +% --------------- +% - french, english : for the name of the algorithm, e.g. +% - boxe, ruled, algoruled, plain : layout of the algorithm +% - noline,lined,vlined : how block are designed. +% - titlenumbered,titlenotnumbered: numbering of title set by \Titleofalgo +% - resetcount, noresetcount : start value of line numbers. +% - algonl : line numbers preceded by algo number +% - shortend, longend : short or long end keyword as endif for e.g. +% +% defaults are; english,plain,resetcount,titlenotnumbered +% +%%%%%%%%%%%%%% +% +% Short summary +% ------------- +% +% algorithm is an environment for writing algorithm in LaTeX2e +% It provide macros that allow you to create differents +% sorts of key words, therefore a set of predefined key word +% is gived. +% +% IT should be used as follows +% +% \begin{algorithm} +% ... +% ... +% \end{algorithm} +% +% +% IMPORTANT : each line MUST end with \; +% +% Note that if you define macros outside algorithm environment they +% are avaible in all the document and particulary you can use then +% inside all algorithms without re-define them. +% +% an example: +% +% \begin{algorithm}[H] +% \SetLine +% \AlgData{this text} +% \AlgResult{how to write algorithm with \LaTeX2e } +% +% initialization\; +% \While{not at end of this document}{ +% read current section\; +% \eIf{understand}{ +% go to next section\; +% current section becomes this one\; +% }{ +% go back to the beginning of current section\; +% } +% } +% \caption{How to write algorithm} +% \end{algorithm} +% +% +%%%%%%%%%%%%%% predefined english keywords +% +% \AlgData{input} +% \AlgResult{output} +% \KwIn{input} +% \KwOut{output} +% \KwData{input} +% \KwResult{output} +% \Ret{[value]} +% \KwTo % a simple keyword +% \Begin{block inside} +% \If{condition}{Then block} % in a block +% \uIf{condition}{Then block} % in a block unended +% \Else{inside Else} % in a block +% \eIf{condition}{Then Block}{Else block} % in blocks +% \lIf{condition}{Else text} % on the same line +% \lElse{Else text} % on the same line +% \Switch{Condition}{Switch block} +% \Case{a case}{case block} % in a block +% \lCase{a case}{case text} % on the same line +% \Other{otherwise block} % in a block +% \lOther{otherwise block} % on the same line +% \For{condition}{text loop} % in a block +% \lFor{condition}{text} % on the same line +% \ForEach{condition}{text loop} % in a block +% \lForEach{condition}{text} % on the same line +% \Repeat{End condition}{text loop} % in a block +% \lRepeat{condition}{text} % on the same line +% \While{condition}{text loop} % in a block +% \lWhile{condition}{text loop} % on the same line +% +% +%%%%%%%%%%%%%% predefined french keywords +% +% \AlgDonnees{input} +% \AlgRes{input} +% \Donnees{input} +% \Res{input} +% \Retour[valeur]} +% \Deb{block inside} +% \KwA % un mot clef simple +% \Si{condition}{Bloc du Alors} % Dans un bloc +% \uSi{condition}{Bloc du Alors} % Dans un bloc non termine +% \eSi{condition}{Bloc du Alors}{Bloc du Sinon} % Dans un bloc +% \lSi{condition}{texte du Alors} % sur la meme ligne +% \lSinon{texte du Sinon} % sur la meme ligne +% \Suivant{Condition}{Bloc de l'instruction} +% \Cas{cas}{Bloc de ce cas} % Dans un bloc +% \lCas{cas}{Bloc de ce cas} % sur la meme ligne +% \Autres{Bloc de l'alternative} % Dans un bloc +% \lAutres{Bloc de l'alternative} % sur la meme ligne +% \Pour{condition}{texte de la boucle} % Dans un bloc +% \lPour{condition}{texte} % sur la meme ligne +% \PourCh{condition}{texte de la boucle} % Dans un bloc +% \lPourCh{condition}{texte} % sur la meme ligne +% \Repeter{End condition}{texte de la boucle} % Dans un bloc +% \lRepeter{condition}{texte} % sur la meme ligne +% \Tq{condition}{texte de la boucle} % Dans un bloc +% \lTq{condition}{texte de la boucle} % sur la meme ligne +% +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% for more complete informations you can see algorithm2e.tex +% +% +%%%%%%%%%%%%%%%%%%%%%%%% Identification Part %%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +\NeedsTeXFormat{LaTeX2e}[1994/12/01] +% +\ProvidesPackage{algorithm2e}[2003/10/10] +% +%%%%%%%%%%%%%%%%%%%%%%%%%%% Initial Code %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% definition of commands which can be redefined in options of the package. +% +\newcounter{AlgoLine} +\setcounter{AlgoLine}{0} +\newcommand{\@ruledskip}{\relax} +\newcommand{\@titleskip}{\relax} +% +\newcommand{\@algoruledstyle}{% +\renewcommand{\@ruledskip}{\medskip}% +\renewcommand{\@titleskip}{\smallskip}% +} %end of \@algoruledstyle +% +\newcommand{\listalgorithmcfname}{} +\newcommand{\algorithmcfname}{} +\newcommand{\algocf@typo}{} +\newcommand{\@algocf@procname}{} +\newcommand{\@algocf@funcname}{} +% +\newcommand{\algocf@style}{plain} +\newcommand{\@ResetCounterIfNeeded}{} +\newcommand{\@titleprefix}{} +% +\newcommand{\algocf@numbering}[1]{\newcommand{\algocf@within}{#1}} +% +\newcommand{\defaultsmacros@algo}{\algocf@defaults@shortend} +% +\newcommand{\algocf@list}{loa} +\newcommand{\algocf@float}{algocf} +% +\newcommand{\algocf@envname}{algorithm} +% +% +%%%%%%%%%%%%%%%%%%%%%% Declaration of Options %%%%%%%%%%%%%%%%%%%%%%%%%%% +% +\RequirePackage{ifthen} +% +\DeclareOption{algo2e}{% + \renewcommand{\algocf@envname}{algorithm2e} +} +% +\newboolean{algocf@slide}\setboolean{algocf@slide}{false} +\DeclareOption{slide}{% + \setboolean{algocf@slide}{true}% +} +% +\DeclareOption{figure}{ +\renewcommand{\algocf@list}{lof} +\renewcommand{\algocf@float}{figure} +} +% +\DeclareOption{english}{% +\renewcommand{\listalgorithmcfname}{List of Algorithms}% +\renewcommand{\algorithmcfname}{Algorithm}% +\renewcommand{\algocf@typo}{}% +\renewcommand{\@algocf@procname}{Procedure} +\renewcommand{\@algocf@funcname}{Function} +} +% +\DeclareOption{french}{% +\renewcommand{\listalgorithmcfname}{Liste des Algorithmes}% +\renewcommand{\algorithmcfname}{Algorithme}% +\renewcommand{\algocf@typo}{\ }% +\renewcommand{\@algocf@procname}{Procédure} +\renewcommand{\@algocf@funcname}{Fonction} +} +% +\DeclareOption{czech}{% +\renewcommand{\listalgorithmcfname}{Seznam algoritm\v{u}}% +\renewcommand{\algorithmcfname}{Algoritmus}% +\renewcommand{\algocf@typo}{}% +\renewcommand{\@algocf@procname}{Procedura} +\renewcommand{\@algocf@funcname}{Funkce} +} +% +\DeclareOption{german}{% +\renewcommand{\listalgorithmcfname}{Liste der Algorithmen}% +\renewcommand{\algorithmcfname}{Algorithmus}% +\renewcommand{\algo@typo}{\ }% +\renewcommand{\@algo@procname}{Prozedur} +\renewcommand{\@algo@funcname}{Funktion} +} +% +\DeclareOption{portugues}{% +\renewcommand{\listalgorithmcfname}{Lista de Algoritmos}% +\renewcommand{\algorithmcfname}{Algoritmo}% +\renewcommand{\algo@typo}{}% +\renewcommand{\@algo@procname}{Procedimento} +\renewcommand{\@algo@funcname}{Fun\c{c}\~{a}o} +} +% +\DeclareOption{plain}{\renewcommand{\algocf@style}{plain}} +\DeclareOption{boxed}{\renewcommand{\algocf@style}{boxed}} +\DeclareOption{ruled}{\renewcommand{\algocf@style}{ruled}} +\DeclareOption{algoruled}{\ExecuteOptions{ruled}\@algoruledstyle} +% +\DeclareOption{algopart}{\algocf@numbering{part}} %algo part numbered +\DeclareOption{algochapter}{\algocf@numbering{chapter}} %algo chapter numbered +\DeclareOption{algosection}{\algocf@numbering{section}} %algo section numbered +% +\DeclareOption{resetcount}{\renewcommand{\@ResetCounterIfNeeded}{\setcounter{AlgoLine}{0}}} +\DeclareOption{noresetcount}{\renewcommand{\@ResetCounterIfNeeded}{}} +% +\DeclareOption{titlenumbered}{% +\renewcommand{\@titleprefix}{% +%\refstepcounter{algocf}\textbf{\algorithmcfname\ \thealgocf\algocf@typo : }}} +\refstepcounter{algocf@float}\AlTitleFnt{\algorithmcfname\ \expandafter\the\algocf@float\algocf@typo : }}} +% +\DeclareOption{titlenotnumbered}{\renewcommand{\@titleprefix}{% + \AlTitleFnt{\algorithmcfname\algocf@typo : }}} +% +\DeclareOption{lined}{\AtBeginDocument{\SetLine}} % \SetLine +\DeclareOption{vlined}{\AtBeginDocument{\SetVline}} % \SetVline +\DeclareOption{noline}{\AtBeginDocument{\SetNoline}} % \Setnoline (default) +% +% line numbered with the counter of the algorithm +\DeclareOption{algonl}{\renewcommand{\theAlgoLine}{\expandafter\the\algocf@float.\arabic{AlgoLine}}} +% +\DeclareOption{longend}{% +\renewcommand{\defaultsmacros@algo}{\algocf@defaults@longend}} +% +\DeclareOption{shortend}{% +\renewcommand{\defaultsmacros@algo}{\algocf@defaults@shortend}} +% +\DeclareOption{noend}{% +\renewcommand{\defaultsmacros@algo}{\algocf@defaults@noend}} +% +%%%%%%%%%%%%%%%%%%%%%%% Execution of Options %%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +\ExecuteOptions{english,plain,resetcount,titlenotnumbered} +% +\ProcessOptions +% +%%%%%%%%%%%%%%%%%%%%%%%%%% Package Loading %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +\RequirePackage{float}[2001/11/08] +% +\RequirePackage{xspace} +% +\ifthenelse{\boolean{algocf@slide}}{\RequirePackage{color}}{} +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Main Part %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +\newcommand{\algocf@name}{algorithm2e} +\newcommand{\algocf@date}{October 27 2003} +\newcommand{\algocf@version}{Release 2.51} +\newcommand{\algocf@id}{\algocf@version\space -- \algocf@date\space --} +\typeout{^^J********************************************************^^JPackage `\algocf@name'\space\algocf@id^^J% + - algorithm2e-announce@lirmm.fr mailing list for^^J announcement about releases^^J% + - algorithm2e-discussion@lirmm.fr mailing list for^^J discussion, comments, questions about the package^^J% + (subscribe by sending an email to sympa@lirmm.fr with subscribe )^^J% + - Author: Christophe Fiorio (fiorio@lirmm.fr)^^J********************************************************^^J} +%% +%% +%% +%% +%% +%% +%%%% hyperref compatibility tricks: Hyperref package defines H counters from + % standard counters (i.e \theHpage from \thepage) and check some particular + % counters of some packages, unfortunately it doesn't do the same for + % algorithm2e package but act as Hcounter was defined. To avoid errors we + % defined \theHalgocf ourself +%%%% +\@ifundefined{theHalgocf}{\def\theHalgocf{\thealgocf}}{}% +\@ifundefined{toclevel@algocf}{\def\toclevel@algocf{0}}{}% +%% +%% +%% +\newcommand{\@defaultskiptotal}{0.5em}%\setnlskip{0.5em} +\newskip\skiptotal\skiptotal=0.5em%\setnlskip{0.5em} +\newskip\skiprule +\newskip\skiptext +\newskip\skiplength +\newskip\algomargin +\newskip\skipnumline +\newskip\skipalgocfslide\skipalgocfslide=1em +\newdimen\algowidth +\newdimen\inoutsize +\newdimen\inoutline +% +\newsavebox{\algocf@inoutbox} +\newsavebox{\algocf@inputbox} +%% +%% +\newcommand{\arg@e}{} +\newcommand{\arg@space}{\ } +\newcommand{\BlankLine}{\vskip 1ex} +%% +\newcommand{\vespace}{1ex} +\newcommand{\SetInd}[2]{% +\skiprule=#1% +\skiptext=#2% +\skiplength=\skiptext\advance\skiplength by \skiprule\advance\skiplength by 0.4pt} +\SetInd{0.5em}{1em} +\algomargin=\leftskip\advance\algomargin by \parindent +\newcommand{\incmargin}[1]{\advance\algomargin by #1} +\newcommand{\decmargin}[1]{\advance\algomargin by -#1} +\newcommand{\setnlskip}[1]{% +\renewcommand{\@defaultskiptotal}{#1}% +\setlength{\skiptotal}{#1}} +%% +%% +\newcommand{\Indentp}[1]{\advance\leftskip by #1\advance \skiptotal by #1} +\newcommand{\Indp}{\advance\leftskip by 1em\advance \skiptotal by 1em} +\newcommand{\Indpp}{\advance\leftskip by 0.5em\advance \skiptotal by 0.5em} +\newcommand{\Indm}{\advance\leftskip by -1em\advance\skiptotal by -1em} +\newcommand{\Indmm}{\advance\leftskip by -0.5em\advance\skiptotal by -0.5em} +%% +% number line style +\newcommand{\nlSty}[1]{\textbf{#1}}% default definition +\newcommand{\Setnlsty}[3]{\renewcommand{\nlSty}[1]{\csname#1\endcsname{#2##1#3}}} +\newcommand{\nl}{\refstepcounter{AlgoLine}\hskip 0pt\llap{% + \scriptsize{\nlSty{\theAlgoLine}}\hskip\skiptotal}\ignorespaces} +\newcommand{\enl}{;\refstepcounter{AlgoLine}\hfill\rlap{% + \scriptsize{\nlSty{\theAlgoLine}}}\par} +\newcommand{\nlset}[1]{\hskip 0pt\llap{% + \scriptsize{\nlSty{#1}}\hskip\skiptotal}\ignorespaces} +% +\@ifundefined{href}{\newcommand{\lnl}[1]{\nl\label{#1}}}{% + \newcommand{\lnl}[1]{\nl\immediate\write\@auxout{\string \newlabel % + {#1}{{\theAlgoLine}{\thepage}{algorithm\relax}{algoline.\theAlgoLine}{}}}% + \ignorespaces}} +\@ifundefined{href}{\newcommand{\lnlset}[2]{\nlset{#2}% + \@bsphack\protected@write\@auxout{}{\string\newlabel{#1}{{#2}{\thepage}}}\@esphack}% + }{% + \newcommand{\lnlset}[2]{\nlset{#2}% + \immediate\write\@auxout{\string\newlabel % + {#1}{{#2}{\thepage}{algorithm\relax}{algoline.#2}{}}}% + \ignorespaces}} +%% +\newcommand{\@endalgoln}{\string; \par}% default definition: printsemicolon +\newcommand{\dontprintsemicolon}{\renewcommand{\@endalgoln}{\par}} +\newcommand{\printsemicolon}{\renewcommand{\@endalgoln}{\string; \par}} +% +%% +%% +% +\newcommand{\AlTitleFnt}[1]{\textbf{#1}}% default definition +\newcommand{\SetAlTitleFnt}[1]{\renewcommand{\AlTitleFnt}[1]{\csname#1\endcsname{##1}}} +\newcommand{\AlFnt}{\relax}% default definition +\newcommand{\SetAlFnt}[1]{\renewcommand{\AlFnt}{#1}} +\newcommand{\KwSty}[1]{\textbf{#1}}% default definition +\newcommand{\SetKwSty}[1]{\renewcommand{\KwSty}[1]{\csname#1\endcsname{##1}}} +\newcommand{\ArgSty}[1]{\emph{#1}}%\SetArgSty{emph} +\newcommand{\SetArgSty}[1]{\renewcommand{\ArgSty}[1]{\csname#1\endcsname{##1}}} +\newcommand{\FuncSty}[1]{\texttt{#1}}%\SetFuncSty{texttt} +\newcommand{\SetFuncSty}[1]{\renewcommand{\FuncSty}[1]{\csname#1\endcsname{##1}}} +\newcommand{\DataSty}[1]{\textsf{#1}}%%\SetDataSty{textsf} +\newcommand{\SetDataSty}[1]{\renewcommand{\DataSty}[1]{\csname#1\endcsname{##1}}} +\newcommand{\CommentSty}[1]{\texttt{#1}}%%\SetDataSty{texttt} +\newcommand{\SetCommentSty}[1]{\renewcommand{\CommentSty}[1]{\csname#1\endcsname{##1}}} +\newcommand{\TitleSty}[1]{#1}%\SetTitleSty{}{} +\newcommand{\SetTitleSty}[2]{\renewcommand{\TitleSty}[1]{% +\csname#1\endcsname{\csname#2\endcsname##1}}} +% +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newcommand{\al@push}[1]{\advance\skiptotal by #1\moveright #1} +\newcommand{\al@pop}[1]{\advance\skiptotal by -#1} +\newcommand{\al@addskiptotal}{\advance\skiptotal by 0.4pt\advance\hsize by -0.4pt} % 0.4 pt=width of \vrule +\newcommand{\al@subskiptotal}{\advance\skiptotal by -0.4pt} % 0.4 pt=width of \vrule +% +\newcommand{\V@line}[1]{\al@push{\skiprule}\hbox{\vrule% + \vtop{\al@push{\skiptext}\vtop{\al@addskiptotal\advance\hsize by -\skiplength #1}\Hlne}}% + \al@pop{\skiprule}\al@subskiptotal\vskip\vespace} +% +\newcommand{\V@sline}[1]{\al@push{\skiprule}\hbox{\vrule% + \vtop{\al@push{\skiptext}\vtop{\al@addskiptotal\advance\hsize by -\skiplength #1\vskip 1ex}}}% + \al@pop{\skiprule}\al@subskiptotal\vskip 1pt\nointerlineskip} +% +\newcommand{\H@lne}{\hrule height 0.4pt depth 0pt width .5em} +% +\newcommand{\No@line}[1]{\par\al@push{\skiprule}\hbox{% + \vtop{\al@push{\skiptext}\vtop{\advance\hsize by -\skiplength #1}\vskip 1pt}}% + \al@pop{\skiprule}} +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% +%% default=NoLine +% +\newcommand{\a@@block}[2]{\No@line{##1}\KwSty{##2}\par} +\newcommand{\a@block}[2]{\a@@block{#1}{#2}} % this to be redefined as a@group in + % case of noend option +\newcommand{\a@group}[1]{\No@line{##1}} +\newcommand{\Hlne}{} +% +% +\newcommand{\SetNoline}{%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Noline +\renewcommand{\a@@block}[2]{\No@line{##1}\KwSty{##2}\par}% +%\long +\renewcommand{\a@group}[1]{\No@line{##1}} +\renewcommand{\Hlne}{}} +% +\newcommand{\SetVline}{%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Vline +\renewcommand{\a@@block}[2]{\V@line{##1}}% +\renewcommand{\a@group}[1]{\V@sline{##1}} +\renewcommand{\Hlne}{\H@lne}} +% +\newcommand{\SetLine}{%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Line +\renewcommand{\a@@block}[2]{\V@sline{##1}\KwSty{##2}\par}% +\renewcommand{\a@group}[1]{\V@sline{##1}} +\renewcommand{\Hlne}{}} +% +\newcommand{\SetNothing}{%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Noline +\renewcommand{\a@@block}[2]{\No@line{##1}\par}% +%\long +\renewcommand{\a@group}[1]{\No@line{##1}} +\renewcommand{\Hlne}{}} +% +%% +%% +% +% +% ``Input :'''s like command where the text stay at the right of the longer +% keyword of KwInOut commands (text of KwInOut commands are all vertically aligned) +\newcommand{\SetKwInOut}[2]{% + \sbox{\algocf@inoutbox}{\hbox{\KwSty{#2}\algocf@typo:\ }}% + \expandafter\ifx\csname InOutSizeDefined\endcsname\relax% if first time used + \expandafter\newcommand\csname InOutSizeDefined\endcsname{}% + \setlength{\inoutsize}{\wd\algocf@inoutbox}% + \else% else keep the larger dimension + \ifdim\wd\algocf@inoutbox>\inoutsize\setlength{\inoutsize}{\wd\algocf@inoutbox}\fi% + \fi% the dimension of the box is now defined. + \expandafter\newcommand\csname#1\endcsname[1]{% + \setlength{\inoutline}{\hsize}\addtolength{\inoutline}{-\inoutsize}% + \parbox[t]{\inoutsize}{\KwSty{#2}\hfill:\mbox{\ }}\parbox[t]{\inoutline}{##1}% + \vskip\vespace\nointerlineskip}% +} +% +%% allow to ajust the skip size of InOut +%% +\newcommand{\ResetInOut}[1]{% + \sbox{\algocf@inoutbox}{\hbox{\KwSty{#1}\algocf@typo:\ }}% + \setlength{\inoutsize}{\wd\algocf@inoutbox}% + } +% +% ``Input :'''s like commands where the text stay at the right of the keyword. +% +\newcommand{\SetKwInput}[2]{% + \expandafter\newcommand\csname#1\endcsname[1]{% + \sbox{\algocf@inputbox}{\hbox{\KwSty{#2}\algocf@typo: }}% + \setlength{\inoutline}{\hsize}\addtolength{\inoutline}{-\wd\algocf@inputbox}% + \parbox[t]{\wd\algocf@inputbox}{\usebox{\algocf@inputbox}}\parbox[t]{\inoutline}{##1}% + \vskip\vespace\nointerlineskip}% + } +% +% comment in the text, first argument is the name of the macro, second is +% the text put before the comment, third is the text put at the end of the comment. +% +\newcommand{\SetKwComment}[3]{% + \expandafter\newcommand\csname#1\endcsname[1]{% + \sbox{\algocf@inputbox}{\hbox{#2}}% + \setlength{\inoutline}{\hsize}\addtolength{\inoutline}{-\wd\algocf@inputbox}% + \parbox[t]{\wd\algocf@inputbox}{\usebox{\algocf@inputbox}}\parbox[t]{\inoutline}{\CommentSty{##1}#3}% + \vskip\vespace\nointerlineskip}% + } +% +% deprecated command, use \SetKwFunction or function and procedure environment instead +% +\newcommand{\SetKwInParam}[3]{% + \typeout{^^JAlgorithm Warning: SetKwInParam #1 deprecated command, use SetKwFunction or function and procedure environment instead^^J} + \expandafter\newcommand\csname#1\endcsname[2]{% + \sbox{\algocf@inputbox}{\hbox{\KwSty{##1#2}}}% + \setlength{\inoutline}{\hsize}\addtolength{\inoutline}{-\wd\algocf@inputbox}% + \parbox[t]{\wd\algocf@inputbox}{\usebox{\algocf@inputbox}}\parbox[t]{\inoutline}{##2\KwSty{#3}}% + \vskip\vespace\nointerlineskip}% + } +% +\newcommand{\SetKw}[2]{% + \expandafter\newcommand\csname @#1\endcsname[1]{\KwSty{#2} \ArgSty{##1}}% + \expandafter\newcommand\csname#1\endcsname{% + \@ifnextchar\bgroup{\csname @#1\endcsname}{\KwSty{#2}\xspace}}% + } +% +\newcommand{\SetKwData}[2]{% + \expandafter\newcommand\csname @#1\endcsname[1]{\DataSty{#2(}\ArgSty{##1}\DataSty{)}}% + \expandafter\newcommand\csname#1\endcsname{% + \@ifnextchar\bgroup{\csname @#1\endcsname}{\DataSty{#2}\xspace}}% + } +% +\newcommand{\SetKwFunction}[2]{% + \expandafter\newcommand\csname @#1\endcsname[1]{\FuncSty{#2(}\ArgSty{##1}\FuncSty{)}}% + \expandafter\newcommand\csname#1\endcsname{% + \@ifnextchar\bgroup{\csname @#1\endcsname}{\FuncSty{#2}\xspace}}% +} +% +\newcommand{\SetKwBlock}[3]{% + \expandafter\newcommand\csname#1\endcsname[1]{% + \KwSty{#2}\par\a@group{##1}\KwSty{#3}\par} + } + % +\newcommand{\SetKwIf}[6]{% + \expandafter\newcommand\csname e#1\endcsname[3]{% + \KwSty{#3} \ArgSty{##1} \KwSty{#4}\par% + \a@group{##2}\KwSty{#5}\par\a@block{##3}{#6}}% + \expandafter\newcommand\csname#1\endcsname[2]{% + \KwSty{#3} \ArgSty{##1} \KwSty{#4}\par\a@block{##2}{#6}}% + \expandafter\newcommand\csname u#1\endcsname[2]{% + \KwSty{#3} \ArgSty{##1} \KwSty{#4}\par\a@group{##2}\par}% + \expandafter\newcommand\csname#2\endcsname[1]{% + \KwSty{#5}\par\a@block{##1}{#6}}% + \expandafter\newcommand\csname l#1\endcsname[2]{% + \KwSty{#3} \ArgSty{##1} % + \KwSty{#4} ##2}% + \expandafter\newcommand\csname l#2\endcsname[1]{% + \KwSty{#5} ##1}% + } +% +\newcommand{\SetKwSwitch}[8]{% + \expandafter\newcommand\csname#1\endcsname[2]{% + \KwSty{#4} \ArgSty{##1} % + \KwSty{#5}\par\a@block{##2}{#8}}% + \expandafter\newcommand\csname#2\endcsname[2]{% + \KwSty{#6} \ArgSty{##1}\par\a@block{##2}{}}% + \expandafter\newcommand\csname l#2\endcsname[2]{% + \KwSty{#6} \ArgSty{##1} ##2}% + \expandafter\newcommand\csname#3\endcsname[1]{% + \KwSty{#7}\par\a@block{##1}{}}% + \expandafter\newcommand\csname l#3\endcsname[1]{% + \KwSty{#7} ##1}% + } +% +\newcommand{\SetKwIfElseIf}[8]{% +\expandafter\newcommand\csname#1\endcsname[2]{% + \KwSty{#4} \ArgSty{##1} % + \KwSty{#5}\par\a@block{##2}{}}% +\expandafter\newcommand\csname l#1\endcsname[2]{% + \KwSty{#4} \ArgSty{##1} % + \KwSty{#5} ##2}% +\expandafter\newcommand\csname#2\endcsname[2]{% + \KwSty{#6} \ArgSty{##1} % + \KwSty{#5}\par\a@block{##2}{}}% +\expandafter\newcommand\csname l#2\endcsname[2]{% + \KwSty{#6} \ArgSty{##1} \KwSty{#5} ##2}% +\expandafter\newcommand\csname#3\endcsname[1]{% + \KwSty{#7}\par\a@block{##1}{#8}}% +\expandafter\newcommand\csname l#3\endcsname[1]{% + \KwSty{#7} ##1}% +} +% +\newcommand{\SetKwFor}[4]{% + \expandafter\newcommand\csname#1\endcsname[2]{% + \KwSty{#2} \ArgSty{##1} \KwSty{#3}\par\a@block{##2}{#4}}% + \expandafter\newcommand\csname l#1\endcsname[2]{% + \KwSty{#2} \ArgSty{##1} \KwSty{#3} ##2}% + } +% +\newcommand{\SetKwRepeat}[3]{% + \expandafter\newcommand\csname#1\endcsname[2]{% + \KwSty{#2}\par\a@group{##2}\KwSty{#3} \ArgSty{##1}\@endalgoln}% + \expandafter\newcommand\csname l#1\endcsname[2]{% + \KwSty{#2} ##2 \KwSty{#3} \ArgSty{##1}}% + } +% +% +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% +\expandafter\ifx\csname algocf@within\endcsname\relax% if \algocf@within doen't exist +\newfloat{algocf}{htbp}{\algocf@list}% default numbering +\else% else we number algo as specified by \algocf@within +\newfloat{algocf}{htbp}{\algocf@list}[\algocf@within]% +\fi +\@namedef{l@algocf}{\@dottedtocline{1}{1.5em}{2.3em}}% +% +\newcommand{\before@algostyle}{\float@style} +\floatstyle{\algocf@style} +\restylefloat{\algocf@float}% +\floatstyle{\before@algostyle}% in order to keep the default for new float +\floatname{algocf}{\algorithmcfname} +\newcommand{\listofalgorithms}{% if algos are figures, we print the list of figures + \ifthenelse{\equal{\algocf@float}{figure}}{\listoffigures% + }{ %else we effectively put the list of algorithms + \listof{algocf}{\listalgorithmcfname}% + }% + }% +%% +\newcommand{\restylealgo}[1]{% + \ifthenelse{\equal{#1}{algoruled}}{% then + \renewcommand{\algocf@style}{ruled}\@algoruledstyle} + {\renewcommand{\algocf@style}{#1}}% else and endif + \floatstyle{\algocf@style}\restylefloat{\algocf@float}% new algo style applied + \floatstyle{\before@algostyle}% in order to keep the default for new float + } % end \restylealgo +% +%% +\newcommand{\@algoskip}{% + \ifthenelse{\equal{\algocf@style}{boxed}}{\medskip}{% + \ifthenelse{\equal{\algocf@style}{ruled}}{\@ruledskip}{\relax}}% +} +% +\newcommand{\@rightmarge}{% + \ifthenelse{\equal{\algocf@style}{plain}}{\relax}{\advance\hsize by -\algomargin}} +% +% In \@initalgo +% \def\; is kept (no use of \newcommand) because we want a local definition, +% so \; keep is meaning outside an algorithm environment. +\newcommand{\@initalgocf}{\@ResetCounterIfNeeded% + \addtolength{\hsize}{-\algomargin}\setlength{\algowidth}{\hsize}% + \@rightmarge% + \let\@mathsemicolon=\;\def\;{\ifmmode\@mathsemicolon\else\@endalgoln\fi}% + \raggedright\AlFnt{}% +}%% end of \@initalgocf +% +\newcommand{\@restorealgo}{% + \setlength{\hsize}{\algowidth}% + \lineskip\normallineskip\setlength{\skiptotal}{\@defaultskiptotal}% + \let\caption=\algocf@oldcaption% + \let\;=\@mathsemicolon}%% end of \@restorealgo +% +%%%%%%% algocf@setcaption +\newcommand{\algocf@setcaption}{% +% \ifthenelse{\equal{\algocf@float}{figure}}{% +% \setcounter{algocf}{\thefigure}}{} +% \ifthenelse{\equal{\algocf@float}{figure}}{}{% do nothing + \ifthenelse{\equal{\algocf@style}{ruled}}{% if ruled then + \let\@oldfloatc@ruled=\floatc@ruled% + \renewcommand{\floatc@ruled}[2]{% + \addtolength{\hsize}{\algomargin}% + \@titleskip\@oldfloatc@ruled{\AlFnt\AlTitleFnt{##1:}}{\AlFnt{}##2}\@titleskip% + \addtolength{\hsize}{-\algomargin}}% + }{%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% else + \let\@oldfloatc@plain=\floatc@plain% + \renewcommand{\floatc@plain}[2]{% + \addtolength{\hsize}{\algomargin} + \@oldfloatc@plain{\AlFnt\AlTitleFnt{##1}}{\AlFnt{}##2}% + \addtolength{\hsize}{-\algomargin} + }% +}}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% endif and enf of \algocf@setcaption +% +\newcommand{\algocf@resetcaption}{% +% \ifthenelse{\equal{\algocf@float}{figure}}{}{% do nothing + \ifthenelse{\equal{\algocf@style}{ruled}}{% + \renewcommand{\floatc@ruled}[2]{\@oldfloatc@ruled{##1}{##2}}% + }{% else + \renewcommand{\floatc@plain}[2]{\@oldfloatc@plain{##1}{##2}}% + }} +% +% -- nocaptionofalgo and restorecaptionofalgo -- +% +\newcommand{\algocf@nocaption}{% + \ifthenelse{\equal{\algocf@style}{ruled}}{% + \let\@oldfloatc@ruled=\floatc@ruled% + \renewcommand{\floatc@ruled}[2]{% then + \addtocounter{algocf}{-1}\@titleskip\@oldfloatc@ruled{}{##2}\@titleskip}% end of renewcom + }{ + \let\@oldfloatc@plain=\floatc@plain}% else ... endif + }%end algocf@nocaption +% +\newcommand{\nocaptionofalgo}{% + \let\@old@setcaption=\algocf@setcaption% + \let\algocf@setcaption=\algocf@nocaption% + } +\newcommand{\restorecaptionofalgo}{% + \let\algocf@setcaption=\@old@setcaption% + } +% ---------------------- algorithm environment +% +% +\newcommand{\@algocfbegin}{% + \ifthenelse{\boolean{algocf@slide}}{\incmargin{\skipalgocfslide}}{}% + \hbox\bgroup\hbox to \algomargin{\hfill}\vbox\bgroup\@algoskip\@initalgocf% + } +\newcommand{\@algocfend}{% + \@algoskip\egroup\hbox to \algomargin{\hfill}\egroup\@restorealgo% + \ifthenelse{\boolean{algocf@slide}}{\decmargin{\skipalgocfslide}}{}% + } +% +\newenvironment{\algocf@envname}[1][htbp]{% + \algocf@setcaption% + \ifthenelse{\equal{\algocf@float}{figure}}{% + \begin{figure}[#1]% + }{ + \begin{algocf}[#1]% + } + \@algocfbegin% + \ifthenelse{\boolean{algocf@slide}}{\parskip 0.5ex\color{black}}{}% + }{% begin + \@algocfend% + \ifthenelse{\equal{\algocf@float}{figure}}{% + \end{figure}% + }{ + \end{algocf}% + } + \algocf@resetcaption} % end + +% +\newenvironment{\algocf@envname*}[1][htbp]{% + \algocf@setcaption% + \ifthenelse{\equal{\algocf@float}{figure}}{% + \begin{figure*}[#1]% + }{ + \begin{algocf*}[#1]% + } + \@algocfbegin% + \ifthenelse{\boolean{algocf@slide}}{\parskip 0.5ex\color{black}}{}% + }{% begin + \@algocfend% + \ifthenelse{\equal{\algocf@float}{figure}}{% + \end{figure*}% + }{ + \end{algocf*}% + } + \algocf@resetcaption} % end +% +%\newenvironment{algorithm}[1][htbp]{% +% \algocf@setcaption\begin{algocf}[#1]\@algocfbegin}{% begin +% \@algocfend\end{algocf}\algocf@resetcaption} % end +% +%\newenvironment{algorithm*}[1][htbp]{% +% \algocf@setcaption\begin{algocf*}[#1]\@algocfbegin}{% begin +% \@algocfend\end{algocf*}\algocf@resetcaption} % end +% +% ---------------------- procedure and function environments +% +% +% -- new style (used in particular in the caption of function and procedure environments) +% +\newcommand{\ProcNameSty}[1]{\FuncSty{#1}}% +\newcommand{\SetProcNameSty}[1]{\renewcommand{\ProcNameSty}[1]{\csname#1\endcsname{##1}}} +\newcommand{\ProcArgSty}[1]{\ArgSty{#1}}% +\newcommand{\SetProcArgSty}[1]{\renewcommand{\ProcArgSty}[1]{\csname#1\endcsname{##1}}} +% three macros to extract parts of the caption +\gdef\algocf@captname#1(#2)#3@{#1} % keep characters before the first brace +\gdef\algocf@captparam#1(#2)#3@{#2} % keep character in between the braces +\gdef\algocf@captother#1(#2)#3@{#3} % keep character after the braces +% +% -- algocf@proc is the generic environment for procedure and function environment. +% +\newboolean{algocf@procstar}\setboolean{algocf@procstar}{false} +\newenvironment{algocf@proc}[1][htbp]{% % begin + % algocf@label should record the value of the reference: the name of the + % procedure + \floatname{algocf}{\algocf@procname} + \def\algocf@label{\relax} % default : no particular label + % now we redefine the way caption works + \ifthenelse{\equal{\algocf@style}{ruled}}{% %%%%%%%%%%%%%%%%%%%%%% if ruled then + \let\@oldfloatc@ruled=\floatc@ruled% the original value is kept + \renewcommand{\floatc@ruled}[2]{% caption is redefined: + \@oldfloatc@ruled{\algocf@procname}% Procedure or Function + {\ProcNameSty{\algocf@captname ##2@}% Name of the procedure in ProcName Style. + \ifthenelse{\equal{\algocf@captparam ##2@}{\arg@e}}{}% if no argument, write nothing + {% else put arguments in ProcArgSty: + \ProcNameSty{(}\ProcArgSty{\algocf@captparam ##2@}\ProcNameSty{)} + }% endif + \algocf@captother ##2@}% at last put the rest of the characters + % + \gdef\algocf@label{\algocf@captname ##2@}}% the ref is recorded in \algocf@label + % macro + }{%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% else other styles + \let\@oldfloatc@plain=\floatc@plain% + \renewcommand{\floatc@plain}[2]{% + \@oldfloatc@plain{\algocf@procname}% Procedure or Function + {\ProcNameSty{\algocf@captname ##2@}% Name of the procedure in ProcName Style. + \ifthenelse{\equal{\algocf@captparam ##2@}{\arg@e}}{}% if no argument, write nothing + {% else put arguments in ProcArgSty: + \ProcNameSty{(}\ProcArgSty{\algocf@captparam ##2@}\ProcNameSty{)} + }% endif + \algocf@captother ##2@% + } + \gdef\algocf@label{\algocf@captname ##2@}}% the ref is recorded in \algocf@label + % macro + }%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% endif + % old version of labels + % +% \let\old@algolabel=\@label% keep the original value of label macro +% \renewcommand{\label}[1]{\immediate\write\@auxout{% redefine label macros: write \algocf@label +% \string\newlabel{##1}{{\algocf@label}{\thepage}}}\ignorespaces}% instead of +% algo counter +% \renewcommand{\@currentlabel}{\algocf@label} + \let\algocf@old@refstepcounter=\refstepcounter% + \renewcommand{\refstepcounter}[1]{\def\@currentlabel{\algocf@label\relax}} + %% the real begin part of the environment + \ifthenelse{\equal{\algocf@float}{figure}}{% + \ifthenelse{\boolean{algocf@procstar}}{\begin{figure*}[#1]}{\begin{figure}[#1]}% + %\begin{figure}[#1] + }{ + \ifthenelse{\boolean{algocf@procstar}}{\begin{algocf*}[#1]}{\begin{algocf}[#1]}% + %\begin{algocf}[#1] + } + \@algocfbegin% begin an algorithm environment + }% Begin part ended, now... + {% start of the end part of the environment + \@algocfend% + \ifthenelse{\equal{\algocf@float}{figure}}{% + \ifthenelse{\boolean{algocf@procstar}}{\end{figure*}}{\end{figure}}% + %\end{figure} + }{ + \ifthenelse{\boolean{algocf@procstar}}{\end{algocf*}}{\end{algocf}}% + %\end{algocf} + } + \algocf@resetcaption% end of algorithm environment + % old version of labels + % \renewcommand{\label}[1]{\old@algolabel{##1}}% restore original label macro + \renewcommand{\refstepcounter}[1]{\algocf@old@refstepcounter{##1}}% +}% end part of the environement ended +% +% +% +% -- procedure and function environments are defined from algocf@proc environment +% +\newenvironment{procedure}[1][htbp]{\setboolean{algocf@procstar}{false}% +\newcommand{\algocf@procname}{\@algocf@procname}\begin{algocf@proc}[#1]}{\end{algocf@proc}} +\newenvironment{function}[1][htbp]{\setboolean{algocf@procstar}{false}% +\newcommand{\algocf@procname}{\@algocf@funcname}\begin{algocf@proc}[#1]}{\end{algocf@proc}} +% + \newenvironment{procedure*}[1][htbp]{\setboolean{algocf@procstar}{true}% + \newcommand{\algocf@procname}{\@algocf@procname}\begin{algocf@proc}[#1]}{\end{algocf@proc}} + \newenvironment{function*}[1][htbp]{\setboolean{algocf@procstar}{true}% + \newcommand{\algocf@procname}{\@algocf@funcname}\begin{algocf@proc}[#1]}{\end{algocf@proc}} + + +% +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% +\newcommand{\Titleofalgo}[1]{\@titleprefix\TitleSty{#1}\par\smallskip} +% +% +% +% ------------------------- Default Definitions +% +% +% +%% +%% +%% +% +\newcommand{\algocf@defaults@common}{ +%\SetKwInOut{AlgDonnees}{Donn\'ees}\SetKwInOut{AlgRes}{R\'esultat} +\SetKwInput{Donnees}{Donn\'ees}% +\SetKwInput{Res}{R\'esultat}% +\SetKwInput{Entree}{Entr\'ees}% +\SetKwInput{Sortie}{Sorties}% +\SetKw{KwA}{\`a}% +\SetKw{Retour}{retourner}% +\SetKwBlock{Deb}{d\'ebut}{fin}% +\SetKwRepeat{Repeter}{r\'ep\'eter}{jusqu'\`a}% +% +\SetKwComment{tcc}{/*}{ */} +\SetKwComment{tcp}{//}{} +% +\SetKwInOut{AlgData}{Data}\SetKwInOut{AlgResult}{Result} +\SetKwInput{KwIn}{Input}% +\SetKwInput{KwOut}{Output}% +\SetKwInput{KwData}{Data}% +\SetKwInput{KwResult}{Result}% +\SetKw{KwTo}{to} +\SetKw{KwRet}{return}% +\SetKw{Return}{return}% +\SetKwBlock{Begin}{begin}{end}% +\SetKwRepeat{Repeat}{repeat}{until}% +% +% --- German keywords +% +% \SetKwInOut{AlgDaten}{Daten}%AlgData +% \SetKwInOut{AlgErgebnis}{Ergebnis}%AlgResult +\SetKwInput{Ein}{Eingabe}%KwIn +\SetKwInput{Aus}{Ausgabe}%KwOut +\SetKwInput{Daten}{Daten}%KwData +\SetKwInput{Ergebnis}{Ergebnis}%KwResult +\SetKw{Bis}{bis}%KwTo +\SetKw{KwZurueck}{zur\"uck}%KwRet +\SetKw{Zurueck}{zur\"uck}%Return +\SetKwBlock{Beginn}{Beginn}{Ende}%Begin +\SetKwRepeat{Wiederh}{wiederhole}{bis}%Repeat +% +% --- Czech keywords +% +% \SetKwInOut{AlgVst}{Vstup}\SetKwInOut{AlgVyst}{V\'{y}stup} +\SetKwInput{Vst}{Vstup}% +\SetKwInput{Vyst}{V\'{y}stup}% +\SetKwInput{Vysl}{V\'{y}sledek}% +% +% --- Portuguese keywords +% +% \SetKwInOut{AlgDados}{Dados}\SetKwInOut{AlgResultado}{Result.} +\SetKwInput{Entrada}{Entrada}% +\SetKwInput{Saida}{Sa\'{i}da}% +\SetKwInput{Dados}{Dados}% +\SetKwInput{Resultado}{Resultado}% +\SetKw{Ate}{at\'{e}} +\SetKw{KwRetorna}{retorna}% +\SetKw{Retorna}{retorna}% +\SetKwBlock{Inicio}{in\'{i}cio}{fim}% +\SetKwRepeat{Repita}{repita}{at\'{e}}% +% --- End +} +% +% +\newcommand{\algocf@defaults@longend}{% +\algocf@defaults@common +\SetKwIf{Si}{Sinon}{si}{alors}{sinon}{finsi}% +\SetKwIfElseIf{gSi}{gSinonSi}{gSinon}{si}{alors}{sinon si}{sinon}{finsi}% +\SetKwSwitch{Suivant}{Cas}{Autre}{suivant}{faire}{cas o\`u}{autres cas}{fin d'alternative}% +\SetKwFor{Pour}{pour}{faire}{finpour}% +\SetKwFor{PourPar}{pour}{faire en parallèle}{finpour}% +\SetKwFor{PourCh}{pour chaque}{faire}{finprch}% +\SetKwFor{Tq}{tant que}{faire}{fintq}% +% +\SetKwIf{If}{Else}{if}{then}{else}{endif}% +\SetKwIfElseIf{gIf}{gElsIf}{gElse}{if}{then}{else if}{else}{endif}% +\SetKwSwitch{Switch}{Case}{Other}{switch}{do}{case}{otherwise}{endsw}% +\SetKwFor{For}{for}{do}{endfor}% +\SetKwFor{ForPar}{for}{do in parallel}{endfpar} +\SetKwFor{ForEach}{foreach}{do}{endfch}% +\SetKwFor{ForAll}{forall the}{do}{endfall}% +\SetKwFor{While}{while}{do}{endw}% +% +% --- German for longend +% +\SetKwIf{Wenn}{Sonst}{wenn}{dann}{sonst}{Ende-wenn}%If +\SetKwIfElseIf{gWenn}{gSonstWenn}{gSonst}{wenn}{dann}{sonst wenn}{sonst}{Ende-wenn}%gIf +\SetKwSwitch{Unterscheide}{Fall}{Anderes}{unterscheide}{tue}{Fall}{sonst}{Ende-Unt.}%Switch +\SetKwFor{Fuer}{f\"ur}{tue}{Ende-f\"ur}%For +\SetKwFor{FuerPar}{f\"ur}{tue gleichzeitig}{Ende-gleichzeitig}%ForPar +\SetKwFor{FuerJedes}{f\"ur jedes}{tue}{Ende-f\"ur}%ForEach +\SetKwFor{FuerAlle}{f\"ur alle}{tue}{Ende-f\"ur}%ForAll +\SetKwFor{Solange}{solange}{tue}{Ende-solange}%While +% +% --- Portuguese +% +\SetKwIf{Se}{Senao}{se}{ent\~{a}o}{sen\~{a}o}{fim se}% +\SetKwIfElseIf{gSe}{gSenaoSe}{gSenao}{se}{ent\~{a}o}{sen\~{a}o se}{sen\~{a}o}{fim se}% +\SetKwSwitch{Selec}{Caso}{Outro}{selecione}{fa\c{c}a}{caso}{sen\~{a}o}{fim selec}% +\SetKwFor{Para}{para}{fa\c{c}a}{fim para}% +\SetKwFor{ParaPar}{para}{fa\c{c}a em paralelo}{fim para} +\SetKwFor{ParaCada}{para cada}{fa\c{c}a}{fim para cada}% +\SetKwFor{ParaTodo}{para todo}{fa\c{c}a}{fim para todo}% +\SetKwFor{Enqto}{enquanto}{fa\c{c}a}{fim enqto}% +} +% +% +\newcommand{\algocf@defaults@shortend}{% +\algocf@defaults@common +\SetKwIf{Si}{Sinon}{si}{alors}{sinon}{fin}% +\SetKwIfElseIf{gSi}{gSinonSi}{gSinon}{si}{alors}{sinon si}{sinon}{fin}% +\SetKwSwitch{Suivant}{Cas}{Autre}{suivant}{faire}{cas o\`u}{autres cas}{fin}% +\SetKwFor{Pour}{pour}{faire}{fin}% +\SetKwFor{PourPar}{pour}{faire en parallèle}{fin}% +\SetKwFor{PourCh}{pour chaque}{faire}{fin}% +\SetKwFor{PourTous}{pour tous les}{faire}{fin}% +\SetKwFor{Tq}{tant que}{faire}{fin}% +% +% +\SetKwIf{If}{Else}{if}{then}{else}{end}% +\SetKwIfElseIf{gIf}{gElsIf}{gElse}{if}{then}{else if}{else}{end}% +\SetKwSwitch{Switch}{Case}{Other}{switch}{do}{case}{otherwise}{end}% +\SetKwFor{For}{for}{do}{end}% +\SetKwFor{ForPar}{for}{do in parallel}{end} +\SetKwFor{ForEach}{foreach}{do}{end}% +\SetKwFor{ForAll}{forall}{do}{end}% +\SetKwFor{While}{while}{do}{end}% +% +% --- German for shortend +% +\SetKwIf{Wenn}{Sonst}{wenn}{dann}{sonst}{Ende}%If +\SetKwIfElseIf{gWenn}{gSonstWenn}{gSonst}{wenn}{dann}{sonst wenn}{sonst}{Ende}%gIf +\SetKwSwitch{Unterscheide}{Fall}{Anderes}{unterscheide}{tue}{Fall}{sonst}{}%Switch +\SetKwFor{Fuer}{f\"ur}{tue}{Ende}%For +\SetKwFor{FuerPar}{f\"ur}{tue gleichzeitig}{Ende}%ForPar +\SetKwFor{FuerJedes}{f\"ur jedes}{tue}{Ende}%ForEach +\SetKwFor{FuerAlle}{f\"ur alle}{tue}{Ende}%ForAll +\SetKwFor{Solange}{solange}{tue}{Ende}%While +% +% --- Portuguese +% +\SetKwIf{Se}{Senao}{se}{ent\~{a}o}{sen\~{a}o}{fim}% +\SetKwIfElseIf{gSe}{gSenaoSe}{gSenao}{se}{ent\~{a}o}{sen\~{a}o se}{sen\~{a}o}{fim}% +\SetKwSwitch{Selec}{Caso}{Outro}{selecione}{fa\c{c}a}{caso}{sen\~{a}o}{fim}% +\SetKwFor{Para}{para}{fa\c{c}a}{fim}% +\SetKwFor{ParaPar}{para}{fa\c{c}a em paralelo}{fim} +\SetKwFor{ParaCada}{para cada}{fa\c{c}a}{fim}% +\SetKwFor{ParaTodo}{para todo}{fa\c{c}a}{fim}% +\SetKwFor{Enqto}{enquanto}{fa\c{c}a}{fim}% +} +% +% +\newcommand{\algocf@defaults@noend}{% +\renewcommand{\a@block}[2]{\a@group{##1}} +\algocf@defaults@common +\SetKwIf{Si}{Sinon}{si}{alors}{sinon}{}% +\SetKwIfElseIf{gSi}{gSinonSi}{gSinon}{si}{alors}{sinon si}{sinon}{}% +\SetKwSwitch{Suivant}{Cas}{Autre}{suivant}{faire}{cas où}{autres cas}{}% +\SetKwFor{Pour}{pour}{faire}{}% +\SetKwFor{PourPar}{pour}{faire en parallèle}{}% +\SetKwFor{PourCh}{pour chaque}{faire}{}% +\SetKwFor{PourTous}{pour tous les}{faire}{}% +\SetKwFor{Tq}{tant que}{faire}{}% +% +\SetKwIf{If}{Else}{if}{then}{else}{}% +\SetKwIfElseIf{gIf}{gElsIf}{gElse}{if}{then}{else if}{else}{}% +\SetKwSwitch{Switch}{Case}{Other}{switch}{do}{case}{otherwise}{}% +\SetKwFor{For}{for}{do}{}% +\SetKwFor{ForPar}{for}{do in parallel}{} +\SetKwFor{ForEach}{foreach}{do}{}% +\SetKwFor{ForAll}{forall}{do}{}% +\SetKwFor{While}{while}{do}{}% +% --- German for noend +\SetKwIf{Wenn}{Sonst}{wenn}{dann}{sonst}{}%If +\SetKwIfElseIf{gWenn}{gSonstWenn}{gSonst}{wenn}{dann}{sonst wenn}{sonst}{}%gIf +\SetKwSwitch{Unterscheide}{Fall}{Anderes}{unterscheide}{tue}{Fall}{sonst}{}%Switch +\SetKwFor{Fuer}{f\"ur}{tue}{}%For +\SetKwFor{FuerPar}{f\"ur}{tue gleichzeitig}{}%ForPar +\SetKwFor{FuerJedes}{f\"ur jedes}{tue}{}%ForEach +\SetKwFor{FuerAlle}{f\"ur alle}{tue}{}%ForAll +\SetKwFor{Solange}{solange}{tue}{}%While +% --- Portuguese +\SetKwIf{Se}{Senao}{se}{ent\~{a}o}{sen\~{a}o}{}% +\SetKwIfElseIf{gSe}{gSenaoSe}{gSenao}{se}{ent\~{a}o}{sen\~{a}o se}{sen\~{a}o}{}% +\SetKwSwitch{Selec}{Caso}{Outro}{selecione}{fa\c{c}a}{caso}{sen\~{a}o}{}% +\SetKwFor{Para}{para}{fa\c{c}a}{}% +\SetKwFor{ParaPar}{para}{fa\c{c}a em paralelo}{} +\SetKwFor{ParaCada}{para cada}{fa\c{c}a}{}% +\SetKwFor{ParaTodo}{para todo}{fa\c{c}a}{}% +\SetKwFor{Enqto}{enquanto}{fa\c{c}a}{}% +} +% +%% +%% +%% +% +% default macros are: +\defaultsmacros@algo +\SetNoline +% +% +%% +%%% +%%%% END \ No newline at end of file diff --git a/algorithmic.sty b/algorithmic.sty new file mode 100644 index 0000000..74d9b71 --- /dev/null +++ b/algorithmic.sty @@ -0,0 +1,187 @@ +% ALGORITHMIC STYLE for LaTeX version 2e +% +% This style file is free software; you can redistribute it and/or +% modify it under the terms of the GNU Lesser General Public +% License as published by the Free Software Foundation; either +% version 2 of the License, or (at your option) any later version. +% +% This style file is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +% Lesser General Public License for more details. +% +% You should have received a copy of the GNU Lesser General Public +% License along with this style file; if not, write to the +% Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithmic}[2005/07/05] +\typeout{Document Style `algorithmic' - environment} +% +\RequirePackage{ifthen} +\RequirePackage{calc} +\RequirePackage{keyval} +\newboolean{ALC@noend} +\setboolean{ALC@noend}{false} +\newcounter{ALC@line} +\newcounter{ALC@rem} +\newcounter{ALC@depth} +\newlength{\ALC@tlm} +% +\DeclareOption{noend}{\setboolean{ALC@noend}{true}} +% +\ProcessOptions +% +% For keyval-style options +\def\algsetup{\setkeys{ALG}} +% +% For indentation of algorithms +\newlength{\algorithmicindent} +\setlength{\algorithmicindent}{0pt} +\define@key{ALG}{indent}{\setlength{\algorithmicindent}{#1}} +\ifthenelse{\lengthtest{\algorithmicindent=0pt}}% + {\setlength{\algorithmicindent}{1em}}{} +% +% For line numbers' delimiters +\newcommand{\ALC@linenodelimiter}{:} +\define@key{ALG}{linenodelimiter}{\renewcommand{\ALC@linenodelimiter}{#1}} + +% +% For line numbers' size +\newcommand{\ALC@linenosize}{\footnotesize} +\define@key{ALG}{linenosize}{\renewcommand{\ALC@linenosize}{#1}} + +% +% ALGORITHMIC +\newcommand{\algorithmicrequire}{\textbf{Require:}} +\newcommand{\algorithmicensure}{\textbf{Ensure:}} +\newcommand{\algorithmiccomment}[1]{\{#1\}} +\newcommand{\algorithmicend}{\textbf{end}} +\newcommand{\algorithmicif}{\textbf{if}} +\newcommand{\algorithmicthen}{\textbf{then}} +\newcommand{\algorithmicelse}{\textbf{else}} +\newcommand{\algorithmicelsif}{\algorithmicelse\ \algorithmicif} +\newcommand{\algorithmicendif}{\algorithmicend\ \algorithmicif} +\newcommand{\algorithmicfor}{\textbf{for}} +\newcommand{\algorithmicforall}{\textbf{for all}} +\newcommand{\algorithmicdo}{\textbf{do}} +\newcommand{\algorithmicendfor}{\algorithmicend\ \algorithmicfor} +\newcommand{\algorithmicwhile}{\textbf{while}} +\newcommand{\algorithmicendwhile}{\algorithmicend\ \algorithmicwhile} +\newcommand{\algorithmicloop}{\textbf{loop}} +\newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop} +\newcommand{\algorithmicrepeat}{\textbf{repeat}} +\newcommand{\algorithmicuntil}{\textbf{until}} +\newcommand{\algorithmicprint}{\textbf{print}} +\newcommand{\algorithmicreturn}{\textbf{return}} +\def\ALC@setref{% + \def\@currentlabel{\theALC@line}% +} +\def\ALC@item[#1]{% +\if@noparitem \@donoparitem + \else \if@inlabel \indent \par \fi + \ifhmode \unskip\unskip \par \fi + \if@newlist \if@nobreak \@nbitem \else + \addpenalty\@beginparpenalty + \addvspace\@topsep \addvspace{-\parskip}\fi + \else \addpenalty\@itempenalty \addvspace\itemsep + \fi + \global\@inlabeltrue +\fi +\everypar{\global\@minipagefalse\global\@newlistfalse + \if@inlabel\global\@inlabelfalse \hskip -\parindent \box\@labels + \penalty\z@ \fi + \everypar{}}\global\@nobreakfalse +\if@noitemarg \@noitemargfalse \if@nmbrlist \refstepcounter{\@listctr}\fi \fi +\sbox\@tempboxa{\makelabel{#1}}% +\global\setbox\@labels + \hbox{\unhbox\@labels \hskip \itemindent + \hskip -\labelwidth \hskip -\ALC@tlm + \ifdim \wd\@tempboxa >\labelwidth + \box\@tempboxa + \else \hbox to\labelwidth {\unhbox\@tempboxa}\fi + \hskip \ALC@tlm}\ignorespaces} +% +\newenvironment{algorithmic}[1][0]{ +\setcounter{ALC@depth}{\@listdepth}% +\let\@listdepth\c@ALC@depth% +\let\@item\ALC@item + \newcommand{\ALC@lno}{% +\ifthenelse{\equal{\arabic{ALC@rem}}{0}} +{{\ALC@linenosize \arabic{ALC@line}\ALC@linenodelimiter}}{}% +} +\let\@listii\@listi +\let\@listiii\@listi +\let\@listiv\@listi +\let\@listv\@listi +\let\@listvi\@listi +\let\@listvii\@listi + \newenvironment{ALC@g}{ + \begin{list}{\ALC@lno}{ \itemsep\z@ \itemindent\z@ + \listparindent\z@ \rightmargin\z@ + \topsep\z@ \partopsep\z@ \parskip\z@\parsep\z@ + \leftmargin \algorithmicindent%1em + \addtolength{\ALC@tlm}{\leftmargin} + } + } + {\end{list}} + \newcommand{\ALC@it}{\refstepcounter{ALC@line}\refstepcounter{ALC@rem}\ifthenelse{\equal{\arabic{ALC@rem}}{#1}}{\setcounter{ALC@rem}{0}}{}\item\ALC@setref} + \newcommand{\ALC@com}[1]{\ifthenelse{\equal{##1}{default}}% +{}{\ \algorithmiccomment{##1}}} + \newcommand{\REQUIRE}{\item[\algorithmicrequire]} + \newcommand{\ENSURE}{\item[\algorithmicensure]} + \newcommand{\PRINT}{\ALC@it\algorithmicprint{}\ \ } + \newcommand{\RETURN}{\ALC@it\algorithmicreturn{}\ \ } + \newcommand{\STATE}{\ALC@it} + \newcommand{\COMMENT}[1]{\algorithmiccomment{##1}} + \newenvironment{ALC@if}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@for}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@whl}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@loop}{\begin{ALC@g}}{\end{ALC@g}} + \newenvironment{ALC@rpt}{\begin{ALC@g}}{\end{ALC@g}} + \renewcommand{\\}{\@centercr} + \newcommand{\IF}[2][default]{\ALC@it\algorithmicif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSE}[1][default]{\end{ALC@if}\ALC@it\algorithmicelse% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\ELSIF}[2][default]% +{\end{ALC@if}\ALC@it\algorithmicelsif\ ##2\ \algorithmicthen% +\ALC@com{##1}\begin{ALC@if}} + \newcommand{\FOR}[2][default]{\ALC@it\algorithmicfor\ ##2\ \algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\FORALL}[2][default]{\ALC@it\algorithmicforall\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@for}} + \newcommand{\WHILE}[2][default]{\ALC@it\algorithmicwhile\ ##2\ % +\algorithmicdo% +\ALC@com{##1}\begin{ALC@whl}} + \newcommand{\LOOP}[1][default]{\ALC@it\algorithmicloop% +\ALC@com{##1}\begin{ALC@loop}} + \newcommand{\REPEAT}[1][default]{\ALC@it\algorithmicrepeat% +\ALC@com{##1}\begin{ALC@rpt}} + \newcommand{\UNTIL}[1]{\end{ALC@rpt}\ALC@it\algorithmicuntil\ ##1} + \ifthenelse{\boolean{ALC@noend}}{ + \newcommand{\ENDIF}{\end{ALC@if}} + \newcommand{\ENDFOR}{\end{ALC@for}} + \newcommand{\ENDWHILE}{\end{ALC@whl}} + \newcommand{\ENDLOOP}{\end{ALC@loop}} + }{ + \newcommand{\ENDIF}{\end{ALC@if}\ALC@it\algorithmicendif} + \newcommand{\ENDFOR}{\end{ALC@for}\ALC@it\algorithmicendfor} + \newcommand{\ENDWHILE}{\end{ALC@whl}\ALC@it\algorithmicendwhile} + \newcommand{\ENDLOOP}{\end{ALC@loop}\ALC@it\algorithmicendloop} + } + \renewcommand{\@toodeep}{} + \begin{list}{\ALC@lno}{\setcounter{ALC@line}{0}\setcounter{ALC@rem}{0}% + \itemsep\z@ \itemindent\z@ \listparindent\z@% + \partopsep\z@ \parskip\z@ \parsep\z@% + \labelsep 0.5em \topsep 0.2em% +\ifthenelse{\equal{#1}{0}} + {\labelwidth 0.5em } + {\labelwidth 1.2em } +\leftmargin\labelwidth \addtolength{\leftmargin}{\labelsep} + \ALC@tlm\labelsep + } +} +{\end{list}} \ No newline at end of file diff --git a/algorithmicx.sty b/algorithmicx.sty new file mode 100644 index 0000000..4677d90 --- /dev/null +++ b/algorithmicx.sty @@ -0,0 +1,786 @@ +% ALGORITHMIC STYLE -- Released 27 APR 2005 +% for LaTeX version 2e +% +% Copyright Szasz Janos +% E-mail szaszjanos@users.sourceforge.net +% +% +% *** INITIALISING *** +% +% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{algorithmicx}[2005/04/27 v1.2 Algorithmicx] +\RequirePackage{ifthen} +\typeout{Document Style algorithmicx 1.2 - a greatly improved `algorithmic' style} +% +\newcounter{ALG@line} +\newcounter{ALG@rem} +\newcounter{ALG@nested} +\newlength{\ALG@tlm} +\newlength{\ALG@thistlm} +\newcounter{ALG@Lnr}% the number of defined languages +\setcounter{ALG@Lnr}{0} +\newcounter{ALG@blocknr}% the number of defined blocks +\setcounter{ALG@blocknr}{0} +\newcounter{ALG@storecount}% number of stored but not restored algorithmic environments +\setcounter{ALG@storecount}{0} +\newcounter{ALG@tmpcounter}% only to decrement things +\newlength\ALG@tmplength% +%\def\algorithmicnoindent{-\ALG@tlm} +% \def\algbackskipbegin{\hskip\ALG@ctlm} +%\def\algbackskip{\hskip-\ALG@thistlm} +%\def\algbackskipend{\hskip-\ALG@tlm} +\def\ALG@defaultindent{\algorithmicindent} +% +% conditional states +% +\def\ALG@newcondstate#1% + {% + \expandafter\edef\csname ALG@x@#1\endcsname% + {\expandafter\noexpand\csname @@ALG@x@#1\endcsname}% + }% +\ALG@newcondstate{notext}% +\ALG@newcondstate{default}% +% +% +% *** ALGORITHMIC *** +% +% +\newcommand\ALG@beginblock[1]% #1 - indentation + {% + \ALG@thistlm\ALG@tlm% + \addtolength\ALG@tlm{#1}% + \addtocounter{ALG@nested}{1}% + \setlength\ALG@tmplength{#1}% + \expandafter\edef\csname ALG@ind@\theALG@nested\endcsname{\the\ALG@tmplength}% + }% +\newcommand\ALG@endblock% + {% + \addtolength\ALG@tlm{-\csname ALG@ind@\theALG@nested\endcsname}% + \addtocounter{ALG@nested}{-1}% + \ALG@thistlm\ALG@tlm% + }% +% +% algorithmic environment +% +\def\ALG@step% + {% + \addtocounter{ALG@line}{1}% + \addtocounter{ALG@rem}{1}% + \ifthenelse{\equal{\arabic{ALG@rem}}{\ALG@numberfreq}}% + {\setcounter{ALG@rem}{0}\alglinenumber{\arabic{ALG@line}}}% + {}% + }% +\newenvironment{algorithmic}[1][0]% + {% + \edef\ALG@numberfreq{#1}% + \def\@currentlabel{\theALG@line}% + % + \setcounter{ALG@line}{0}% + \setcounter{ALG@rem}{0}% + % + \let\\\algbreak% + % + \expandafter\edef\csname ALG@currentblock@\theALG@nested\endcsname{0}% + \expandafter\let\csname ALG@currentlifetime@\theALG@nested\endcsname\relax% + % + \begin{list}% + {\ALG@step}% + {% + \rightmargin\z@% + \itemsep\z@ \itemindent\z@ \listparindent2em% + \partopsep\z@ \parskip\z@ \parsep\z@% + \labelsep 0.5em \topsep 0.2em%\skip 1.2em + \ifthenelse{\equal{#1}{0}}% + {\labelwidth 0.5em}% + {\labelwidth 1.2em}% + \leftmargin\labelwidth \addtolength{\leftmargin}{\labelsep}% Ok. the perfect leftmargin :-)) + \ALG@tlm\z@% + }% + \setcounter{ALG@nested}{0}% + \ALG@beginalgorithmic% + }% + {% end{algorithmic} + % check if all blocks are closed + \ALG@closeloops% + \expandafter\ifnum\csname ALG@currentblock@\theALG@nested\endcsname=0\relax% + \else% + \PackageError{algorithmicx}{Some blocks are not closed!!!}{}% + \fi% + \ALG@endalgorithmic% + \end{list}% + }% +% +% +% *** Functional core *** +% +% +\def\ALG@makeentity#1% execute the entity (#1) + {% + \def\ALG@thisentity{#1}% + \expandafter\ifx\csname ALG@b@\ALG@L @#1@0\endcsname\relax% + \let\ALG@makenobeginrepeat\ALG@makenobegin\ALG@makenobeginrepeat% this entitie ends or continues blocks + \else% + \let\ALG@makebeginrepeat\ALG@makebegin\ALG@makebeginrepeat% this entitie can open blocks + \fi% + \ALG@entitiecommand% + }% +% +\def\ALG@makebegin% executes an entitie that can open blocks + {% + \expandafter\let\expandafter\ALG@thislifetime\csname ALG@currentlifetime@\theALG@nested\endcsname% + \ifx\ALG@thislifetime\relax% + \let\ALG@makebeginrepeat\ALG@doentity% in infinite block I can open my block + \else% + \ifnum\ALG@thislifetime>0\relax% + \ifnum\ALG@thislifetime>65534\else% + \setcounter{ALG@tmpcounter}{\ALG@thislifetime}% the block has 'space' for another included block + \addtocounter{ALG@tmpcounter}{-1}% + \expandafter\edef\csname ALG@currentlifetime@\theALG@nested\endcsname{\arabic{ALG@tmpcounter}}% + \fi% + \let\ALG@makebeginrepeat\ALG@doentity% + \else% the block needs to be closed + \expandafter\ifx\csname ALG@b@\ALG@L @\ALG@thisentity @\csname ALG@currentblock@\theALG@nested\endcsname\endcsname\relax% + \ALG@closebyforce% I can not close this block, continue after it is closed by force +% \ALG@makebegin% + \else% + % the block would be closed automatically, but this entitie can close it, so let's do it with the entity + \let\ALG@makebeginrepeat\ALG@doentity% + \fi% + \fi% + \fi% + \ALG@makebeginrepeat% + }% +% +\def\ALG@makenobegin% executes an entitie that can not open blocks + {% + \expandafter\ifx\csname ALG@currentlifetime@\theALG@nested\endcsname\relax% + \let\ALG@makenobeginrepeat\ALG@doentity% an infinite block must be broken + \else% + \expandafter\ifx\csname ALG@b@\ALG@L @\ALG@thisentity @\csname ALG@currentblock@\theALG@nested\endcsname\endcsname\relax% + \ALG@closebyforce% the block must be ended by force, + \else% + \let\ALG@makenobeginrepeat\ALG@doentity% I can continue / end this block, let's do it + \fi% + \fi% + \ALG@makenobeginrepeat% + }% +% +\def\ALG@dobegin% + {% + \ALG@beginblock{\csname ALG@i@\ALG@L @\ALG@thisentity @\ALG@thisblock\endcsname}% + \expandafter\edef\csname ALG@currentblock@\theALG@nested\endcsname{\csname ALG@b@\ALG@L @\ALG@thisentity @\ALG@thisblock\endcsname}% + \expandafter\ifx\csname ALG@c@\ALG@L @\ALG@thisentity @\ALG@thisblock\endcsname\relax% + \expandafter\let\csname ALG@currentlifetime@\theALG@nested\endcsname\relax% + \else% + \expandafter\edef\csname ALG@currentlifetime@\theALG@nested\endcsname{\csname ALG@c@\ALG@L @\ALG@thisentity @\ALG@thisblock\endcsname}% + \fi% + }% +% +\def\ALG@doend% + {% + \ALG@endblock% + }% +% +\def\ALG@doentity% the number of the closed block, the entitie + {% + \edef\ALG@thisblock{\csname ALG@currentblock@\theALG@nested\endcsname}% + \expandafter\ifx\csname ALG@b@\ALG@L @\ALG@thisentity @\ALG@thisblock\endcsname\relax% + \def\ALG@thisblock{0}% + \fi% + \ALG@getentitytext% + \ifnum\ALG@thisblock=0\else\ALG@doend\fi% + \ifx\ALG@text\ALG@x@notext% + \item[]\nointerlineskip%\vskip-\prevdepth\nointerlineskip% bug: if there are no text and no lines, then this is wrong + \else% + \item% + \fi% + \noindent\hskip\ALG@tlm% + \expandafter\ifnum0=\csname ALG@b@\ALG@L @\ALG@thisentity @\ALG@thisblock\endcsname\else% + \ALG@dobegin% + \fi% + \def\ALG@entitiecommand{\ALG@displayentity}% + }% +% +\def\ALG@getentitytext% + {% + \expandafter\let\expandafter\ALG@text\csname ALG@t@\ALG@L @\ALG@thisentity @\ALG@thisblock\endcsname% + \ifx\ALG@text\ALG@x@default% + % block specific - default + \expandafter\let\expandafter\ALG@text\csname ALG@t@\ALG@L @\ALG@thisentity\endcsname% + \ifx\ALG@text\ALG@x@default% + % block specific - default, language specific - default + \def\ALG@text{\ALG@deftext{\ALG@thisentity}}% + \fi% + \fi% + }% +% +\def\ALG@deftext{\csname ALG@deftext@\ALG@L\endcsname}% +% +\def\ALG@displayentity% + {% + \ifx\ALG@text\ALG@x@notext% + \let\ALG@text\relax% + \fi + \ALG@text% + }% +% +\def\ALG@closebyforce% + {% + \ALG@endblock% + }% +% +\def\ALG@closeloops% closes all finite blocks + {% + \expandafter\ifx\csname ALG@currentlifetime@\theALG@nested\endcsname\relax% + \else% only if it is finite + \ALG@closebyforce% the block must be ended by force, + \ALG@closeloops% the command still runs + \fi% + }% +% +% +% *** Low level block/entitie defining commands *** +% +% +\def\ALG@bl@{0}% the BIG block +\let\ALG@bl@@\ALG@bl@% the BIG block +% +% Create a block +% +\def\ALG@createblock#1% create the block #1, if it does not exists + {% + \@ifundefined{ALG@bl@\ALG@Ld @#1}% needs to be created? + {% + \addtocounter{ALG@blocknr}{1}% increment the block counter + \expandafter\edef\csname ALG@bl@\ALG@Ld @#1\endcsname{\arabic{ALG@blocknr}}% set the block number + }% + {}% + }% +% +% Get the block number +% +\def\ALG@getblocknumber#1{\csname ALG@bl@\ALG@Ld @#1\endcsname}% +% +% Create an entitie +% +\def\ALG@createentitie#1% create the entitie #1, if it does not exists + {% + \expandafter\ALG@edefcmd\csname #1\endcsname{\noexpand\ALG@makeentity{#1}}% + \@ifundefined{ALG@t@\ALG@Ld @#1}% the entity text is defined in this language? + {% + \expandafter\let\csname ALG@t@\ALG@Ld @#1\endcsname\ALG@x@default% + }% + {}% + }% +% +\def\ALG@createtext#1#2% #1 = closed block; #2 = entitie; creates \ALG@t@#2@#1 + {% + \expandafter\let\csname ALG@t@\ALG@Ld @#2@#1\endcsname\ALG@x@default% + }% +% +% End and Continue block +% +\def\ALG@endandcontinueblock#1#2#3#4#5% #1 = new block; #2 = old block; #3 = entitie; #4 = credits; #5 = indent + {% + \ifthenelse{\equal{#3}{}}{}% execute only if the entity is not empty + {% + \ALG@createentitie{#3}% create the entitie + \ALG@createblock{#2}% create the old block, if needed + \ifthenelse{\equal{#1}{}}% whe need to open a new block? + {\expandafter\edef\csname ALG@b@\ALG@Ld @#3@\ALG@getblocknumber{#2}\endcsname{0}}% no, just close the old one + {% yes, + \ALG@createblock{#1}% create the block + \expandafter\edef\csname ALG@b@\ALG@Ld @#3@\ALG@getblocknumber{#2}\endcsname{\ALG@getblocknumber{#1}}% ending the old block opens a new one + \ifthenelse{\equal{#4}{}}% infinite or finite credits? + {\expandafter\let\csname ALG@c@\ALG@Ld @#3@\ALG@getblocknumber{#2}\endcsname\relax}% infinite credits + {\expandafter\edef\csname ALG@c@\ALG@Ld @#3@\ALG@getblocknumber{#2}\endcsname{#4}}% finite credits + \ifthenelse{\equal{#5}{}}% default or specified indentation + {\expandafter\let\csname ALG@i@\ALG@Ld @#3@\ALG@getblocknumber{#2}\endcsname\ALG@defaultindent}% default indentation + {\expandafter\edef\csname ALG@i@\ALG@Ld @#3@\ALG@getblocknumber{#2}\endcsname{#5}}% indentation is specified + }% + \ALG@createtext{\ALG@getblocknumber{#2}}{#3}% + }% + }% +% +% macros used in declarations +% +\def\ALG@p@endtext@E{\algrenewtext{\ALG@v@end}}% +\def\ALG@p@endtext@xE{\algrenewtext[\ALG@v@newblock]{\ALG@v@end}}% +\def\ALG@p@endtext@nE{\algnotext{\ALG@v@end}}% +\def\ALG@p@endtext@xnE{\algnotext[\ALG@v@newblock]{\ALG@v@end}}% +\def\ALG@p@endtext@{}% +% starttext defines are more compex -- care must be taken for the optional parameters +\def\ALG@p@starttext@S{\ALG@p@s@process{\algrenewtext}}% +\def\ALG@p@starttext@C{\ALG@p@s@process{\algrenewtext}}% +\def\ALG@p@starttext@xC{\ALG@p@s@process{\algrenewtext[\ALG@v@oldblock]}}% +\def\ALG@p@s@process#1% + {% + \ifthenelse{\equal{\ALG@v@start}{}}% + {\ALG@p@endtext}% + {\@ifnextchar{[}{\ALG@p@s@getparamcount{#1}}{\ALG@p@s@simple{#1}}}% + }% +\def\ALG@p@s@getparamcount#1[#2]% + {% + \@ifnextchar{[}{\ALG@p@s@getdefparam{#1}{#2}}{\ALG@p@s@param{#1}{#2}}% + }% +\def\ALG@p@s@getdefparam#1#2[#3]% + {% + \ALG@p@s@defparam{#1}{#2}{#3}% + }% +\def\ALG@p@s@simple#1#2{#1{\ALG@v@start}{#2}\ALG@p@endtext}% +\def\ALG@p@s@param#1#2#3{#1{\ALG@v@start}[#2]{#3}\ALG@p@endtext}% +\def\ALG@p@s@defparam#1#2#3#4{#1{\ALG@v@start}[#2][#3]{#4}\ALG@p@endtext}% +% the rest of the crew +\def\ALG@p@starttext@nS{\algnotext{\ALG@v@start}\ALG@p@endtext}% +\def\ALG@p@starttext@nC{\algnotext{\ALG@v@start}\ALG@p@endtext}% +\def\ALG@p@starttext@xnC{\algnotext[\ALG@v@oldblock]{\ALG@v@start}\ALG@p@endtext}% +\def\ALG@p@starttext@{\ALG@p@endtext}% +\def\ALG@p@indent@def#1{\def\ALG@v@indent{#1}\ALG@p@setup}% +\def\ALG@p@indent@{\def\ALG@v@indent{}\ALG@p@setup}% +\def\ALG@p@credits@def#1{\def\ALG@v@credits{#1}\ALG@p@indent}% +\def\ALG@p@credits@{\ALG@p@indent}% +\def\ALG@p@end@def#1{\def\ALG@v@end{#1}\ALG@p@credits}% +\def\ALG@p@end@{\def\ALG@v@end{}\ALG@p@credits}% +\def\ALG@p@start@def#1{\def\ALG@v@start{#1}\ALG@p@end}% +\def\ALG@p@start@{\def\ALG@v@start{}\ALG@p@end}% +\def\ALG@p@oldblock@def#1{\def\ALG@v@oldblock{#1}\ALG@p@start}% +\def\ALG@p@oldblock@{\def\ALG@v@oldblock{}\ALG@p@start}% +\newcommand\ALG@p@newblock[1][]{\def\ALG@v@newblock{#1}\ALG@p@oldblock}% +\def\ALG@p@setup% + {% + \ifthenelse{\equal{\ALG@v@newblock}{}}% + {% + \ifthenelse{\equal{\ALG@v@start}{}}% + {% + \PackageError{algorithmicx}{Block or starting entitie must be specified!!!}{}% + }% + {% + \let\ALG@v@newblock\ALG@v@start% + }% + }% + {% + }% + \ALG@endandcontinueblock% + {\ALG@v@newblock}{\ALG@v@oldblock}{\ALG@v@start}% + {\ALG@v@credits}{\ALG@v@indent}% + \ALG@endandcontinueblock% + {}{\ALG@v@newblock}{\ALG@v@end}% + {}{}% + \ALG@p@starttext% + }% +% +% param handling +% +\newcommand\ALG@p@def[2][def]% + {% + \expandafter\let\csname ALG@p@#2\expandafter\endcsname\csname ALG@p@#2@#1\endcsname% + }% +\def\ALG@p@undef{\ALG@p@def[]}% +% +\def\ALG@p@ons{\ALG@p@def{start}}% +\def\ALG@p@onS{\ALG@p@def{start}\ALG@p@def[S]{starttext}}% +\def\ALG@p@onc{\ALG@p@def{oldblock}\ALG@p@def{start}}% +\def\ALG@p@onC{\ALG@p@def{oldblock}\ALG@p@def{start}\ALG@p@def[C]{starttext}}% +\def\ALG@p@one{\ALG@p@def{end}}% +\def\ALG@p@onE{\ALG@p@def{end}\ALG@p@def[E]{endtext}}% +\def\ALG@p@onxC{\ALG@p@def{oldblock}\ALG@p@def{start}\ALG@p@def[xC]{starttext}}% +\def\ALG@p@onxE{\ALG@p@def{end}\ALG@p@def[xE]{endtext}}% +\def\ALG@p@onnS{\ALG@p@def{start}\ALG@p@def[nS]{starttext}}% +\def\ALG@p@onnC{\ALG@p@def{oldblock}\ALG@p@def{start}\ALG@p@def[nC]{starttext}}% +\def\ALG@p@onnE{\ALG@p@def{end}\ALG@p@def[nE]{endtext}}% +\def\ALG@p@onxnC{\ALG@p@def{oldblock}\ALG@p@def{start}\ALG@p@def[xnC]{starttext}}% +\def\ALG@p@onxnE{\ALG@p@def{end}\ALG@p@def[xnE]{endtext}}% +\def\ALG@p@onb{\def\ALG@v@credits{}}% +\def\ALG@p@onl{\def\ALG@v@credits{1}}% +\def\ALG@p@onL{\ALG@p@def{credits}}% +\def\ALG@p@oni{\ALG@p@def{indent}}% +% +\def\ALG@p@main#1% + {% + \@ifundefined{ALG@ps@\ALG@p@state @#1}% + {% + \csname ALG@ps@\ALG@p@state @other\endcsname{#1}% + }% + {% + \csname ALG@ps@\ALG@p@state @#1\endcsname% + }% + \ALG@p@rec% + }% +% STATE : <> +\expandafter\def\csname ALG@ps@@]\endcsname{\let\ALG@p@rec\relax}% +\def\ALG@ps@@s{\ALG@p@ons}% +\def\ALG@ps@@S{\ALG@p@onS}% +\def\ALG@ps@@c{\ALG@p@onc}% +\def\ALG@ps@@C{\ALG@p@onC}% +\def\ALG@ps@@e{\ALG@p@one}% +\def\ALG@ps@@E{\ALG@p@onE}% +\def\ALG@ps@@N{\typeout{algdef: 'N' obsoloted, use 'nE'.}\ALG@p@onnE}% +\def\ALG@ps@@b{\ALG@p@onb}% +\def\ALG@ps@@l{\ALG@p@onl}% +\def\ALG@ps@@L{\ALG@p@onL}% +\def\ALG@ps@@i{\ALG@p@oni}% +\def\ALG@ps@@x{\def\ALG@p@state{x}}% +\def\ALG@ps@@n{\def\ALG@p@state{n}}% +\def\ALG@ps@@other#1{\typeout{algdef: Ignoring unknown token #1}}% +% STATE : x +\def\ALG@ps@x@C{\def\ALG@p@state{}\ALG@p@onxC}% +\def\ALG@ps@x@E{\def\ALG@p@state{}\ALG@p@onxE}% +\def\ALG@ps@x@N{\def\ALG@p@state{}\typeout{algdef: 'xN' obsoloted, use 'xnE'.}\ALG@p@onxnE}% +\def\ALG@ps@x@n{\def\ALG@p@state{xn}}% +\def\ALG@ps@x@other#1% + {% + \typeout{algdef: Ignoring 'x' before '#1'.}% + \def\ALG@p@state{}% + \def\ALG@p@rec{\let\ALG@p@rec\ALG@p@main\ALG@p@rec#1}% + }% +% STATE : n +\def\ALG@ps@n@S{\def\ALG@p@state{}\ALG@p@onnS}% +\def\ALG@ps@n@C{\def\ALG@p@state{}\ALG@p@onnC}% +\def\ALG@ps@n@E{\def\ALG@p@state{}\ALG@p@onnE}% +\def\ALG@ps@n@x{\def\ALG@p@state{nx}}% +\def\ALG@ps@n@other#1% + {% + \typeout{algdef: Ignoring 'n' before '#1'.}% + \def\ALG@p@state{}% + \def\ALG@p@rec{\let\ALG@p@rec\ALG@p@main\ALG@p@rec#1}% + }% +% STATE : xn +\def\ALG@ps@xn@C{\def\ALG@p@state{}\ALG@p@onxnC}% +\def\ALG@ps@xn@E{\def\ALG@p@state{}\ALG@p@onxnE}% +\def\ALG@ps@xn@x{\typeout{algdef: Ignoring 'x' after 'xn'.}}% +\def\ALG@ps@xn@n{\typeout{algdef: Ignoring 'n' after 'xn'.}}% +\def\ALG@ps@xn@other#1% + {% + \typeout{algdef: Ignoring 'xn' before '#1'.}% + \def\ALG@p@state{}% + \def\ALG@p@rec{\let\ALG@p@rec\ALG@p@main\ALG@p@rec#1}% + }% +% STATE : nx +\def\ALG@ps@nx@C{\def\ALG@p@state{}\ALG@p@onxnC}% +\def\ALG@ps@nx@E{\def\ALG@p@state{}\ALG@p@onxnE}% +\def\ALG@ps@nx@x{\typeout{algdef: Ignoring 'x' after 'nx'.}}% +\def\ALG@ps@nx@n{\typeout{algdef: Ignoring 'n' after 'nx'.}}% +\def\ALG@ps@nx@other#1% + {% + \typeout{algdef: Ignoring 'nx' before '#1'.}% + \def\ALG@p@state{}% + \def\ALG@p@rec{\let\ALG@p@rec\ALG@p@main\ALG@p@rec#1}% + }% +% +% +% *** User level block/entitie commands *** +% +% +% +% algdef{switches}... -- the king of all definitions in the algorithmicx package +% +\newcommand\algdef[1]% + {% + \ALG@p@undef{oldblock}% + \ALG@p@undef{start}% + \ALG@p@undef{end}% + \def\ALG@v@credits{}% + \ALG@p@undef{credits}% + \ALG@p@undef{indent}% + \ALG@p@undef{starttext}% + \ALG@p@undef{endtext}% + \def\ALG@p@state{}% + \let\ALG@p@rec\ALG@p@main% + \ALG@p@rec#1]% + \ALG@p@newblock% + }% +% +% a lot of other macros are provided for convenience +% +\def\algblock{\algdef{se}}% +\def\algcblock{\algdef{ce}}% +\def\algloop{\algdef{sl}}% +\def\algcloop{\algdef{cl}}% +\def\algsetblock{\algdef{seLi}}% +\def\algsetcblock{\algdef{ceLi}}% +\def\algblockx{\algdef{SxE}}% +\def\algblockdefx{\algdef{SE}}% +\def\algcblockx{\algdef{CxE}}% +\def\algcblockdefx{\algdef{CE}}% +\def\algsetblockx{\algdef{SxELi}}% +\def\algsetblockdefx{\algdef{SELi}}% +\def\algsetcblockx{\algdef{CxELi}}% +\def\algsetcblockdefx{\algdef{CELi}}% +\def\algloopdefx{\algdef{Sl}}% +\def\algcloopx{\algdef{xCl}}% +\def\algcloopdefx{\algdef{Cl}}% +% algloopx is not correct, use algloopdefx +% +% Text output commands +% +\newcommand\algrenewtext[2][]% [block]{entity} + {% + \ifthenelse{\equal{#2}{}}{}% + {% + \ifthenelse{\equal{#1}{}}% + {% + \expandafter\let\csname ALG@t@\ALG@Ld @#2\endcsname\relax% + \expandafter\newcommand\csname ALG@t@\ALG@Ld @#2\endcsname% + }% + {% + \expandafter\let\csname ALG@t@\ALG@Ld @#2@\ALG@getblocknumber{#1}\endcsname\relax% + \expandafter\newcommand\csname ALG@t@\ALG@Ld @#2@\ALG@getblocknumber{#1}\endcsname% + }% + }% + }% +% +\def\ALG@letentitytext#1#2% [block]{entity} + {% + \ifthenelse{\equal{#2}{}}{}% + {% + \ifthenelse{\equal{#1}{}}% + {% + \expandafter\let\csname ALG@t@\ALG@Ld @#2\endcsname% + }% + {% + \expandafter\let\csname ALG@t@\ALG@Ld @#2@\ALG@getblocknumber{#1}\endcsname% + }% + }% + }% +% +\newcommand\algnotext[2][]% [block]{entity} + {% + \ALG@letentitytext{#1}{#2}\ALG@x@notext% + }% +% +\newcommand\algdefaulttext[2][]% [block]{entity} + {% + \ALG@letentitytext{#1}{#2}\ALG@x@default% + }% +% +\def\ALG@notext*{\algnotext}% +\def\algtext{\@ifnextchar{*}{\ALG@notext}{\algrenewtext}}% +% +% +% *** LANGUAGE SWITCHING *** +% +% +% +\newcommand\algnewlanguage[1]% + {% + \@ifundefined{ALG@L@#1}% needs to be created? + {}% + {% + \PackageError{algorithmicx}{Language '#1' already defined!}{}% + }% + \addtocounter{ALG@Lnr}{1}% increment the language counter + \expandafter\edef\csname ALG@L@#1\endcsname{\arabic{ALG@Lnr}}% set the language number + \edef\ALG@Ld{\csname ALG@L@#1\endcsname}% + \expandafter\let\csname ALG@bl@\ALG@Ld @\endcsname\ALG@bl@% the BIG block + \expandafter\let\csname ALG@bl@\ALG@Ld @@\endcsname\ALG@bl@% the BIG block + \algdef{SL}[STATE]{State}{0}{}% + \expandafter\def\csname ALG@deftext@\ALG@Ld\endcsname{\textbf}% + \algnewcommand\algorithmiccomment[1]{\hfill\(\triangleright\) ##1}% + \algnewcommand\algorithmicindent{1.5em}% + \algnewcommand\alglinenumber[1]{\footnotesize ##1:}% + \algnewcommand\ALG@beginalgorithmic\relax% for user overrides + \algnewcommand\ALG@endalgorithmic\relax% for user overrides + }% +% +\newcommand\algsetlanguage[1]% + {% + \@ifundefined{ALG@L@#1}% needs to be created? + {% + \PackageError{algorithmicx}{Language '#1' is not yet defined!}{}% + }{}% + \edef\ALG@L{\csname ALG@L@#1\endcsname}% + }% +% +\newcommand\algdeflanguage[1]% + {% + \@ifundefined{ALG@L@#1}% needs to be created? + {% + \PackageError{algorithmicx}{Language '#1' is not yet defined!}{}% + }{}% + \edef\ALG@Ld{\csname ALG@L@#1\endcsname}% + }% +% +\newcommand\alglanguage[1]% + {% + \algdeflanguage{#1}% + \algsetlanguage{#1}% + }% +% +% +% *** Defining language dependent stuff *** +% +% +\def\ALG@eatoneparam#1{}% +\def\ALG@defbasecmd#1#2% + {% + \edef\ALG@tmp{\expandafter\ALG@eatoneparam\string #2}% + \@ifundefined\ALG@tmp{\edef #2{\noexpand\csname ALG@cmd@\noexpand\ALG@L @\ALG@tmp\endcsname}}{}% + \expandafter#1\csname ALG@cmd@\ALG@Ld @\ALG@tmp\endcsname% + }% +\newcommand\algnewcommand{\ALG@defbasecmd\newcommand}% +\newcommand\algrenewcommand{\ALG@defbasecmd\renewcommand}% +\def\ALG@letcmd{\ALG@defbasecmd\let}% +\def\ALG@defcmd{\ALG@defbasecmd\def}% +\def\ALG@edefcmd{\ALG@defbasecmd\edef}% +% +% +% *** OTHERS *** +% +% +\def\BState{\State \algbackskip}% +\def\Statex{\item[]}% an empty line +\newcommand\algrenewcomment{\algrenewcommand\algorithmiccomment}% +\def\Comment{\algorithmiccomment}% +\def\algref#1#2{\ref{#1}.\ref{#2}}% +\algnewlanguage{default}% +\algsetlanguage{default}% +% +% +% *** Line breaks *** +% +% +\newcommand\algbreak% for multiline parameters !!! needs fix + {% + \item% +% \hskip\ALG@parindent%!!! not yet implemented +% \hskip-\algorithmicindent% + }% +% +\def\ALG@noputindents% + {% + \hskip\ALG@tlm% + }% +% +% +% *** algorithm store / restore *** +% +% +% store +% +\ALG@newcondstate{mustrestore}% +\def\algstore% + {% + \renewcommand\ALG@beginblock% + {% + \PackageError{algorithmicx}{The environment must be closed after store!}{}% + }% + \@ifstar{\ALG@starstore}{\ALG@nostarstore}% + }% +\def\ALG@nostarstore#1% save all infos into #1 and terminate the algorithmic block + {% + \addtocounter{ALG@storecount}{1}% + \expandafter\global\expandafter\let\csname ALG@save@mustrestore@#1\endcsname\ALG@x@mustrestore% + \ALG@starstore{#1}% + }% +\def\ALG@starstore#1% + {% + \@ifundefined{ALG@save@line@#1}{}% + {\PackageError{algorithmicx}{This save name '#1' is already used!}{}}% + \def\ALG@savename{#1}% + \expandafter\xdef\csname ALG@save@totalnr@\ALG@savename\endcsname{\theALG@nested}% + \expandafter\xdef\csname ALG@save@line@\ALG@savename\endcsname{\theALG@line}% + \expandafter\xdef\csname ALG@save@numberfreq@\ALG@savename\endcsname{\ALG@numberfreq}% + \expandafter\xdef\csname ALG@save@rem@\ALG@savename\endcsname{\theALG@rem}% + \let\ALG@storerepeat\ALG@store% + \ALG@storerepeat% + }% +\def\ALG@store% simply terminate all open blocks + {% + \ifnum\theALG@nested=0\let\ALG@storerepeat\relax% + \else% + \expandafter\xdef\csname ALG@save@currentblock@\ALG@savename @\theALG@nested\endcsname% + {\csname ALG@currentblock@\theALG@nested\endcsname}% + \expandafter\ifx\csname ALG@currentlifetime@\theALG@nested\endcsname\relax% + \else% + \expandafter\xdef\csname ALG@save@currentlifetime@\ALG@savename @\theALG@nested\endcsname% + {\csname ALG@currentlifetime@\theALG@nested\endcsname}% + \fi% + \expandafter\xdef\csname ALG@save@ind@\ALG@savename @\theALG@nested\endcsname% + {\csname ALG@ind@\theALG@nested\endcsname}% + \ALG@closebyforce% + \fi% + \ALG@storerepeat% + }% +% +% restore +% +\def\algrestore% + {% + \@ifstar{\ALG@starrestore}{\ALG@nostarrestore}% + }% +\def\ALG@starrestore% + {% + \let\ALG@restorerem\relax% + \let\ALG@restorereprem\relax% + \ALG@restoremain% + }% +\def\ALG@nostarrestore% + {% + \let\ALG@restorerem\ALG@restoreremovesave% + \let\ALG@restorereprem\ALG@restorerepremovesave% + \ALG@restoremain% + }% +\def\ALG@restoreremovesave% + {% + \expandafter\global\expandafter\let\csname ALG@save@totalnr@\ALG@savename\endcsname\relax% + \expandafter\global\expandafter\let\csname ALG@save@line@\ALG@savename\endcsname\relax% + \expandafter\global\expandafter\let\csname ALG@save@rem@\ALG@savename\endcsname\relax% + \expandafter\global\expandafter\let\csname ALG@save@totalnr@\ALG@savename\endcsname\relax% + \expandafter\global\expandafter\let\csname ALG@save@numberfreq@\ALG@savename\endcsname\relax% + }% +\def\ALG@restorerepremovesave% + {% + \expandafter\global\expandafter\let\csname ALG@save@currentblock@\ALG@savename @\theALG@tmpcounter\endcsname\relax% + \expandafter\global\expandafter\let\csname ALG@save@currentlifetime@\ALG@savename @\theALG@tmpcounter\endcsname\relax% + \expandafter\global\expandafter\let\csname ALG@save@currentlifetime@\ALG@savename @\theALG@tmpcounter\endcsname\relax% + \expandafter\global\expandafter\let\csname ALG@save@ind@\ALG@savename @\theALG@tmpcounter\endcsname\relax% + }% +\def\ALG@restoremain#1% restore all infos from #1 in an open algorithmic block + {% + \ifnum\theALG@line=0% + \else\PackageError{algorithmicx}{Restore might be used only at the beginning of the environment!}{}% + \fi% + \def\ALG@savename{#1}% + \expandafter\ifx\csname ALG@save@totalnr@\ALG@savename\endcsname\relax% + \PackageError{algorithmicx}{Save '\ALG@savename'\space not defined!!!}{}% + \fi% + \@ifundefined{ALG@save@mustrestore@\ALG@savename}{}% + {% + \addtocounter{ALG@storecount}{-1}% + \expandafter\global\expandafter\let\csname ALG@save@mustrestore@\ALG@savename\endcsname\relax% + }% + \setcounter{ALG@line}{\csname ALG@save@line@\ALG@savename\endcsname}% + \edef\ALG@numberfreq{\csname ALG@save@numberfreq@\ALG@savename\endcsname}% + \setcounter{ALG@rem}{\csname ALG@save@rem@\ALG@savename\endcsname}% + \setcounter{ALG@tmpcounter}{\csname ALG@save@totalnr@\ALG@savename\endcsname}% + \setcounter{ALG@nested}{0}% + \ALG@restorerem% + \let\ALG@restorerepeat\ALG@restore% + \ALG@restorerepeat% + }% +\def\ALG@restore% + {% + \ifnum\theALG@tmpcounter>0% + \expandafter\edef\csname ALG@currentblock@\theALG@tmpcounter\endcsname% + {\csname ALG@save@currentblock@\ALG@savename @\theALG@tmpcounter\endcsname}% + \expandafter\ifx\csname ALG@save@currentlifetime@\ALG@savename @\theALG@tmpcounter\endcsname\relax% + \expandafter\let\csname ALG@currentlifetime@\theALG@tmpcounter\endcsname\relax% + \else% + \expandafter\edef\csname ALG@currentlifetime@\theALG@tmpcounter\endcsname% + {\csname ALG@save@currentlifetime@\ALG@savename @\theALG@tmpcounter\endcsname}% + \fi% + % + \ALG@beginblock{\csname ALG@save@ind@\ALG@savename @\theALG@tmpcounter\endcsname}% + \ALG@restorereprem% + \addtocounter{ALG@tmpcounter}{-1}% + \else\let\ALG@restorerepeat\relax% + \fi% + \ALG@restorerepeat% + }% +\AtEndDocument% + {% + \ifnum\theALG@storecount>0\relax% + \PackageError{algorithmicx}{Some stored algorithms are not restored!}{}% + \fi% + }% \ No newline at end of file diff --git a/algpseudocode.sty b/algpseudocode.sty new file mode 100644 index 0000000..e045bfe --- /dev/null +++ b/algpseudocode.sty @@ -0,0 +1,92 @@ +% PSEUDOCODE ALGORITHMIC STYLE -- Released 27 APR 2005 +% for LaTeX version 2e +% +% Copyright Szasz Janos +% E-mail szaszjanos@users.sourceforge.net +% Based on Peter Williams's algorithmic.sty +% +\NeedsTeXFormat{LaTeX2e}% +\ProvidesPackage{algpseudocode}% +\RequirePackage{ifthen}% +\RequirePackage{algorithmicx}% +\typeout{Document Style - pseudocode environments for use with the `algorithmicx' style}% +% +\def\ALG@noend{f}% +\newboolean{ALG@compatible}% +\setboolean{ALG@compatible}{false}% +% +\DeclareOption{noend}{\def\ALG@noend{t}}% +\DeclareOption{end}{\def\ALG@noend{f}}% +\DeclareOption{compatible}{\typeout{For compatibility mode use algcompatible.sty!!!}\setboolean{ALG@compatible}{true}}% +\DeclareOption{noncompatible}{\setboolean{ALG@noncompatible}{false}}% +\ProcessOptions% +% +% *** DECLARATIONS *** +% +\algnewlanguage{pseudocode}% +\alglanguage{pseudocode}% +% +% *** KEYWORDS *** +% +\algnewcommand\algorithmicend{\textbf{end}} +\algnewcommand\algorithmicdo{\textbf{do}} +\algnewcommand\algorithmicwhile{\textbf{while}} +\algnewcommand\algorithmicfor{\textbf{for}} +\algnewcommand\algorithmicforall{\textbf{for all}} +\algnewcommand\algorithmicloop{\textbf{loop}} +\algnewcommand\algorithmicrepeat{\textbf{repeat}} +\algnewcommand\algorithmicuntil{\textbf{until}} +\algnewcommand\algorithmicprocedure{\textbf{procedure}} +\algnewcommand\algorithmicfunction{\textbf{function}} +\algnewcommand\algorithmicif{\textbf{if}} +\algnewcommand\algorithmicthen{\textbf{then}} +\algnewcommand\algorithmicelse{\textbf{else}} +\algnewcommand\algorithmicrequire{\textbf{Require:}} +\algnewcommand\algorithmicensure{\textbf{Ensure:}} +\algnewcommand\algorithmicreturn{\textbf{return}} +\algnewcommand\textproc{\textsc} +% +% *** DECLARED LOOPS *** +% +\algdef{SE}[WHILE]{While}{EndWhile}[1]{\algorithmicwhile\ #1\ \algorithmicdo}{\algorithmicend\ \algorithmicwhile}% +\algdef{SE}[FOR]{For}{EndFor}[1]{\algorithmicfor\ #1\ \algorithmicdo}{\algorithmicend\ \algorithmicfor}% +\algdef{S}[FOR]{ForAll}[1]{\algorithmicforall\ #1\ \algorithmicdo}% +\algdef{SE}[LOOP]{Loop}{EndLoop}{\algorithmicloop}{\algorithmicend\ \algorithmicloop}% +\algdef{SE}[REPEAT]{Repeat}{Until}{\algorithmicrepeat}[1]{\algorithmicuntil\ #1}% +\algdef{SE}[IF]{If}{EndIf}[1]{\algorithmicif\ #1\ \algorithmicthen}{\algorithmicend\ \algorithmicif}% +\algdef{C}[IF]{IF}{ElsIf}[1]{\algorithmicelse\ \algorithmicif\ #1\ \algorithmicthen}% +\algdef{Ce}[ELSE]{IF}{Else}{EndIf}{\algorithmicelse}% +\algdef{SE}[PROCEDURE]{Procedure}{EndProcedure}% + [2]{\algorithmicprocedure\ \textproc{#1}\ifthenelse{\equal{#2}{}}{}{(#2)}}% + {\algorithmicend\ \algorithmicprocedure}% +\algdef{SE}[FUNCTION]{Function}{EndFunction}% + [2]{\algorithmicfunction\ \textproc{#1}\ifthenelse{\equal{#2}{}}{}{(#2)}}% + {\algorithmicend\ \algorithmicfunction}% +% +\ifthenelse{\equal{\ALG@noend}{t}}% + {% + \algtext*{EndWhile}% + \algtext*{EndFor}% + \algtext*{EndLoop}% + \algtext*{EndIf}% + \algtext*{EndProcedure}% + \algtext*{EndFunction}% + }{}% +% +% *** OTHER DECLARATIONS *** +% +\algnewcommand\Require{\item[\algorithmicrequire]}% +\algnewcommand\Ensure{\item[\algorithmicensure]}% +\algnewcommand\Return{\algorithmicreturn{} }% +\algnewcommand\Call[2]{\textproc{#1}\ifthenelse{\equal{#2}{}}{}{(#2)}}% +% +% +% +\ifthenelse{\boolean{ALG@compatible}}% + {% + \ifthenelse{\equal{\ALG@noend}{t}}% + {\RequirePackage[noend]{algcompatible}}% + {\RequirePackage{algcompatible}}% + }% + {}% +% \ No newline at end of file diff --git a/ch1.tex b/ch1.tex new file mode 100644 index 0000000..ca117a8 --- /dev/null +++ b/ch1.tex @@ -0,0 +1,121 @@ +\chapter{Introduction} + +This is a qualitative study.\\ +Its analytic lens is phenomenography.\\ +The research question is what are the conceptions of proof we find in the population of students of computer science (and engineering). + +\begin{quote} +Black and Williams 1998 stated ``When instructors understand what students know and how they think --- and the use that knowledge to make more effective instructional decisions --- significant increases in student learning occur'' \cite{black1998inside}%Black, Paul and Dylan William, Inside the Black box: Raising standards through classroom assessment Granada Learning 1998 +\end{quote} + +A student's approach to learning has been seen, empirically\cite[around 35]{marton1997learning} to be predictive of their learning outcome. +In looking at, and developing categories for, students' ways of experiencing their learning, we obtain insight into their approach, and can hope to improve their outcomes. + +Marton\cite[p. 36]{marton1997learning} has defined that one conception (of a thing, $x$) differs from another, for the purposes of phenomenography, by the existence of a distinct manner in which participants were found to voice the way they thought about $x$. The categories of conceptions (also, conceptualizations) include two overriding categories,\cite[p. 35]{marton1997learning} the first being "a learning task, some facts to memorize", and the second having as objective "a way to change oneself, to see things in a new light, to relate to earlier learning, and to relate to a (changed) world. At the next level of drawing distinctions, S{\"a}lj{\"o}\cite{1979} has found five qualitatively distinct conceptualizations, and Marton\cite{1993} has found six distinct conceptualizations falling into the two overriding, task and objective. + +\begin{enumerate} +\item learn as increase knowledge +\item learn as increase and be able to reproduce knowledge +\item be able to apply new knowledge +\item acquiring new meaning, multiple ways of thinking about things, changed perspective, improved understanding, thinking more logically +\item modified perspective, multiple perspectives, dynamic perspective +\item changing the person +\end{enumerate} + + +Marton and Booth\cite[p. 78]{marton1997learning} observe that successive understandings increase in completeness as they move toward a theoretical understanding. + + +Selden and Selden\cite{kaput1998research} include, in their questions regarding teaching and learning mathematics, that instructors aim for their students to ``achieve the kind of organizing and integrated use of language'' used in the mathematics community. + +D\"orfler\cite[p. 122]{dorfler2000means} complements the idea of concept, saying " ' What is the concept $xy$?' should be substituted, or at least complemented, by such questions as 'Which actions can be recorded and/or guided by the concept $xy$?' \ldots Learners must indulge in the discourse \ldots mathematical objects \ldots are discursive objects. This means they come into existence exclusively by and within the discourse, even if this discourse ascribes to them existence an properties of an objective and independent character. " + +Wittgenstein said \cite[p. 19--20]{wittgenstein1989wittgenstein} "To understand a phrase, we might say, is to understand its use. \ldots Similarly, you only understand an expression when you know how to use it". + + +So, we are inquiring into student conceptualizations, as shown by the students' use of their concepts, and by the students' reflections (in interviews) upon their concepts. + + $$While there are many aspects of students' conceptualizations of proofs that are interesting, we concentrate our attention onto proofs that seem to be useful in showing the correctness, progress, termination, safety and resource utilization of algorithms.$$ +It is important for students of computer science +%, and of computer science and +%engineering (called, in the following, computer science) + to comprehend, +apply, and synthesize proofs. +%, and to be able to synthesize simple proofs. +These skills +are needed because proofs are used to demonstrate the resource needs and +performance effects of algorithms, as well as for safety, liveness, and correctness +/accuracy. +We claim herein that some students, having learned an algorithm, are not certain of +the problem environment in which this kind of algorithm is effective, and as a +result are reluctant to apply the algorithm. +It is desirable for students to be able +%correctly, to develop internal conviction, and +to ascertain that an algorithm is a +good match for a problem, which can sometimes be proved, otherwise their knowledge of the algorithm is less +useful. + +It is important for instructors to impart, efficiently and effectively, knowledge +about proof to the students. We will be using phenomenography. + Phenomenography and its outgrowth, variation +theory, \cite{marton1981phenomenography,svensson1997theoretical,marton1997learning,marton2005unit} provide insight into ways to help students discern specific +points. The points, whose emphasis is conjectured to be most beneficial, are +identified by a qualitative research process. +We propose to research these questions: +\begin{itemize} +\item What do students think a proof is? +\item How do students attempt to understand proofs? +\item What do students think a proof is for? +\item What do students use proof for (if anything), in particular in circumstances +other than when assigned? +\item Do students exhibit any consequence of inability in proof, such as, avoiding +using recursion? +\item What kind of structure do students notice, do student make use of, in +proof? +\item How familiar and/or comfortable are students with different (specific) +proof techniques: induction, construction, contradiction? +\item What do students think it takes to make an argument valid? + +\end{itemize} + + + +These questions are interesting because with the curriculum we are trying to +build capabilities into the students, that will enable them to tackle various +problems they may encounter. Moreover, we wish the students to develop the +ability to have, in the terminology of Harel and Sowder\cite{harel1998students}, conviction with an internal source, and to be correct in their +convictions. As new situations emerge, and as students who have graduated +find the occasion to modify an algorithm to a new situation, we want these +individuals to be able to know that their modified algorithms are appropriate. +Thus it is important to know to what extent the students are absorbing the +knowledge about proof we are trying to impart. It is important that they +understand this algorithm-applicability purpose of proof, so that they can +judge applicability for themselves, and it is important to know what hindrances +they are experiencing, so that we can help the students overcome them. It is +important that they recognize that there is structure in proofs, and that they +can construct % architect + their own proofs, because we cannot foresee every situation our +students may experience. +Because we are greatly concerned that students should apply their knowledge +of proof to algorithm related contexts they may subsequently encounter, the +split between what is performed for assessment, and what students prefer for +their own use is significant to us. +Phenomenographic research yields critical factors, which are ideas whose emphasis +is thought to be particularly helpful in deepening student understanding. +Thus the relevance of this research to the curriculum is that the work will +generate suggestions about points to emphasize. + +Chapter 2 discusses the design of the research study. Chapter 3 discusses the +phenomenographic research perspective, and the epistemological framework. +Chapter 4 discusses the methodologies applied in the several studies, including +sections on sample selection, data collection, techniques of data analysis and +approaches to validity and reliability, including reflection on researcher bias +and assumptions. Chapter 5 describes the unprocessed results of each study. +Chapter 6 discusses data analysis of each study, and the interpretation. Chapter +7 discusses validation and reliability. Chapter 8 discusses related work. +Chapter 9 concludes the description of completed work. +Chapter 10 offers a perspective on future directions. +An appendix contains an assessment instrument for incoming to discrete math. + + + diff --git a/ch10.tex b/ch10.tex new file mode 100644 index 0000000..f734585 --- /dev/null +++ b/ch10.tex @@ -0,0 +1,124 @@ +\chapter{Conclusion} +\begin{quote}Harel and Sowder \cite[p. 277?] {harel1998students}by their natures, teaching experiments and interview studies do not give definitive conclusions. They can, however, offer indications of the state of affairs and a framework in which to interpret other work.\end{quote} + + + +Are CS students' conceptualizations more like Harel and Sowder, or more like Tall? +Are the several schemes (Pirie Kieren, etc. complementary? reconcilable? Is one more likely than another based on cognitive neuroscience of language? (proofs are in a language after all)) + + + +This research suggests that suitable question for a larger study +\section{ Recognizing an Endpoint} +A qualitative study is thought to be finished when an internally consistent +narrative, compatible with the data, both situating the data and explaining +them, has been produced. +For our research questions, a model, accompanied by a narrative combining +the information obtained from inquiry about these topics will complete the +work. Data from our extended student body, that provide a persuasive model +containing categories of conceptualizations, and that are closely enough related +that some insight about concepts differentiating adjacent categories can +be inferred, are thought sufficient to generate this narrative. The proposed +differentiating concepts are thought to have the potential to become material +for a larger survey, thereby providing a starting point for new work. +I expect to find a model similar to that of Harel and Sowder 1998[?], but +modified because of the different emphases on material in computer science +compared to mathematics. First, students of computer science should be very +familiar with the idea of consciously constructing, examining and evaluating a +process, from their study of algorithms. Because of this, the category internalization +might be subsumed by the category interiorization. +From empirical data, we know that there are students of computer science +who think that proofs might be irrelevant to their career; it would be hard to +imagine a mathematics student who thought so. CS students who do not think +proof is part of their career might be relatively content with conceptualizations +corresponding to outside sources of conviction. We found computer science +students whose conception of proof includes that a single example is sufficient +for proving a universally quantified statement. We found computer science +students whose conception of proof is that definitions are barely interesting, +and who find demonstrations based on definitions unconvincing. Because our +findings were not quantitative, we could not compare the population of categories. +Nevertheless, the relationships between categories, and the resulting +critical factors, might be different, especially in the area of Harel and Sowder's +internalization and interiorization. +Because the scope is broader, involving proof for deciding whether or not an +algorithm is suitable for a problem, I expect we will find more categories, +related to algorithms and their applicability. +The product of a phenomenographical investigation is categories of conceptualization +and critical aspects that distinguish one category from the previous. +One hopes that by identifying critical aspects, suggestions about what to emphasize +when teaching, and what to seek in assessments are also clarified. This +investigation is intended to develop insight into students understandings of +proofs, that are the meanings they have fashioned for themselves, based on how +they have interpreted what they have heard or read. By examining some of +these understandings, we might find directions in which to improve our teaching. +Moreover, observations about the conceptualizations of students early in +the curriculum can forewarn instructors, helping them recognize the preparation +of incoming students. Perhaps we could use this to prepare remediation +materials. +For example, we can use UML diagrams and ``trie'' data structures to emphasize +definitions for families of concepts. We can choose groups of examples, +and non-examples of proofs whose correctness turns on the qualification that +distinguishes a subclass from its immediate superclass. +Beyond this, one may hope that qualitative research suggests worthwhile questions +for larger scale investigations. + +Application of findings about students +of mathematics to students of computer science is fraught by differences +in the preparation and interests related to algorithms. One likely difference is +motivation: students of mathematics know that proof is the principal means +of discourse in their community, but students of computer science might not +be aware of the importance of proof to their work. Not all differences favor +students of mathematics. In particular, the categories internalization and +interiorization of Harel and Sowder’s 1998 model\cite{harel1998students} are apt to be, in students +interested in algorithms, more closely related, than in students of mathematics. +There may be a difference regarding abstraction. Both mathematics and +computer science deal in abstraction, and students in both disciplines struggle +with it. \cite{mason1989mathematical,hazzan2003students}. In mathematics, following Vi\`ete, \cite{viete2006analytic}, single letter variable names +are used. These are thought to support the learning of abstraction, for example, Gray and Tall \cite[p. 121]{gray1994duality} observe ``we want to encompass the growing compressibility of knowledge characteristic of successful mathematicians. Here, not only is a single symbol viewed in a flexible way '' + and +in computer science abstraction, one way to exhibit abstraction is UML diagrams. Because the +``trie'' structure and International Standards Organization ISO standard 11179 +are computer science approaches to management of definitions, it could be that +computer science students would be more accessible to noticing the desirability +of concept definitions over concept images (see R\"osken and Rolka, \cite{rosken2007integrating} and +Rasslan and Tall \cite{rasslan2002definitions}). It would be interesting to know whether any of several +approaches reported by Weber [?] could be used, perhaps in modified form, for +instruction of students of computer science. The Action Process Object Schema +approach of Dubinsky \cite{dubinsky2002apos} sounds compatible with computer science students' +interests. An approach due to Leron and Dubinsky uses computer programming +\cite{leron1983structuring}, another \cite{leron1995abstract} is directed more to learning group theory than to learning proof +construction. Also specific to students concerned with algorithms, we may +wish to extend the notion of social constructivism from that of Piaget \cite{}, [?] and +of Vygotsky, [?] where it was necessarily a person with whom the learner was +communicating, and therefore with whom it was necessary to share a basis for +communication, to include a compiler and runtime execution environment, as +students of computing disciplines must also comply with rules (e.g., syntax) +used in these systems. Recalling the work of Papert and Harel\cite{harel1991constructionism}, we might +call this constructivism with constructionism. Constructionism is an approach +to learning in which the person learns through design and programming. +A cluster of related problems exists, which includes what students conceptualizations +are, about some elements of proof they should understand: +\begin{itemize} +\item what internal representations do students use? +\item Is there a gamut of internal representations, and does that help with abstraction? +\item mathematization, which is the ability to represent problems in mathematical +notation +\item interiorization, which is the ability to examine and discuss the process of +creating proof +\item comprehension of simple proofs, which is the ability to see that, and why, +an argument is convincing +\item proof analysis, which includes the ability to analyze simple proofs to +recognize structure +\item problem recognition, which is the ability to see that a problem is one that +matches a known solution technique +\item transformational approach, which is considering the consequences of +varying features of the problem +\item axiomatic approach, which is the exploration of the consequences of +definitions +\item construction of valid arguments, which is to synthesize deductions with +component parts, including warrants +\end{itemize} + +\section{Application of Findings} + +\section{ Perspective on Future Directions} \ No newline at end of file diff --git a/ch11.tex b/ch11.tex new file mode 100644 index 0000000..906427a --- /dev/null +++ b/ch11.tex @@ -0,0 +1,242 @@ +\chapter{Future Work} +Anecdotal evidence suggests that pleasantness and fun, which are intrinsic rewards, help students pay attention and remember. Make use of the natural experiment --- some students will have enjoyed the material. Are these the ones who remember better? and does the nature of enjoyment make any difference in understanding productivity aesthetics? +\section{Helping Students Discern Derivation for Proof of Correctness} +Recall that variation theory holds that students cannot discern a thing unless contrast is provided. +Pang has pointed out that, for persons aware of only one language, ``speaking'' and ``speaking their language'' are conflated. +Only when the existence of a second language is known, does the idea of speaking become separated from the ide of speaking a specific language. +We may wish to alert students to the ability to derive code from requirements mathematically. +We could show them, for example, an even function. +We could show them how to construct a function that is even. +We could show them how to construct a function that is odd. +This might hep them see the difference between writing code and testing it afterwards, and deriving the code to be correct by construction. + + +Variation theory and cognitive science suggest the teacher should make an effort to show positive and negative examples and to point out what causes one to be positive and the other negative to help discern the relevant features. Have you noticed this practice? Did you find it helpful?\\ + +Engagement with the material\\ +Please rank order the factors that might help you e engaged wit theh material\\ +job related\\ +prereque\\ +have been curious about\\ +fun\\ +competition\\ +beautiful\\ +(Does this happen often)\\ +(Does this matter to you?)\\ +What, if anything, makes you engage with the material?\\ + Neurophysiology suggest that animation in overheads makes it easier to be alert to material, that figures draw attention more easily than text. + Plesae comment on what if any things make animation helpful to you, or whether you find some animation helpful. + If you find figures helpful, can you comment on how they help? Do you find it easier to pay attention to figures than to text? + +\section{Use of Conceptualizations} + +Suppose we wish to incorporate into our curriculum on software engineering, material on both verification by formal methods, and also code derivation from specifications. +We might wish to have our students able to recognize a specification that can be satisfied +by a transition system, so that they can ascertain that a representation of that transition system that can be converted automatically into code implementation is an available approach. +We would need it to be, that the mathematical arguments for the transformations of requirements +to Floyd-Hoare-triples, for example, convince the students. +Knowing the range of the state of preparedness of the incoming students allows us to plan the amount of time to devote to background material, +and which background material should be provided. +Suppose we wished to make use of higher order logic, so that we could employ relations as arguments +to functions. +We might, for example, wish to pass a +graph constraining how a computation should be carried out. +We would like the students to appreciate the mapping between a recursive +implementation and proof by mathematical induction. +We would like the students to discern when a recursion is a tail recursion. +We would like the students to appreciate the mapping between a tail recursion and iteration. +On the one hand we have an idea which mathematical tools we wish to use, and on +the other hand we have an idea +of the extent of the students' conceptualization. +With these we can begin to design an instructional approach. +\subsection{Recognize a specification that can be satisfied by a transition system} +For this, they should know what a transition system is. +There is a state, so we wish to represent a store, and the states it may take on. +There is a way to change the state, so we wish to represent transitions, and the idea of a path from +state to state. +They should understand how a transition system can be represented in code, and that this can be carried out automatically. +Path algebra furnishes a rigorous description of these processes. +Path algebra out to be accessible to the students. +We could introduce (typed) lambda calculus to the students with path algebra as its first use. +Now that we have Java 8 which provides anonymous functions, we can also offer a coded version for +exploration. +Having the use of typed lambda calculus for path algebra, we can then use it to describe the effect of instruction in the context of Floyd-Hoare triples. +Program derivation can be illustrated. +Because we always prefer the students to apply what they comprehend, +it is important to have exercises. +Students should perform derivation, so that they come to appreciate that it can be automated. + + +\subsection{Composition} +Because derived components can be expected to be composed, either in sequence or in parallel, it +is important that the students understand this at a rigorous level. +As we can expect to be passing as arguments, procedures to be composed, the need for +higher order logic is evident. +\subsection{Invariants} +The role of invariants in assuring the correctness of composition provides motivation for consideration of invariants. +\subsection{Provability} +With transition systems as a first example of what can be correct by construction, and invariant +as a tool for provability, students can see that a way to design code with the prospect of fewer bugs is possible, at least in some circumstances. +\subsection{User of Bridging Material} +The material on mathematical tools we wish to use should be introduced at a level that addresses the +conceptualizations the students bring to the course. +Because the students bring different levels of preparedness to the class, some +self-assessment might be included, to guide the student to the starting poing corresponding to his or her current ideas. +The self-assessment can make use of the concepts used in the course. +For example, during the course, the idea of invariants is used. +Self-assessment can include questions posed to determine a student's understanding +of the nature and role of an invariant, and direct the student to explanations that may be +helpful, according to the results of the self-assessment. +From this vantage point, other techniques of proving, including contradiction and contrapositive, are motivated. +\subsection{Summary} +The less-developed end of the range in the students' conceptualizations identifies the starting point of explanatory background material that should be provided. +The needs of the course determine the ending point of the explanatory background +material. +The major themes in the students' conceptualizations make evident the +critical aspects, that distinguish on conceptualization from another, and therefore +suggest the self-assessment questions that should be furnished, to help students know where to begin improving. +An alternative to having analyzed the conceptualizations among the students is to use on a +student case-by-case basis, a sort of failure modes and effects analysis, whereby the effect of lacking a certain understanding can be predicted to cause a certain pattern of confusion on the part of the +student, and that confusion is used to discover what way is best to help that particular individual. +Different parts of the background material become motivated at different times within the course. +It could help the students to provide a key from possible trouble spots to relevant background material. +\subsection{Example} +We use the model of students' conceptualizations shown in () to provide background material for a course in software engineering organized around the concept of provability-driven development. +Finding the calculational approach of Gries\cite{}, which provides relatively succinct proofs, matching well with the phenomenology of Rota, who found that short proofs were more beautiful and more memorable, we prefer this style. +From the range of conceptualizations, we choose to include symbolization, and formation of valid arguments stressing that rules of inference satisfy guards upon the transformations we can make as we transition from one statement to another. +Which of the following describes a while loop executing?\\ +boolean done = false;\\ +while(!done)\{\\ +statements which eventually change done to true\} + +\begin{itemize} +\item ($\neg$ done)(statements)(done) +\item ($\neg$)(statements)(d) +\item($\neg$p)(statements)(p) +\item(p)(statements)($\neg$p) +\item all of the above +\item none of the above +\end{itemize} + +Which of the following describes two statements executing in sequence (where, for any $i$, $s_i$ denotes a state of the variables being used by the program)? Please note that reading the value of variable does not change the state. + +\begin{itemize} +\item (in state $s_0$)(print ``Hello, world'')(print x) (in state $s_0$) +\item (in state $s_0$)(x=x+1)(print x) (in state $s_0$) +\item (in state $s_0$)(x=x+1)(print x) (in state $s_1$) +\item 1 and 3 but not 2 +\end{itemize} + +Please note that the questions have been designed to help you notice the content being explored. If you find that the phrasing of the questions is helping you arrive at the correct answer, you should choose to study the material. Variables, which can be individual letters, or names, either in computer programs or mathematical statements, are used to represent ideas. In programs, meaningful +variable names have been shown to increase the speed and correctness of comprehension \cite{} In mathematical statements, single letter variable names have been shown to improve the skill of abstraction. +Thus we choose to employ meaningful variable names for now, but will tend to replace them with single letters later. +You have probably seen variables in high school algebra, for example in the equation for a line, typically written as $y=mx+b$. +Here, $y$, the vertical position on a graph, is calculated from $m$, the slope of the line, and $b$, the vertical offset when $x=0$. A family of parallel lines can be generated by keeping one value for $m$, and setting different values for $b$. +Thus we see that a variable can refer to a single value, and a variable can also refer to different single values at a time. +For any one point along a line, when the value of $x$ refers to a single value, the single values of $x,m$ and $b$ can be used to calculate a single value for $y$. +It is, however, also possible to think of the values of horizontal axis all together, and refer to that idea by a single variable $x$. +If you are familiar with a programming language, such as MATLAB\textregistered, that supports vector variables, you will have seen single variable that can refer to many individual values at once. +Likewise, you may have worked with arrays of one ore more dimensions; reflecting on this, the array name (without specified indices) can be though of as referring to the entire array. +Keeping that idea in mind, we can contemplate the mathematical expression $0 \leq x \leq 1$. +When $x$ is an integer, we have that the integers 0 and 1 satisfy this description. +Depending upon context, $x$ may represent the range including these. +changing the universe of discourse from integers to reals, the expression $x<3$ represents, depending upon context, not necessarily only a single, yet-to-be-determined real number that also has the property of being less than 3, but also it can be that $x$ represents all real numbers less than 3. + + +\subsection{Logical Operators} +We wish students to understand strengthening and weakening of conditions. +We wish student to understand the idea of a precondition as a disclaimer, and also as a guard. +We wish students to be able to negate statements with multiple quantifiers. +We have seen from investigating the conceptualizations that students can have trouble even negating statements with single quantifiers. +\subsection{Relations} +We want students to understand relations, because we want them to see the pairing of an input state and an output state, as a result of a transformation by a computation, as a relation. +\subsection{Rules of Inference} +Calculational proofs\cite{are these Gries?} seem to suggest strongly the way to proceed. +Stepping through examples of these might help students comprehend +\subsection{Internalization and Interiorization} +Recall that internalization has been achieved when a student can perform a process correctly, not necessarily recognizing the circumstances in which that process is appropriate. +What distinguishes interiorization from internalization is that the student can examine and discuss the process, beyond being able to carry it out. +It is important for the software engineering course that students can examine and discuss the process of program derivation from requirements. +Recognition of the circumstances in which automatic program derivation can be performed is an important part of understanding requirements. +We combine internalization and interiorization because our interviews have not addressed topics that the participants cannot discuss. +We have however found student testimony that process that can be carried out confidently are nevertheless not used due to lack of a means to determine whether the process is appropriate to circumstances. +Which, if any, of the requirements described below can be satisfied by a finite state machine? + +\begin{itemize} +\item Recognize whether or not a string could have been generated by a regular expression +\item Recognize whether or not a string could have been generated by at least one of a set of regular expressions +\item Recognize whether or not a string could have been generated by juxtaposition of strings, each of which could have been generated by at least one of a set of regular expressions +\item all of the above +\item none of the above +\end{itemize} +Is this a mapping from a recursive algorithm to a proof by mathematical induction? +The base case or cases of the recursive definition map to the base case or cases of the proof, and the recursive call or calls are always invoking with a problem of a smaller size, and the inductive step is always working with a premise that is assumed to be true. +In both recursive algorithms and inductive steps, the next problem is solved making use of a previous solution. +Is this a mapping from a concrete example of a proof to a proof in a more abstract circumstance?\\ +Concrete\\ +There is a commercially available car, a deLorean.\\ +There is an unreachable goal, time-travel.\\ +Spielberg has shown us that if only we had a ``flux-capacitor'' to attach to the deLorean, we could have time-travel.\\ +Therefore we conclude that the flux-capacitor must also be unreachable, by the following logic:\\ +If we had the flux-capacitor and the deLorean, we would get time travel.\\ +We cannot get time-travel.\\ +So, we cannot have the flux-capacitor and the ddLorean.\\ +We can get the deLorean.\\ +So, it must be that we cannot get the flux-capacitor.\\ +Relatively Abstract\\ +There is a simple algorithm, $M$, by which we can determine whether two finite sets have any elements in common.\\ +There is an unreachable goal, $A_{TM}$.\\ +Sipser has shown us that, if only we had $E_TM$ and $M$, we could have $A_{TM}$.\\ +We cannot get $A_{TM}$.\\ +So, we cannot have $E_{TM}$ together with $M$.\\ +We can have $M$.\\ +So, it must be that we cannot get $E_{TM}$.\\ +(I'm thinking pictures would help.) +In symbols:\\ +$\neg A_{TM}$\\ +$M \land E_{TM} \rightarrow A_{TM} $\\ +$\neg A_{TM} \rightarrow \neg(M \land E_{TM})$\\ +$\neg(M \land E_{TM})$\\ +$\neg M \lor \neg E_{TM}$\\ +$M$\\ +$\neg E_{TM}$ + +\subsection{Perceptual} +\subsection{Transformational} +\subsection{Axiomatic} +To detect +\subsection{What Do You Say After You Say HelloWorld?} +This is a software engineering course, organized around the idea of provability driven development. +We want to impart the desire to approach software engineering problems with methods of formalizing calculation checking. +Mathematics provides what is necessary for proofs, by means that include precise definitions. +We would write definitions of program function in a style admitting proof. +We will use finite automata. +So, a section on proof, followed by a section on finite automata, formal definitions of things we use, +clients, servers, files, streams, What sort of things are we aiming to prove? +liveness, safety, accuracy, i/o relations for component based systems resource utilization including time utility functions. +The construction technique needs to be proven. +BL, statecharts, Wise computing This goes with composition of systems. +Unlink (in a book on formal methods)Wing, we do not pick one, rather, we relate (multiple possibilities to one another?) them, like ISO standard communication stack and those defined things live in the space of abstractions, i.e., many different operational sequences covered by one invariant. +What impact does provability have on these? +structure in types data structures meets provability (recursive data structure, proof by induction) +can we represent data structures as finite automata? +Is there a reason why not to do this? e.g., would it not be sufficiently general? +representing datatypes with algebras Hoare 1985 Milner 1980 models, \cite{milner1978theory} with math, might have more properties that we want to use, vs. +theories, with which we create only our desired properties. +Z, VDM, emphasize models over theories, +Z VDM Larch algebraic specification language would we want to use Tempo instead of OBJ? +A formal method has an assertion language, for example, first order predicate logic. +A formal method has a specification language, wich in turn has a syntax and a semantics. +The syntax contains rules for formulating syntactically correct (legal) terms. + +Mitchell \cite[p. 35] (Foundation of Programming Languages) says Hilbert-style proofs system consists of axioms and proof rules. +axiom provable be definition\\ +a proof is a structured object build from formulae, according to constraints established by a set of axioms and rules of inference. + +Arcavi et al.\cite[p. 56]{arcavi1998teaching}''Work in cognitive science\cite{mcleod1992research} has shown that students' beliefs about the nature of a subject may have profound effects on their learning of it % (McLeod 1992) Research of affect in mathmatics education: A reconceptualization In Doublas A. Grouws (Ed.) Handbook of research on mathematics teaching and learning [pp. 575-596 NY Macmillan] + +One approach to teaching students to generalize is used by Schoenfeld (page 60 and earlier), who teaches his students heuristics, including one from Polya, about problems with fewer requirements + +Researchers have noticed that students, having learned procedures, have not necessarily learned to apply them. +Cipra 1995 UME Trends The bumpy road to reform +Culotta 1992 The calculus of education reform science 255 \ No newline at end of file diff --git a/ch2.tex b/ch2.tex new file mode 100644 index 0000000..afb17fb --- /dev/null +++ b/ch2.tex @@ -0,0 +1,95 @@ +\chapter{Design of the Study} +This work is a qualitative study, the underlying philosophy is constructivist, +the research perspective is phenomenography, as extended to variation theory, +and the epistemological framework is a layered collection of intellectual disciplines. +At the highest level of integration, computer science and mathematics +reside, supported by studies in memory and attention, including computational +complexity applied to cognitive neuroscience, and neurophysiology. +This study is qualitative because + we seek to be able to describe the nature of the various +understandings achieved by the students, rather than the relative frequency +with which any particular understanding is obtained. + +% the focus is on determining what questions +%would be posed, in the process of continuous curriculum adaptation and improvement +%the meaning students are making of their specific educational experiences. + +\section{Population Studied} +In a phenomenographic study, it is desirable to sample widely to obtain as broad as possible a view of the multiple ways of experiencing a phenomenon within the population of interest.\cite{marton1997learning} which in turn cites Glaser and Strauss 1967\cite{glaser1968discovery} We studied, by interview, homework and test, undergraduate students who have taken courses involving proof. Typically but not always, these are students majoring in computer science. Some of these undergraduate students are dual majors, in computer science and mathematics. We interviewed graduate students emphasizing those who have been teaching assistants for courses involving proofs. We interviewed faculty who have been taught courses involving proof. We have interviewed former students who have graduated from the department. We have interviewed undergraduates who transferred out of the department. + +\section{Chronology of the Design} +The design of this study began while teaching Introduction to the Theory of +Computing. While helping students learn the pumping lemma for regular +languages, and trying to understand from where the several difficulties arose, +I became curious about the bases of these difficulties. One example was that +a student felt strongly that a variable, a letter, denoting repetitions in a mathematical +formulation, could only stand for a single numeric value, rather than a +domain. Subsequently I have learned that symbolization is a category identified +by Harel and Sowder \cite{harel1998students}, for students of mathematics learning proofs. Our +student is a vignette of our computer science student population harboring +some of the same conceptualizations. As a consequence of this opinion, the +student felt that showing that a mathematical formulation had a true value +was equivalent to demonstrating a true value for a single example, rather than +demonstrating a true value for a domain. Here we see evidence for the category +Harel and Sowder \cite{harel1998students} call (is it inductive, perceptual?) where an example +is thought to provide proof of a universal statement. Later, while helping students +study the relationship between context free grammars and pushdown +automata, I learned from the students that many of them did not find inductive +proofs convincing. Subsequently I have learned that Harel and Sowder \cite{harel1998students} created +a category called axiomatic reasoning. In axiomatic reasoning, students +begin with accepted information, such as axioms and premises, and apply rules +of inference to deduce the desired goal. This category had not always been +reached by their students, similarly to ours. As will be seen, later interview data showed, +some of our students learn to produce the artifact of a proof by mathematical +induction by procedure. They learn the parts, and they supply the parts +when asked, but are not themselves convinced. (McGowan and Tall report a similar situation.) This matches with two other +categories created by Harel and Sowder \cite{harel1998students}, internalization and interiorization. +Still later, when leading a course on ethical reasoning for issues related to computer +science, I found that most of the students did not notice that methods +of valid deductive argumentation were tools that they might apply to defend +their opinions. +Thus the idea of exploring the nature of the students' degrees of preparation +for understanding and creating proofs appeared. +First, interviews about proofs in general were conducted, with a broad interview +script. + +%The students almost all selected proofs by mathematical induction. + + +During analysis of these data, a more elaborate interview script was developed, +aiming at the ideas of domain, range, relation, mapping, function, the ideas of +variable, as in programs and mathematical formulations, and abstraction. +Some students emphasized that mathematical definitions are analogous to +definitions in natural languages, and that mathematical discourse is carried +out in the mathematical language created by these definitions. +The capabilities for expression and care bestowed by these definitions invest +mathematical reasoning with its persuasive power. +Thus both the reasoning processes, using concepts and the clearly defined +mathematical concepts together provide the ability of mathematical argumentation +to be convincing. Students who appreciated this found it invigorating. +Other students had different reactions to definitions. Thus, the role of definitions +and language became another area of exploration. +The difference between a domain and a single point in a domain can be seen as +a level of abstraction. If something is true for a single point in a domain, but is +also true for every single point in the domain, then the point can be seen as a +generic particular point, representative of the domain. This concept of ability +to represent is related to the idea of abstraction. +We saw data in this study that affirmed the observations of others, that students +do not always easily recognize the possibility of abstraction. + +\section{Parts of the Study} +The study was devoted to proofs, a subject that can be subdivided. +Part of the study was aimed at the idea of domain, directed at the concept that +though a variable could identify a scalar, it might also represent a set. +Part of the study was aimed at the activity of abstraction, because some students +exhibited the ability to operate at one level of abstraction, not necessarily a +concrete level, yet the ability to traverse between that level of abstraction and +a concrete level seemed to be absent. Other students claimed to be able to +understand concrete examples with ease, but to encounter difficulty when +short variable names were used within the same logical argument. + +%\subsection{Order of Exploration} +%The order of exploration was data driven, thus the material was sought sometimes +%in reverse order of the curriculum, almost as if seeking bedrock by starting +%at a surface, and working downwards. + diff --git a/ch3.tex b/ch3.tex new file mode 100644 index 0000000..95b8134 --- /dev/null +++ b/ch3.tex @@ -0,0 +1,212 @@ +\chapter{Research Perspective and Epistemological Framework} + +The work of others has contributed to the research perspective and the epistemological framework\footnote{In the psychological sense, rather than that of Brouwer}. + +Marton developed the phenomenographic research perspective, which is broadly applicable to education. + +Many researchers have contributed to the literature on educating students in the use of proof. + +Significant work has been done on teaching computer science students about mathematical proof. + + + + + + + +\section{Phenomenography and Variation Theory} + +%These (now combined) are important. + +%First there was phenomenography, which focused on the interface between the +%student and the material. + +%Then there was variation theory. +Svensson\cite{svensson1997theoretical} has written on the theoretical foundations of phenomenography. From Svensson we learn that +phenomenography is a research orientation. +This orientation has as its purpose, to describe conceptions. The context in which these conceptions are of interest is mainly, but not entirely, education. +This orientation is associated with an approach; this pair forms a research specialization. +Svensson also tells use that the name phenomenography was coined in 1981 by Ference Marton. +The approach in phenomenography is about the way of arriving at the descriptions of conceptions. + It is a kind of contextual analysis. +Phenomenographic descriptions are amenable to comparison. These descriptions make use of categories. An open, explorative form of data collection is used. During analysis, the data are interpreted. The nature of the conceptualizations which are collectively the object of the description is the meaning that something has to the individual, i.e., the individual's understanding. Thus it is empirical and subjective. Moreover, the conceptualizations are regarded as occurring in a social context, and are qualitative in nature. Phenomenography does not include a position on the nature of reality.\cite[p. 165]{svensson1997theoretical} Nevertheless, phenomenography is concerned with the relation between dependence of conceptions / knowledge upon external reality. Because our conceptions are about mathematical proof, we may evade the distinctions between ideal and real external world, as we are dealing with mental constructions. However, the social nature of creating convincing arguments ensures that these mental constructions must be shared. + +The approach will necessarily involve descriptions of meaning, and of similarities and differences in meaning. +By empirically determining similarities and differences of meaning, we might detect the absence of general agreement on meaning. +Categories of description are developed. These cluster more similar conceptualizations, so that distinctions among categories emerge. Because the category represents its members, abstraction occurs, reducing the number of individual ideas being considered, and summarizing the data. + +Dahlin\cite[p. 328]{dahlin2007enriching} recounts that variation theory was a development upon phenomenography that brought in dynamic elements to the description of conceptualizations. "The concepts of discernment, variation and simultaneity are the core of variation theory. In order for learning to take place, the learner has to discern a critical aspect or dimension of variation in the phenomenon; she has to see how this aspect can vary; and she has to become simultaneously aware of the possible 'values' along this dimension of variation in order to compare them." + +Variation is seen as occurring among conceptualizations, and as occurring during the learning. That is, the teacher may emphasize variation of an aspect of the material being taught, and may emphasize that values taken on along this dimension of variation are significant for the material being taught. This emphasis serves to help students discern not only the dimension of variation, but the factor that is changing; change of the factor calls attention to the factor. Were that factor constant, it might not be noticed. Variation among the categories of description extends the outcome space, such that more distinct conceptualizations are found.\cite[p. 124--125]{marton1997learning}. The outcome space is a complex of categories of description, capturing different ways of experiencing, comprising distinct groupings of aspects of the phenomenon and relationships among them. Often, but not always, in the form of set inclusion, these relationships can capture conceptualizations that are more includsive, or complex, or built including more layers of experience. + + +Variation theory\cite{marton2013meanings} suggests that critical aspects, which are particular ideas, are necessary\cite{marton2006some} for meaning making (understanding) to progress from one level of conceptualization to a more advanced level. + +The research approach associated with variation theory has the goal of identifying these specific ideas, which, on the basis of an identification of the conceptualizations present in a student population, empirically are seen to differentiate one level of conceptualization from another. + +Variation theory uses these so-called critical factors. They are emphasized in teaching, specifically by varying them, and considering the consequences. For example, we may highlight the significance of climate zones by considering the variation in annual rainfall from one zone to another. We may make salient the distinction between the ideas of language as contrasted with speech, the difference between speaking (in general), and speaking in a specific language (in particular) by acquainting children with the existence of a second language. (In the context of only one language, the distinction still exists, but might not be so readily described or learned.) + +Marton and Pang\cite{marton2006some} "identify some necessary conditions of learning. To learn +something, the learner must discern what is to be learned (the object of learning). Discerning +the object of learning amounts to discerning its critical aspects. To discern an +aspect, the learner must experience potential alternatives, that is, variation in a dimension +corresponding to that aspect, against the background of invariance in other aspects +of the same object of learning. (One could not discern the color of things, for instance, +if there was only one color.) The study results illustrate that what students learn in a sequence +of lessons is indeed a function of the pattern of variation and invariance constituted +in that sequence. All teachers make use of variation and invariance in their teaching, +but this study shows that teachers informed by a systematic framework do it more +systematically, with striking effects on their students' learning." + +\subsection{An example of applying variation theory} + +A commonly used example of a proof utilizing one application of modus ponens is: + +All men are motal.\\ +Socrates is a man.\\ +Socrates is mortal.\\ + +Variation theory tells us we must vary critical factors, for students to discern them. Some examples of variation are:\\ + +Some men are mortal.\\ +Socrates is a man.\\ +Socrates is mortal, maybe, but not necessarily. \\ + +The quantifier "All" matters. We don't get the desired result when we use some. When we have removed insignificant items from our proof, what's left matters. It's easy to find elements to vary that will affect the outcome. + +All men are mortal.\\ +John Doe is a man.\\ +Socrates is mortal.\\ + +What's different here is, we have lost the warrant for Socrates being mortal. Without that, we cannot know for sure that Socrates is mortal. + +All men are mortal.\\ +Socrates is a person.\\ +Socrates is mortal.\\ + +This time we've kept our attention on Socrates, but we have lost the warrant. To have a warrant, we must remain within the domain granted by the axiom. + +All men are mortal.\\ +Socrates is a man.\\ +Socrates is an orator.\\ + +The final statement, though true, is not justified by any warrant. + +All men are mortal.\\ +Socrates is a man.\\ +Socrates is mortal. + + +\subsection{Variation Theory and Conjunctions} + +Marton and Booth\cite{marton1997learning} have observed that increased differentiation, i.e., specialization, and also integration in the ways in which we experience the world are the results of learning. + +The mind quickly learns certain specializations. +We know this from single neuron experiments\cite{fried2014single}. +Consistent with this, from cognitive neuroscience we know that specializations that are conjunctions of positive literals of existing concepts are easy to learn and that conjunctions containing literals that are not existing concepts, but are negations of existing concepts may not be\cite{valiant2000circuits}. +By examining the conceptualizations present in the population of learners, we can hope to find clusters from which we can learn features whose values differentiate the clusters. It is these features, called in variation theory "critical factors", which instructors should emphasize, showing in their positive and negative form. Showing this variable in its positive and negative literals, and the effect of this variation on the conjunction being studied, is expected to be very helpful to the students\cite{marton1997learning}. + + + + +\section{Constructivism} + +%Describe what +Constructivism entails +the idea that students learn by +aggregating new information onto their present conceptions. + +\begin{quote} +Whilst part of what we perceive comes through our senses from the object before us, another part (and it may be the larger part) always comes out of our own head\\--William James +\end{quote}\cite{van2011slow} + +\subsection{Constructivism of Piaget} +Piaget, an eminent evolutionary biologist\cite{dixon200320}, intensively studied his children, making daily notes for over 3000 days, studying the development of their intelligence, the ability through which they adapted to their environment. Piaget focused on developmental breakthroughs demonstrated by his children.[p.28]. He saw their intellectual functioning as adaptation through natural selection, just as in other aspects of biology. Reflexes are identified as the starting point from which knowledge structures that underlie all thinking are built. Similar to an axiom in an axiomatized context, reflexes do not have to be proved/developed prior to use. Reflexes adapt to the environment. The infant learns to associate additional stimuli beyond those present at birth, to retrieve and enact the behavior of feeding. They learn to distinguish which person holds them in a way that, with one person but not the other, corresponds to feeding. + +It is the nature of adaptation that implies constructivism. Dixon\cite[p. 30]{dixon200320} reminds us of Piaget's view, that an organism begins with what is present in its brain, and adapts that as a foundation upon which can be built a collection of knowledge. + +Dixon\cite[p. 30]{dixon200320} calls our attention to Piaget's observation that "they would exercise their schemas apparently just for the enjoyment of the exercise." Enjoyment, in light of more recent knowledge of the role of dopamine in reinforcing memory, is a key observation. + +Dixon\cite[p. 31]{dixon200320} reports Piaget's surmise that "the \ldots is not longer a reflexive island, passively responding to environmental stimulation, but is being coordinated with other activities \ldots there was a certain amount of circularity involved". Those of an engineering bent of mind may observe that positive feedback in a loop in which pleasure reinforces memory will encourage the construction, by adaptation, of preferred behaviors. + +Dixon\cite[p. 31]{dixon200320} describes Piaget's categorization of adaptation of reflexes involving only the child, vs. incorporating external objects. The orienting reflex forms the basis from which the child adapts to choosing to pay attention. Children would try to re-create an interesting visual event. Piaget mentions the joy associated with this secondary circular reaction. This adaptation occurs with auditory as well as visual input. Dixon\cite[p. 32]{dixon200320} reports "Lucienne at once moves her whole body, and especially her feet, to make the noise last. She has a demented expression of mingled fear and pleasure, but she continues." + +In light of today's understanding of the role of cholinergic as well as dopaminergic involvement in memory and attention\cite{}, the observations of mingled fear and pleasure seem prescient. + +Subsequently, Dixon\cite[p. 32]{dixon200320} reports "babies start showing that they can do things on purpose \ldots we start seeing the integration of some schemas into the service of other schemas". Piaget arranged experiments whereby babies exhibited means-ends action. Dixon\cite[p. 32]{dixon200320} reports "What Piaget is describing here is that Jacqueline can use one schema, \ldots to help her enact another schema \ldots. This is intellectual adaptation of the best kind -- getting what you want!" The emphasis on reward might be due to Dixon, or to Piaget, but the idea of reward is present in both. Constructions, at least some of the time, are associated with reward, in a feedback loop. Moreover, we can see utility in having rewarding combinations be remembered. We can also see the utility of frightening combinations being remembered. + +According to Dixon\cite[p. 34]{dixon200320} Piaget believed that babies explore, learning the expand the domain over which their schemas have been seen to operate. In the next, i.e. sixth, substage children exhibit use of their schemas through imagination. The example given, in which Lucienne wishes to open a box, can be seen as evidence of making an analogy. Dixon\cite[p. 34]{dixon200320} reports "She looks at the slit with great attention: then several times in succession, she opens and shuts her mouth, at first slightly, then wider and wider: Apparently Lucienne understands the existence of a cavity subjacent to the slit and wishes to enlarge the cavity." Dixon\cite[p. 35]{dixon200320} describes "represented the problem in a different way -- using her imagination. Once she removed the problems from its physical form and represented it mentally, she was able to invent a solution that wasn't previously possible. She pretended her mouth was the slit of the matchbox. By bringing this mental image into play, Lucienne was able to manipulate the image in a new way. Specifically, she was able to pretend she was opening and closing the matchbox by opening and closing her mouth. And once she was able to do this, she made the connection that to get the chain out of the matchbox all she had to do was open the matchbox wider than it already was". + + The use of analogy implies the existence of a process that develops, stores and retrieves analogies. One may wonder how analogies are retrieved. + +%Piaget, Vygotsky and Bruner worked with the idea that students learn by +%aggregating new information onto their present conceptions. + +%didactical obstacle see McGowan Tall 2010 Jour Math Behav +McGowen and Tall\cite{mcgowen2010metaphor} suggest that "it is even more important to take into account the particular mental structures available to the individual that have been built from experience that the individual has 'met-before'." They say [p. 170] "New experiences that build on prior experiences are much better remembered and what does not fit into prior experience is either not learned or learned temporarily and easily forgotten." + +Is the easier remembering related to analogy making? Exactly like what we learned before, in analogy to what we learned before vs. disruptive of what we learned before + +%McGowen and Tall\cite{mcgowen2013flexible}, citing +Thompson \cite{thompson1994students} states ``\ldots an instructor who fails to understand how his/her students are thinking about a situation will probably speak past their difficulties. Any symbolic talk that assumes students have an image like that of the instructor will not communicate. Students need a different kind of remediation, a remediation that orients them to construct the situation in a mathematically more appropriate way % Thompson 1994 p. 32. +%Thompson P N 1994 Students, functions and the undergraduate curricular in Dubinsky, Schoenfeld and Kaput Research in collegiate mathematics education I, CBMS issue in math education vol 4 pp 21-44. + +\subsection{Social Constructivism} +%Need to define social constructivism +Lev Vygotsky founded the idea of social constructivism, which can be summarized as learning is facilitated by interactions in a group. + +According to Cole and Scribner\cite[p. 1]{vygotsky1978mind}, Vygotsky "and his colleagues sought to develop a Marxist theory of human intellectual functioning". They say[p. 5--6] that "What Vygotsky sought was a comprehensive approach that would make possible description \textit{and} explanation of higher psychological functions in terms acceptable to natural science. To Vygotsky, explanation meant a great deal. It included identification of the brain mechanisms underlying a particular function; it included a detailed explication of their developmental history to establish the relation between simple and complex forms of what appeared to be the same behavior; and, importantly, it included specification of the societal context in which the behavior developed." + +According to Cole and Scribner\cite[p. 6]{vygotsky1978mind}, "In stressing the social origins of language and thinking, Vygotsky was following the lead of influential French sociologists, but to our knowledge he was the first modern psychologist to suggest the mechanisms by which culture becomes a part of each person's nature. Insisting that psychological functions are a product of the brain's activity, he became an early advocate of combining experimental cognitive psychology with neurology and physiology. Finally, by claiming that all of these should be understood in terms of a Marxist theory of the history of human society, he laid the foundation for a unified behavioral science." + +According to Cole and Scribner\cite[p. 7]{vygotsky1978mind}, " Vygotsky believed that the internalization of culturally produced sign systems brings about behavioral transformations and forms the bridge between early and later forms of individual development. Thus for Vygotsky, in the tradition of Marx and Engels, the mechanism of individual developmental change is rooted in society and culture." + +According to Cole and Scribner\cite[p. 22]{vygotsky1978mind}, Vygotsky, in Tool and in Child Development, took note of the work of Shapiro and Gerke. "In their view, social experience exerts its effect through imitation; when the child imitates the way adults use tools and objects, she masters the very principle involved in a particular activity. They suggest that repeated actions pile up, one upon another, as in a multi-exposure photograph; the common traits becomes clear and the differences become blurred. \ldots they do not take into account the changes occurring in the internal structure of the child's intellectual operations. " + +According to Cole and Scribner\cite[p. 24]{vygotsky1978mind},Vygotsky wrote that "Although practical intelligence and sign use can operate independently of each other in young children, the dialectical unity of these systems in the human adult is the very essence of complex human behavior. Our analysis accords symbolic activity a specific \textit{organizing} function that penetrates the process of tool use and produces fundamentally new forms of behavior." + +According to Cole and Scribner\cite[p. 25--26]{vygotsky1978mind},Vygotsky wrote that "A child's speech is as important as the role of action in attaining the goal. Children not only speak about what they are doing; their speech and action are part of \textit{one and the same complex psychological function}, directed toward the solution of the problem at hand. \ldots Using words \ldots the child achieves a much broader range of activity \ldots planning future action." + +According to Cole and Scribner\cite[p. 36--37]{vygotsky1978mind}, Vygotsky believed that "The possibility of combining elements of the past and presetn visual fields (for instance, tool and goal) in one field of attention leads in turn to a basic reconstruction of another vital function, \textit{memory}. Through verbal formulations of past situations and activities, the child frees himself from the limitations of direct recall; he succeeds in synthesizing the past and present to suit his purposes. The changes that occur in memory are similar to those that occur in the child's perceptual field \ldots The child's memory not only makes fragment of the past more available, but also results in a \textit{new method of uniting the elements of past experience with the present}. Created with the help of speech, the time field for action extends both forward and backward. \ldots This emerging psychological system in the child now encompasses two new functions: \textit{intentions and symbolic representation of purposeful action}". + +According to Cole and Scribner\cite[p. 37]{vygotsky1978mind}, Vygotsky noted that "Lewin\cite{lewin1938will} \textbf{right person wrong book} gives a clear-cut definition of voluntary activity as a product of the historical-cultural development of behavior". + +Vygotsky believed that speech reorganized perception, and created new relations among psychological functions.\cite[p. 38]{vygotsky1978mind}. He believed that people, though capable of memory unrelated to words, \textit{eidetic} memory, proceeded to a new memory utilizing signs, and that "these sign operations are the product of specific conditions of \textit{social} development".\cite[p. 39]{vygotsky1978mind} + +Vygotsky\cite[p. 49]{vygotsky1978mind} wrote with a change indeveloopmental level there occurs a change not so much in the structre of a single function (whic, for example we may call memory) as in the character of those functions with the aid of which remembering takes place; what changes is the \textit{interfunctional} relations that connect memory with other functions. + +An example of how the meaning of signs evolves in a social context is given by Vygotsky\cite[p. 56]{vygotsky1978mind}: A child reaches for an object, and the gesture is only a reach, but a person responds to the reach with assistance in obtaining the desired object, and the reach acquires the meaning of pointing. +In this way, the meaning is socially constructed. + + + +\section{Perspective and Epistemology from Mathematics Education} +Part of the research perspective is formed by the goals for what students learning proof should know: according to Ball et al.\cite[p, 32 -- 34]{loewenberg2003mathematical} "These activities -- mathematical representation, attentive use of mathematical language and definitions, articulated and reasoned claims, rationally negotiated disagreement, generalizing ideas, and recognizing patterns -- are examples of what we mean by \textit{mathematical practices}. \dots These practices and others are essential for anyone learning and doing mathematics proficiently. \ldots investing in understanding these 'process' dimensions of mathematics could have a high payoff for improving the ability of the nations' schools to help all students develop mathematical proficiency". +Ball goes on to say\cite[p. 37]{loewenberg2003mathematical} "Another critical practice -- the fluent use of symbolic notations -- is included in the domain of representational practice. Mathematics employs a unique and highly developer symbolic language upon which many forms of mathematical work and thinking depend. Symbolic notation allows for precision in expression. It is also efficient -- it compresses complex ideas into a form that makes them easier to comprehend and manipulate. Mathematics learning and use is critically dependent upon one's being able to fluently and flexibly encode ideas and relationships. Equally important is the ability to accurately decode what others have written." + +Even more tightly focused on proofs, Ball continues \cite[p. 37--38]{loewenberg2003mathematical} "A second core mathematical practice for which we recommend research and development is the work of justifying claims, solutions, and methods. \textit{Justification} centers on how mathematical knowledge is certified and established as 'knowledge'. Understanding a mathematical idea means both knowing it and also knowing why it is true. For example, knowing that rolling a 7 with two dice is more likely than rolling a 12 is different from being able to explain why this is so. Although 'understanding' is part of contemporary education reform rhetoric, the reasoning of justification, upon which understanding critically depends, is largely missing in much mathematics teaching and learning. Many students, even those at university level, lack not only the capacity to construct proofs -- the mathematician's form of justification -- but even lack an appreciation of what a mathematical proof is." +\subsection{Phenomenology Applied to Mathematical Proofs} + +We wish to point out a distinction between +phenomenography and phenomenology. +Phenomenology might be more familiar: it has been used by mathematician +Gian-Carlo Rota to describe the beauty in mathematics, particularly in proofs. +Rota\cite{rota1997phenomenology} points out that proofs that are perceived by mathematicians as beautiful are easier to remember. +\subsection{Phenomenology Applied to Problem Solving} +Phenomenology has also been invoked by mathematician Alan Schoenfeld in modeling teaching behavior. +His lesson segments are chosen for phenomenological integrity.\cite[p. 91]{kaput1998research}. +He states \cite[p. 91]{kaput1998research} ``develop knowledge and skills, pursue connection, extensions, generalizations to know how to make good conjectures and know how to prove them, have a sense of what it means to understand mathematics and good judgment about when they do. Have the tools that will enable them to do so. That means having a rich knowledge base, a wide range of problem solving strategies and good meta-cognitive behavior'' +He had, earlier on the same page, described meta-cognitive behavior as reflecting and acting on what you know. + +\section{Cognitive Science} +Cognitive science includes modeling plausible functioning of the brain. It helps us notice constraints that computational complexity illuminates, on how learning, including memory and retrieval of information, might be carried out. + +\section{Neuroscience / Neurophysiology} + +Though Marton and Booth\cite[p. 114]{marton1997learning} state that description of experience is autonomous from the student's nervous system, nevertheless we believe that supportive evidence from natural science can be of interest. + +In education with assessment, instructors transmit information towards the student and attempt to elicit signs of learning from the student. +Neuroscience enables us to investigate stages of progress in learning that may occur starting from the moments at or just after the transmission through the event of assessment. +For example, single neuron measurements show that conjuncts of variables having positive literals, as described by Valiant\cite{valiant2000circuits} in cognitive science, are learned in one showing, into medial temporal lobe tissue. +Functional magnetic resonance imaging (fMRI) combined with electro-encephalography (EEG) show that slow wave sleep is a process that supports memory formation in other locations in the brain. +Moreover, these technologies show us that exposing students to educational stimuli of multiple modalities rather than single modalities (e.g., sight and sound vs. only sight) changes the area within the brain in which the information is stored. These show us that transmitting with multiple modalities increases the ease of recall of information. These show us that if we wish information to be subject to recall when relevant, rather than what Whitehead\cite{whitehead1959aims} calls inert knowledge, we should concern ourselves about how the information is transmitted. These provide guidance about how we can plan for better assessment results by facilitating recall, in turn by shaping our transmission strategies. diff --git a/ch4.tex b/ch4.tex new file mode 100644 index 0000000..22cb8b2 --- /dev/null +++ b/ch4.tex @@ -0,0 +1,186 @@ +\chapter{Methodology} +Knowledge about how students conceptualize has a qualitative nature. For +qualitative research, methodology varies, but has standard parts: design of the +study, sources and their selection, data, the process of analysis, the interpretation, +and the approach to validation. Sample selection is recorded and reported +so that others may judge transferability to their own context. Interviews are +the principle technique used by phenomenographical research. Documents +can also be used. Normal conduct of teaching can also provide data that can +be used, if in an anonymous, aggregate form. Both deductive and inductive +analysis provide qualitative data. +\section{Design of the Studies} +We +conducted over 30 interviews. +Our interview participants included undergraduate and graduate students of (\textbf{how do we want to say this}). Most of the graduate student interviews were among teaching assistants in courses that taught and/or used proofs. We also included faculty of courses that involved proofs. + +Information learned in tutoring and lecturing inspired the research questions. +We used exams to study errors in application of the pumping lemma for regular +languages. We used early interviews to explore proof, adapting to the +student preference for proof by mathematical induction and incorporating the use of recursive +algorithms. We used homework +to observe student attempts at proofs. +We used later interviews to investigate the remaining questions mentioned earlier. +\textbf{Need to make this true: We used homework to observe student familiarity/facility +with different (specific) proof techniques: induction, construction, contradiction, +and what students think it takes to make an argument valid.} + + +\section{Sample Selection} + +\textbf{Need even more detail than what's here. It could alternatively be put in subsections.} +Students from the University of Connecticut who have taken or are taking the +relevant courses were offered the opportunity to be interviewed. The students +who volunteered were mostly male, mostly traditionally aged undergraduates, +though some graduate students also volunteered. Some students were +domestic, and some international. Some students were African-American, +some Asian, some Caucasian, some Latino/a, some with learning disabilities +such as being diagnosed as on the autistic spectrum. +\subsection{Proofs Using the Pumping Lemma for Regular Languages} +In a recent course offering to forty-two students, of whom thirty-four were men and eight women, +forty-one traditional aged, +%one former Marine somewhat older, one collegiate athlete (a +%woman), + there were three students having Latin-heritage surnames, 1/4 of the +students had Asian heritage, 2 had African heritage, and 8 were international +students. Each student individually took the final exam. A choice among +five questions was part of the final exam; one required applying the pumping +lemma. Half the students (21/42) selected this problem. These were 17 men +and 4 women. Three quarters of those (15/42) selecting the pumping lemma +got it wrong. These students, who chose the pumping lemma problem and +subsequently erred on it, form the population of our study. +\subsection{Proofs by Mathematic Induction} +We studied students who were taking, or who had recently taken, a course +on Discrete Systems required of all computer science, and computer science and +engineering students. +Volunteers were solicited from all students attending the Discrete Systems +courses. +Interviews of eleven students were transcribed for this study. Participants +included 2 women and 9 men. Two were international students, a third was a +recent immigrant. + +\subsection{Domain, Range, Mapping, Relation, Function, Equivalence in Proofs} +Students taking, or having taken, discrete systems, especially students who +had sought help while taking introductory object oriented programming volunteered +to be interviewed. + +\section{Data Collection} +Our corpus included interview transcripts, homework, practice and real tests, +observations from individual tutoring sessions, and group help sessions. Interview +transcripts were analyzed with thematic analysis. Homework, practice +and real tests were analyzed for proof attempts. Data from individual tutoring +sessions and group help sessions was also informative. Aggregate, anonymous +data was used. + +\subsection{Interviews} +\subsection{Documents} +\subsubsection{Proofs Using the Pumping Lemma for Regular Languages} +The study was carried out on the exam documents. The interpretation was informed +by remembering events that occurred in the natural conduct of lectures, +help sessions and tutoring. +One method of assessing whether students understood the ease of application +of the pumping lemma to a language to be proved not regular was offering a +choice between using the Myhill-Nerode theorem with a strong hint or using +the pumping lemma. The pumping lemma problem, which could very easily +have been solved by application of the Myhill-Nerode theorem, especially with +the supplied hint, was designed, when tackled with the pumping lemma, to +require, for each possible segmentation, a different value of $i$ (the number of +repetitions) that would create a string outside of the language. The intent was +to separate students who understood the meaning of the equation's symbols, +and the equation itself, from those students engaged in a manipulation with at +most superficial understanding. +\subsubsection{Proofs by Mathematic Induction} +Interviews were solicited in class by general announcement, and by email. +Interviews were conducted in person, using a voice recorder. No further +interview script, beyond these following few questions, was used. The interviews +began with a general invitation to discuss students' experience with and +thoughts on proofs from any time, such as high school, generally starting with + +\begin{itemize} +\item ``Tell me anything that comes to your mind on the subject of using proofs, +creating proofs, things like that.'' +\end{itemize} +and then following up with appropriate questions to get the students to elaborate +on their answers. +Additional questions from the script that were used when appropriate included +\begin{itemize} +\item ``Why do you think proofs are included in the computer science curriculum?'', +\item ``Do you like creating proofs?'' +\end{itemize} +and, after proof by induction was discussed, +\begin{itemize} +\item “Do you see any relation between proof by induction and recursive algorithms?”. +\end{itemize} + +Almost every student introduced and described proof by mathematic induction as experienced +in their current or recent class. +\section{Expanded semi-structured interview protocol for domain, range, language, equivalence class in Proofs} +\section{Expanded semi-structured interview protocol for definitions, language, reasoning in Proofs} +\section{Data Analysis} + +Describing how analysis was done in detail is really important. +How do you do phenomenography? + +Is this the way everything was analyzed? + +Marton and Booth\cite[p. 133]{marton1997learning} describe a desirable analysis technique: + +Apply the principle of focusing on one aspect of the object and seeking its dimension of variation while holding other aspects frozen. %partial derivative +Remember to apply both perspectives, that pertaining to the individual and that pertaining to the collective. +Establish a perspective with boundaries, within which looking for variation. +\begin{enumerate} +\item seartch for extracts from data, that might pertain to perspective +\item inspect them in context of own interview +\item inspect them in context of other extracts all interviews on the same theme +\end{enumerate} + +\begin{enumerate} +\item select one aspect of the phenomenon and inspect across all subjects +\item select another aspect +\item whole interview -- to see where these two aspects lie relative to other aspects, and to background +\end{enumerate} + +\begin{enumerate} +\item all of research problems, one problem at a time, whole transcripts that have particularly interesting ways of handling problem +\end{enumerate} + +Keep going, clarity will emerge. + +Result: identify a number of qualitatively different ways in which phenomenon has been experienced (not forgetting different methods of expression)\cite[p. 133]{marton1997learning}. +Overlap of the material at the collective level is expected. + +assume that what people say is logical from their point of view\cite[p. 134]{marton1997learning}, citing Smedlund\cite{smedslund1970circular} + + + + +Data were analyzed using a modified version of thematic analysis, which is +in turn a form of basic inductive analysis.\cite{Merriam2002,Merriam2009,braun2006using,fereday2008demonstrating,boyatzis1998transforming} Using thematic analysis, we +read texts, including transcripts, looked for “units of meaning”, and extracted +these phrases. Deductive categorization began with defined categories, and +sorted data into them. Inductive categorization “learned” the categories, in +the sense of machine learning, which is to say, the categories were determined +from the data, as features and relationships found among the data suggested +more and less closely related elements of the data. A check on the development +of categories compared the categories with the collection of units of meaning. +Each category was named by either an actual unit of meaning (obtained during +open coding) or a synonym (developed to capture the essence of the category). +A memo was written to capture the summary meaning of the category. +Next a process called axial coding, found in the literature on grounded theory, +\cite{strauss1990basics,kendall1999axial,glaser2008conceptualization} was applied. This process considered each category in turn as a central +hub; attention focused on pairwise relations between that central category +with each of the others. The strength and character of the posited relationship +between each pair of categories was assessed. On the basis of the relationships +characterized in this exercise, the categories with the strongest interesting relationships +were promoted to main themes. A diagram showing the main +themes and their relationships, qualified by the other, subsidiary themes and +the relationships between the subsidiary and main themes was prepared to +present the findings. Using the process of constant comparison, the structure +of these relationships was reviewed in the light of the meanings of the categories. +A memo was written about each relationship in the diagram, referring +to the meaning of the categories and declaring the meaning of the relationship. +A narrative was written to capture the content of the diagram. Using the +process of constant comparison, the narrative was reviewed to see whether it +captured the sense of the diagram. Units of meaning were compared with the +narrative and their original context, to see whether the narrative seemed to +capture the meaning. The products of the analysis were the narrative and the +diagram. diff --git a/ch5.tex b/ch5.tex new file mode 100644 index 0000000..65d16a3 --- /dev/null +++ b/ch5.tex @@ -0,0 +1,52 @@ +\chapter{Data} + +\section{Interview} +Some students remembered taking proofs in high school in geometry. +Some students were taking proofs contemporaneously in philosophy. +Some of the students studying proof in philosophy found them disturbing, expressing a preference for geometrical proofs. +Some students remembered having to furnish proofs of geometrical facts, also facts about prime numbers and sets. +Some students knew that CSE2500 treated proofs because they would be used in later courses. Students did not know why proofs would be used later, and were generally happy to hear some example uses. +Though students were asked whether they made use of proofs spontaneously, none of those interviewed gave an example. +Some students preferred to articulate with code, and some (who were dual computer science / math) sometimes preferred mathematical symbols, depending upon the context. +Some students do wish to convince themselves of things, such as tractable execution times, and correctness. Though students were asked whether they made use of proofs for this purpose, none of those interviewed claimed to do so, rather they mentioned going carefully over their algorithm construction, and considering cases. + +In interviews, the students almost all chose to discuss proofs by mathematical induction. + +\subsection{What do students think a proof is?} +One participant opined "Some students think proof is a magical incantation." + +Some students do not recognize a proof when they are looking at one. When asked "Were we doing proofs today?", such a student said "No." When asked, "Did we not show that certain things must always be the case when certain contextual requirements were met?", the answer was "Yes, oh, I guess that's a proof." When asked, "Why didn't it appear to be a proof?", the answer was "It didn't start by saying 'Proof:', and it didn't end by saying 'QED', or that box." + +Some students say that a proof is a sequence of statements, starting with one distinguished statement, called a premise and ending with a distinguished statement, what we wanted to prove. + +Some students say "What's a lemma?". Some students cannot, when asked for credit, identify the use of structure, such as a lemma, in a proof. + +Some students know that proof ought to be a convincing argument. Some of these are not convinced by a proof by induction. When assured that they would enjoy a certain proof in introduction to the theory of computation, because it was a proof by induction, voices in a class claimed, "We never 'got' that". + + +\subsection{How do students approach understanding a proof?} + +Some students + +\subsection{How do students approach understanding a proof?} +\subsection{What do students use proof for, when not assigned?} +\subsection{Do students exhibit any consequence of inability in proof?} +\subsection{What kind of structure do students notice in proofs?} +\subsection{What do students think it takes to make an argument valid?} + +\section{Homework} +Table : Some example errors +Let x be empty +$|xy| \leq p, so xy = 0^p$\\ +$|xy| \leq p; let \; x = 0^{p+r}, y = 0^{p+r}, 0 < r < p$\\ +Let’s choose $|xy| = p$\\ +$0^{p+1}0^b1^p \neq 0^{p+1}1^p \therefore xy^2z \not\in \mathcal{L}$ +where $\mathcal{L} = \{0^i1^j, i \neq j\}$\\ +we choose $s = 0^{p+1}1^p$ within $|xy|$\\ +thus $\neq 0^p1^{p+1}$\\ +Let $x = 0^a, y = 0^b1^a$\\ +$x = 0^{p-h}, y = 0^h$\\ +$x = 0^i, y = 0^i, z = 0^i1^j$ + + + diff --git a/ch6.tex b/ch6.tex new file mode 100644 index 0000000..398b86f --- /dev/null +++ b/ch6.tex @@ -0,0 +1,420 @@ +\chapter{Data Analysis and Interpretation} + +The product of analysis in a phenomenographic study, is a set of categories, and relationships \textit{among} them. + +Marton and Booth\cite[p. 135]{marton1997learning} state "in the late stages of analysis, our researcher [has] a sharply structured object of research, with clearly related faces, rich in meaning. She is able to bring into focus now one aspect, now another; she is able to see how they fit together like pieces of a multidimensional jigsaw puzzle; she is able to turn it around and see it against the background of the different situations that it now transcends." + +Using Marton's overriding categorization of task and objective, we can consider that some students do not know, at least when they are studying CSE2500, that they need to be able to understand some proofs, to be good developers. Therefore, they can logically approach the study of proof in CSE2500 as a task, having some facts that they must memorize. Other students, including those with dual majors in math, wish to improve themselves by improving their ability to couch arguments in mathematical terms and both ascertain facts for themselves and convince others. Students who are aware that there are computer-science related purposes for proof, for example, in the study of algorithms they will be using proofs to understand resource consumption, will recognize the study as having the objective to improve themselves vis-a-vis dealing with proof. + + +Because the relationships are expected to form a partial order, corresponding to set inclusion of subsets of the complete (with respect to the objective of teaching) understanding of the information being taught, we can say relationships \textit{between} categories. + +The set inclusion relationship can be that a deeper understanding includes a more superficial understanding. +It may also be that a deeper understanding qualifies a more superficial understanding, such as being applicable in a restricted domain. Thus, understanding of a liquid as being divisible to any degree can be qualified as to scale such as macroscopic, microscopic and so on. + +In a phenomenographic study, this partial order is referred to as a hierarchical order. + +The objective of teaching, as will be in some parts of this study, the components of proof, may have many parts, called, in phenomenology, internal structure. The granularity of the subdivision of the objective of teaching results in the number of parts in the internal structure. If we let $n$ denote the number of parts obtained with a specific granularity, we see that the number of subsets will be $2^n$, which will be inconveniently large unless the granularity is sufficiently coarse. Thus, we choose a granularity resulting in approximately 4 elements of internal structure. + +Thus, when the teaching objective is, what is a proof, we may limit the granularity, such that the internal structure of a proof is, for example, +\begin{enumerate} +\item that particular statement which is to be proved +\item axioms, premises, suppositions, cases +\item other statements +\item warrants (rules of inference) +\end{enumerate} + +We might choose to pursue finer granularity in some cases, for example, we might pursue "What is a statement?", because instructors have found that not all students arriving in CSE3502 have the same depth of understanding of statement, and some do not have sufficiently deep understanding of "statement" to be able to comprehend a proof. + + +Marton and Booth\cite[p. 22]{marton1997learning} call our attention to learners directing their attention to the sign vs. to the signified. With proofs, Polya \cite{} has mentioned a procedural approach to executing a proof, without understanding, as have Harel and Sowder \cite{harel1998students}, and Tall\cite{tall2001symbols}. Weber and Alcock\cite{weber2004semantic} have observed and described students omitting understanding of warrants in proofs. In each of these cases, the sign is provided, but the signified is at best incompletely understood. + +Analysis can usefully illuminate learning processes, taking note of the temporal domain\cite{marton1997learning}. This has been used by Booth in her analysis of how students understand the process of programming\cite{marton1997learning}. + +[p. 136]\cite{marton1997learning} important to be looking whether conceptualizations appear in a certain case, in a certain period of time (such as, when see proofs again in 3500, 3502, are they recognized as proofs, some no some yes, are they helpful as proofs, or troublesome, some helpful, some not, "never did get that") + +\section{Analysis of Interviews} + +Data were analyzed using a modified version of thematic analysis, which is +in turn a form of basic inductive analysis.\cite{Merriam2002,Merriam2009,braun2006using,fereday2008demonstrating,boyatzis1998transforming} Using thematic analysis, we +read texts, including transcripts, looked for “units of meaning”, and extracted +these phrases. Deductive categorization began with defined categories, and +sorted data into them. Inductive categorization “learned” the categories, in +the sense of machine learning, which is to say, the categories were determined +from the data, as features and relationships found among the data suggested +more and less closely related elements of the data. A check on the development +of categories compared the categories with the collection of units of meaning. +Each category was named by either an actual unit of meaning (obtained during +open coding) or a synonym (developed to capture the essence of the category). +A memo was written to capture the summary meaning of the category. +Next a process called axial coding, found in the literature on grounded theory, +\cite{strauss1990basics,kendall1999axial,glaser2008conceptualization} was applied. This process considered each category in turn as a central +hub; attention focused on pairwise relations between that central category +with each of the others. The strength and character of the posited relationship +between each pair of categories was assessed. On the basis of the relationships +characterized in this exercise, the categories with the strongest interesting relationships +were promoted to main themes. A diagram showing the main +themes and their relationships, qualified by the other, subsidiary themes and +the relationships between the subsidiary and main themes was prepared to +present the findings. Using the process of constant comparison, the structure +of these relationships was reviewed in the light of the meanings of the categories. +A memo was written about each relationship in the diagram, referring +to the meaning of the categories and declaring the meaning of the relationship. +A narrative was written to capture the content of the diagram. Using the +process of constant comparison, the narrative was reviewed to see whether it +captured the sense of the diagram. Units of meaning were compared with the +narrative and their original context, to see whether the narrative seemed to +capture the meaning. The products of the analysis were the narrative and the +diagram. + + +\subsection{Themes / Categories} +\begin{itemize} +\item Definitions\\ +Students divided into (1)those who found definitions boring, difficult to pay attention to, and undesirable compared to examples, from which they preferred to induce their own definitions, and (2) those who had caught on to the idea that definitions were the carefully crafted building blocks of reasoning. +\item Procedures +Students sometimes learned what was desired in a proof, but learned to produce it by procedure, and were not themselves convinced. +\item Context +Students asked whether the topics for examples and exercises, such as prime numbers, had relevance to programming, with which they had experience, but not unrelated to the topics. +Students did not know the context in which the proofs, or procedure version of proof, was applicable, so, for example, did not apply proof by mathematic induction to recursive algorithms, and did not know how to tell whether recursive algorithms would be applicable. +\item Concrete vs. Abstract +Some students felt quite comfortable with the application of rules of inference to concrete items, but had difficulty transferring application of those rules to mathematical symbols. +\item Symbolization +consistent with Harel and Sowder's 1998 categorization of concepts, we found students who would attempt to write in symbols, but not understand what was denoted, and consequently were uncertain about appropriate operations. Some of these students were glad to see a progression from pseudocode with long variable names to pseudocode with short variable names to mathematical symbolization (formula translation (FORTRAN) in reverse). +\item Applicability of single examples +Some students believed that a few examples constituted a proof. These examples were not generic particular, nor were they transformational, in the sense of Harel and Sowder's 1998 model. +\item Substructure +Students familiar with methods, in the sense of object-oriented programming, and with construction of programs involving multiple method calls, did not always recognize that proofs could be built from multiple lemmas, although they did understand that axioms could be applied. +\item Proofs are used, in computer science, to show resource consumption (complexity class), properties of models of computation, and computability/decidability. No occasion was identified, other than assignment, when students recognized they were undertaking proofs. + +\end{itemize} +\subsection{Relationships} + +\section{Analysis of Homework and Tests} +\subsection{Proofs} +Proofs submitted on homework and tests were analyzed in several respects. +The overall approach should be valid. For example, students who undertook to prove that the converse was true did not use a valid approach. +The individual statements should each be warranted. +Use of structure, such as lemmas, and care that cases form a partition of the relevant set are gladly noticed. +Proof attempts that lose track of the goal, and proof attempts that assert with insufficient justification, the goal are noted. +\subsection{Pumping Lemmas} +We wrote descriptions for each error. Some example descriptions +are in Table II. +A handful of students did exhibit their reasoning that for +all segmentations there would exist at least one value of 𝑖 that +would generate a string outside the language. +We categorized the errors as misunderstandings of one or +more of: +1) ∣𝑥𝑦∣ ≤ 𝑝 permits ∣𝑥𝑦∣ < 𝑝\\ +2) 𝑥 is the part of the string prior to the cycle\\ +3) 𝑦 is the part of the string which returns the state of +the automaton to a previously visited state\\ +4) 𝑧 is the part of the string after the (last) cycle up to +acceptance\\ +5) 𝑝 − 1 characters is the maximum size of a string +that need not contain a cycle, (strings of length 𝑝 +or greater must reuse a state)\\ +6) 𝑖 is the number of executions of 𝑦\\ +7) There must be no segmentation for which pumping +is possible, if pumping cannot occur.\\ +8) A language is a set of strings.\\ +9) A language class is a set of languages.\\ +Categories are shown in the chapter on results (labelled table iii).\\ + + + + +\section{Help Session and Tutoring} +some students, who do know that any statement must and can, be +either true or false, thought implications must be true. + + + + + +\section{Analysis} +\section{Interpretation} +Here I want to put the ideas about definitions and abstraction. Without abstraction +definitions are more cumbersome to remember and operate with. This +discourages use of the axiomatic proof conceptions, because they are based on +definitions. +What about Valiant? His establishing of definitions in circuits in the mind by +conjunctions, and by disjunctions, of ideas. Without abstraction for definitions, +this is more cumbersome. + +Is intuition helping or opposing our educational objectives? Can we get help from it? + +\subsection{Productive and Counterproductive Beliefs} +What do they ``know'', and what do they ``know that isn't so''. +Some will be conscious, some will be unconscious. +\subsection{Productive and Counterproductive Momentum} +What are they trying to learn? Is it aligned with the departmental curriculum? the course goals? +\section{Published papers} +Three papers in this area were published: +\begin{itemize} + +\item CCSCNE: Categorizing the School Experience of Entering Computing +Students \cite{smith2013categorizing} +\item FIE: Mathematization in Teaching Pumping Lemmas \cite{smith2013mathematization} +\item Koli Calling: Computer Science Students’ Concepts of Proof by Induction\cite{smith2014computer} + +\end{itemize} +\subsection{Categories of Experience of Entering Students} +Undergraduate students beginning study of the computing disciplines present +various degrees of preparedness\cite{smith2013categorizing}. Some had no experience, some had had +informal experience, and some had had formal classes. The formal classes +extended from using applications to building applications. Informal experience +ranged from editing configuration files, such as background colors, to full time +jobs extended over multiple summers. +After publishing this paper, we encountered more related information. For +example, consistent with the work of Almstrum\cite{almstrum1996investigating}, we found that, about implications, +some students, who do know that any statement must and can, be +either true or false, thought implications must be true. Some interview participants +enjoyed a modified Moore method\cite{cohen1982modified} geometry class in middle school, +and relished opportunities to create proofs (not yet published). Other students +were not so well prepared. + + + + +\subsection{Representation/Symbolization in Pumping Lemmas} +We found that some students may lack facility in notation. For example, in the +application of the pumping lemma, students are expected to understand the +role of $i$, in the context that a string $s$, having component substrings $x$, $y$ and $z$, +can be used to generate other strings, of the form $xy^iz$, where $i$ gives the number +of copies of the substring $y$. Moreover, students are expected to understand that +the subdivision of a string of length $p$, $\sigma_1^a\sigma_2^{p-a}$, where $a \in \{0,1,\ldots,p\}$ +uses $a$ as a parameter, a free variable, not one necessarily bound to a single instance +of a natural number, but a representation of a domain. An excerpt of the errors found on tests is shown in Table . Trigueros et +al. \cite[ p. 3]{jacobs2008developing} have observed that ``students are often unclear about the different +ways letters are used in mathematics''. We have seen this +lack of understanding in a situation in which it was proposed as evidence that +a single example, namely $\sigma_1^a\sigma_2^{p-a}$, formed a proof for a universally quantified +statement. +Some of our results were consistent with the framework described by Harel +and Sowder in 1998\cite{harel1998students}. We found students holding conceptualizations that +Harel and Sowder's 1998 model calls symbolization. Harel and Sowder have +identified another category of conceptualization, that correctly applied transformation +and axiomatic arguments. Some students expressed enthusiasm for +the power that inheres to building arguments with carefully specified component +ideas, in particular how the absence of ambiguity permitted arguments to +extend to great length while remaining valid. Not all of the students had developed +axiomatic conceptualizations of proof. About definitions, we collected +preliminary data on students' conceptualizations of definitions used in proofs. +Some students thought definitions were boring. Some students thought that +they could infer definitions from a few examples. Concerning executive function, +we found that some students do not state the premises clearly, and some +students did not keep track of their goal. About rules of inference, we found +Figure 5.3.1: Some categories / conceptualizations found among students of +introduction to the theory of computing, and published at FIE. +that some students apply invalid approaches to inference. + +We have found students holding conceptualizations +that Harel and Sowder's 1998 model\cite{harel1998students} calls symbolization: We have found +that some students may lack facility in notation. For example, in the application +of the pumping lemma, students are expected to understand the role of $i$, +in the context that a string $s$, having component substrings $x$, $y$ and $z$, can be +used to generate other strings, of the form $xy^iz$, where $i$ gives the number of +copies of the substring $y$. Moreover, students are expected to understand that +the subdivision of a string of length $p$, expressed as $\sigma_1^a\sigma_2^{p-a}$, where $a \in \{0,1,\ldots,p\}$ +uses $a$ as a parameter, a free variable, not one necessarily bound to a single instance +of a natural number, but a representation of a domain. +Trigueros et al.\cite[p. 3]{jacobs2008developing} have observed that ``students are often unclear about the different way letters are used in mathematics.'' + We saw this +lack of understanding in a situation in which it was proposed as evidence that +a single example, namely $\sigma_1^a\sigma_2^{p-a}$, formed a proof for a universally quantified +statement. An excerpt of the errors found on tests is shown in Table . + +Table : Some example errors\\ +Let x be empty\\ +$|xy| \leq p, so xy = 0^p$\\ +$|xy| \leq p; let x = 0^{p+r}, y = 0^{p+r}, 0 < r < p$\\ +Let’s choose $|xy| = p$\\ +$0^{p+1}0^b1^p \neq 0^{p+1}1^p \therefore xy^2z \not\in \mathcal{L}$\\ +where $\mathcal{L} = \{0^i1^j, i \neq j\}$\\ +we choose $s = 0^{p+1}1^p$ within $|xy|$\\ +thus $\neq 0^p1^{p+1}$\\ +Let $x = 0^a, y = 0^b1^a$\\ +$x = 0^{p-h}, y = 0^h$\\ +$x = 0^i, y = 0^i, z = 0^i1^j$\\ +Figure 5.3.3: Some categories / conceptualizations found among students of +introduction to the theory of computing, and published at FIE. + +Some of our results were consistent with the framework described by Harel +and Sowder in 1998[?]. We found students holding conceptualizations that +Harel and Sowder's 1998 model calls symbolization. Harel and Sowder have +identified another category of conceptualization, that correctly applied transformation +and axiomatic arguments. Some students expressed enthusiasm for +the power that inheres to building arguments with carefully specified component +ideas, in particular how the absence of ambiguity permitted arguments to +extend to great length while remaining valid. Not all of the students had developed +axiomatic conceptualizations of proof. About definitions, we collected +preliminary data on students' conceptualizations of definitions used in proofs. +Some students thought definitions were boring. Some students thought that +they could infer definitions from a few examples. Concerning executive function, we found that some students do not state the premises clearly, and some +students did not keep track of their goal. About rules of inference, we found +that some students apply invalid approaches to inference. +\subsection{Abstract Model for Proof by Mathematical Induction and Recursion} +Far from finding agreement that (a) theorems are true as a consequence of +the definitions and the premise, and that (b) proofs serve to show how the +consequence is demonstrated from the premise, axioms and application of +rules of inference, instead we found a variety of notions about proof, including +the well-known procedural interpretation \cite{tall2008transition,weber2004traditional,tall2001symbols}, and the well-known empirical +misconception \cite{harel1998students}. The conceptualization that definitions are not necessarily +of interest compared with the procedures seemed different in kind from the +concept image / concept definition discoveries of R\"osken et al. \cite{rosken2007integrating}. +Interviews with students revealed that some students saw generation of a proof +by mathematic induction as a procedure to be followed, in which they should +produce a base case, and prove it, and should produce an induction step, and +prove that. This was consistent with Weber [?, p. 4-426] who has stated ``in +the studies that I conducted, it was more often the case that undergraduates +applied procedures that were not meaningful to them.'' He went on to give a +quotation from a participant [?, p. 4-426] ``And I prove something and I look at +it, and I thought, well, you know, it's been proved, but I still don't know that I +even agree with it [laughs]. I'm not convinced by my own proof!'' Some of the +students interviewed did not know why this procedure generated a convincing +argument. Polya[?] has written a problem involving all girls being blue-eyed; +a similar problem appears in Sipser \cite{sipser2012introduction} about all horses being the same color. +The purpose of this exercise is to make students aware that the truth of the +inductive step must apply when the base case appears as the premise. In some +cases, this point was not clear to the students. +Students' conceptualizations of proof by mathematical induction can support +their choice to apply recursive algorithms. One student reported success at +both mathematical induction and recursive algorithm application without ever +noticing any connection. This student opined that having learned recursion +with figures, and proof by mathematical induction without figures, that no +occasion for the information to spontaneously connect occurred. Students reporting +ability to implement assigned problems recursively, but not the ability +to understand proof by mathematical induction also reported that ability to +write recursive programs did not result in recognition of when recursive solutions +might be applicable in general. Students reporting ability to implement +assigned problems recursively, and also the ability to prove using mathematical +induction also reported preferring to implement recursive solutions in +problems as they arose. + + (Say something about how this is consistent with the procedural conceptualization, bifurcation in Tall's writing.) +Our work on students' choices of algorithmic approaches was consistent with +work by other researchers in computer science education\cite{booth1997phenomenography} on conceptualizations +of algorithms. Our work served to unify that of mathematician educators +with computer science educators, by providing a plausible explanation why +the conceptualizations of recursive algorithms that were found, might exist. +\begin{figure} +\centering +%\includegraphics[width=0.7\linewidth]{./} +\caption{Categories of Student Conceptualizations of Proof by Induction +that Recursion Works} +\end{figure} + +Figure 5.3.2: +\begin{table}[h] +\caption{The Outcome Space for Proofs by Induction} +\begin{tabular}{|p{.2cm}|p{6cm}|p{6cm}|} +\hline & Category & Description \\ +\hline 1 & Following procedure & The method is learned, without understanding \\ +\hline 2 & Understands base case & The idea that a base case is proved by an existence +proof, often with a specific example\\ +\hline 3 & Understands implication & The idea that an implication is proved by +assuming the premise is not used\\ +\hline 4 & Does not understand connection & Sees the implication and proves it well, but +does not anchor the succession to a base +case \\ +\hline 5 & Does understand the argument & Understands the argument \\ +\hline 6 & Knows why recursion works & Can tailor the argument to explain recursive +algorithms \\ +\hline 7 & Appreciates data structures supporting recursion & Can see the benefit to algorithm from recursive data structure \\ +\hline +\end{tabular} +\end{table} + + + +\section{Helping Students Discern Abstraction} +Recall that variation theory holds that students cannot discern a thing unless +contrast is provided. Pang has pointed out that [], for persons aware of only +one language, ``speaking'' and ``speaking their language'' are conflated. Only +when the existence of a second language is known, does the idea of speaking +become separated from the idea of speaking a specific language. +(Here is a specialization (Hofstadter), formation of a new conjunct (Valiant), see Besold 2015) +Abstraction is important in computer science, and is worthy of investigation. +Inquiry into students' conceptualizations of formalization using symbols, symbolization, +has shown similar results among students of mathematics and of +computer science [?, ?]. Student populations contain the conceptualization that +proofs ought to be expressed using symbols, and some proof attempts show +that not all students are able to formalize meaningfully. Mathematics and computer +science pedagogies differ on the recommended style of variable names in +symbolization. In mathematics, there is a preference for single letter variable +names, and in computer science it is recognized that longer variable names assist +readers in understanding. In mathematics the use of single variable names +is preferred because it is thought to contribute to cultivating students' ability +to learn abstraction. If, in computer science education, we apply variation +Table 5.3.5: The Outcome Space for Proofs by Induction\\ +Category Description\\ + 1 Following procedure The method is learned, without understanding\\ + 2 Understands base case The idea that a base case is proved by an existence +proof, often with a specific example\\ +3 Understands implication The idea that an implication is proved by +assuming the premise is not used\\ +4 Does not understand connection +Sees the implication and proves it well, but +does not anchor the succession to a base +case\\ +5 Does understand the argument +Understands the argument\\ +6 Knows why recursion +works\\ +Can tailor the argument to explain recursive +algorithms\\ +7 Appreciates data structures +supporting recursion\\ +Can see the benefit to algorithm from recursive +data structure\\ +theory, we gain confidence in the idea that students may discern the process +of abstraction as we vary the names of the variables. We could imagine deriving +code from a requirement about a specific class, and using corresponding +variable names, and we could show the process of promoting the code into a +more general class in the inheritance hierarchy, changing the variable names to +correspond to the more general domain of objects. Thus we can borrow from +the approach used by mathematics education, but make it more explicit, taking +advantage of computer science's explicit treatment of inheritance hierarchies in +object oriented code. Seeking evidence of students' conception of abstraction, +we could examine overridden methods to see whether variable names in more +and less general implementations bear that relation to one another. + +\section {Algebra} +In middle or high school algebra students became familiar with the use of letters in equations, +and solving equations which resulted in individual values, or no value, being attached to the letters. + +Ideally the ability to understand expressions, to formulate pre- and post conditions would be acquired. +As we have seen that this occurs sometimes, but does not always occur, +there may be benefit to some students to review this idea. +We might choose to emphasize abstraction in this process. + +\section{Geometry} +In high school geometry, formal proofs of geometric properties are covered. +Students are exposed to a form for argument, and are given examples of use of rules of inference to perform logical deduction. +We have seen that sometimes this process is appreciated in enough generality to be recognized +as an example of argumentation. +We have seen as well, that some students found this process entirely specific to geometry, +doubting that it had broader application. + +\section{Seeing a Broader Context} + +It may be that some students do not see a separation between the activity of formalization on the one hand, +and the application area of finding solutions to equations on the other. +It may be that some students do not see a separation between the activity of deducing using logic on the one hand, and the application area of learning geometric facts on the other. +It seems consistent with neglecting opportunities for abstraction, that these separations are not always seen, +Speciation, an idea which uses abstraction, providing a hierarchy of properties animals and plants might have, was not recognized early or universally. So, it is +not surprising that abstraction, which involves choice about which details to defer, and which to regard as significant, is not always obvious. +In the machine learning perspective, features can be learned. +What do I want to say, it takes some effort to recognize features? +There might be a way to formulate choice of features such that some better efficiency is gained by thinkingof the features in that order vs. another order. +(Such as, we never have to think about some features for some parts of the tree.) +If we think about knowledge being organized in neural networks, such that abstraction has a physical manifestation, we can see that ideas between which there is little distance (by some measure, neurons, glia?) in the tree will more frequently elicit one another by linkages at the metabolic level. +At the neural level, modifications for efficiency are constantly taking place (Do we have this from Kandel and Squire?). +We might wish to exploit this in the way we teach, to exhibit the abstraction deliberately, to minimize the amount of neural connection remodeling that would occur in the process of providing an efficient neural connection remodeling that would occur in the process of providing an efficient neural representation. +Being able to learn by analogy testifies to the utility of having a neural representation that corresponds to abstraction. +Students who are working without hierarchical organization of concepts are at a disadvantage. +\section{Mathematics tests in high school that involve proving} +What can we learn from students of computer science who excelled in reasoning to this level? + + diff --git a/ch7.tex b/ch7.tex new file mode 100644 index 0000000..2542d83 --- /dev/null +++ b/ch7.tex @@ -0,0 +1,750 @@ +\chapter{Results} + +The results of a phenomenographic study comprise a set of categories of description of ways of experiencing (or capability for experiencing [p. 126]) a phenomenon, and relations among those categories. + +Marton and Booth\cite[p. 125]{marton1997learning} give criteria for the quality of a set of descriptive categories. +The collective experience, over all participants in the study should be included. +The individual categories should each stand in clear relation to the phenomenon of the investigation so that each category tells us something distinct about a particular way of experiencing the phenomenon. +The categories have to stand in a logical relationship with one another, a relationship that is frequently hierarchical. +Finally the systems should be parsimonious, which is to say that as few categories should be explicated as is feasible and reasonable, for capturing the critical variation in the data. + +late stages of analysis able to see aspects/facets of research object, +see how they fit together like jigsaw pieces, +see it against background, and communicate it to others. + +There are results for each of the research questions, and some combined results. + +While mainly we are discussing proof in general, it can help to think about one proof at a time. Applying the analytical framework of Marton and Booth\cite[p.43]{marton1997learning} +\begin{table}[placement] +\caption{Outcome space for what is proof, with temporal facet} +\begin{tabular}{|p{4cm}|p{4cm}|p{4cm}|}\hline +Acquiring & Knowing & Making Use of\\\hline\hline +see the steps & remembering the steps & write it out\\\hline +understand the steps & remembering the meaning & produce the meaning\\\hline +understand steps and warrants & understanding the meaning & be able to apply the proof to simple examples\\\hline +analyzed the structure, determine the warrants & understand the relevance & be able to apply the proof in general, know its context of applicability\\\hline +\end{tabular} + +\end{table} +Our goal might be in the lower right, and for some students who do not arrive that far, they might arrive at any of its three neighbors in the chart. + +We are looking for ways of experiencing, for example, one way is, proofs only apply to number facts, vs. proof techniques are separable from number facts and can be used on other domains. + + + +\section{What do students think a proof is?} + + +Some students, when asked what they think a proof is, will report that they think it is a list of true mathematically formulated statements, demonstrating the truth of a mathematically formulated statement. Some students report that a proof has a goal, a statement to be proved true. +Some students know that the identified goal does not have to be known to be true in advance of the first proof. + +Sometimes, though, students have the idea that the proof is an exhibit of their ability to connect known facts, including the goal as a known fact. + + + +Some students, for example some taking philosophy, understand a proof more generally as not having a requirement for a mathematical formulation. Some of these have expressed dislike of such less precisely articulated statements. + +Some students, when prompted, will acknowledge that warrants for these statements are required. Axioms and agreed facts do not require warrants. +Some students, but not all, recognize that premises do not require warrants. +Some students, but not all, recognize that suppositions, as premises, do not require warrants. +Some students, but not all, recognize that cases, as suppositions, do not require warrants. +Some students, but not all, know that progress from one statement to the next, a transformation of a statement, requires a warrant. + +Some of the optional syntactic ornamentation of a proof, such as literal text "Proof:", and "QED" or $\qed$, are used by some students as proxies for the proof. As in the research by Harel and Sowder\cite{harel1998students}, which they describe as "ritual proof", we find in our research that some students claim to recognize a proof when they see these artifacts, and claim they have not seen a proof when they do not see these artifacts. + +Some students are aware that proof, as encountered in class, ought to be a convincing argument. +These students feel that something is wrong when they are not convinced by the proof technique they have learned to execute in a procedural fashion. + +Some students know that proof is convincing others, and also ascertaining for oneself. Of these, some find that proof is convincing for some facts they regard as mathematical, yet do not think proof is applicable to programs as large as those with which they plan to be involved. +Some of these students have not yet acquired the perspective that proving theorems about the number of instruction executions, and/or memory locations needed are both numerical and also applicable to and relevant for software development. + + +\begin{figure}[h] +\centering +\includegraphics[width=0.7\linewidth]{/home/theresesmith/Documents/2015Fall/Research/Thesis/whatThemes} +\caption{Conceptualizations found for what a proof is} +\label{fig:whatThemes} +\end{figure} +\begin{table} + \caption{Critical factors for what a proof is} +\begin{tabular}{|c|c|c|} +\hline Lesser Conceptualization & Better Conceptualization & Critical Factor\\ \hline +\hline List of Known Facts & List of Warranted Facts & Warrants\\ +\hline List of Warranted Facts & Means of Discovery & Tool rather than\\ & & demonstration to teachers\\ \hline +\end{tabular} + \end{table} + +\newpage +\section{How do students approach understanding a proof?} +Those students who felt they understood some proofs approached them by checking whether they felt each line of a proof was true. +Some of these mentioned that a statement should be warranted by previous statements. + +\begin{figure}[h] +\centering +\includegraphics[width=0.7\linewidth]{/home/theresesmith/Documents/2015Fall/Research/Thesis/howThemes} +\caption{Conceptualizations of how to comprehend a proof} +\label{fig:howThemes} +\end{figure} +\begin{table} + \caption{Critical factors for what a proof is} +\begin{tabular}{|c|c|c|} +\hline Lesser Conceptualization & Better Conceptualization & Critical Factor\\ \hline +\hline List of Known Facts & List of Warranted Facts & Warrants\\ +\hline List of Warranted Facts & Means of Discovery & Tool rather than\\ & & demonstration to teachers\\ \hline +\end{tabular} + \end{table} + +\newpage +\section{What do students think a proof is for?} +Some students think that proofs are not applicable to what they do. They think they do not need to know it. Because they do not need to know it, they logically conclude that learning to produce a "proof" procedurally is enough, because, it earns full credit. + +Some students combine the learning about proof with the subject matter that is used to exercise proof techniques; they think proof is for demonstrating facts about numbers. + +Some students claim that they never produce proofs unless assigned to do so in class. + +Let us call the statement to be proved, the target, so as to more clearly articulate the variety of student thinking, by escaping the connotations of "statement to be proved". + +Perhaps not surprisingly in light of the teaching of proof, some students think the purpose of proof is to demonstrate that they can construct a sequence of statements that connects the truth of the premises to the truth of the target. Some of these students regard the truth of the target to be known beforehand. As the purpose of the proof is to exhibit their ability to produce an argument, it is not surprising that students say they never construct proofs unless they are assigned to do so. It is not surprising in this context, that students opt for a procedural approach, learning the parts, for example, of a proof by induction, learning to provide a proof for a base case, and learning to take a premise as a given and a conclusion of an implication to be proved. Some students do not understand why this procedure constructs a proof. Some express an unease -- they wish for the proof procedure to be convincing, to themselves. They are glad when they learn why the procedure does produce a convincing argument. + +Some students recognize proof being used in class, for example in algorithms class and in introduction to the theory of computing. + + + + +Some students felt that proof was for finding out that a mathematical expression was true, or false. Some students knew that some statements could be proved undecidable. + +\begin{figure}[h] +\centering +\includegraphics[width=0.7\linewidth]{/home/theresesmith/Documents/2015Fall/Research/Thesis/whyThemes} +\caption{Conceptualizations about why to study proofs} +\label{fig:whyThemes} +\end{figure} +\begin{table} + \caption{Critical factors for what a proof is} +\begin{tabular}{|c|c|c|} +\hline Lesser Conceptualization & Better Conceptualization & Critical Factor\\ \hline +\hline List of Known Facts & List of Warranted Facts & Warrants\\ +\hline List of Warranted Facts & Means of Discovery & Tool rather than\\ & & demonstration to teachers\\ \hline +\end{tabular} + \end{table} + +\newpage +\section{What do students use proof for, when not assigned?} +Some students claim they never use proofs when not assigned. + +It is not the case that any student, even when prompted, said they chose to carry out a proof without being directed to do so. +This could easily be due to a misunderstanding of the definition of proof. + +\newpage +\section{Do students exhibit any consequence of inability in proof?} +Some students said that they knew how to craft recursive procedures, and enjoyed doing so when assigned problems designated as suitable for recursive implementations. +Some students said they did not employ recursive procedures in situations without a designation that recursive procedures were appropriate. They claimed not to be able to tell when recursive procedures were applicable. + +\newpage +\section{What kind of structure do students notice in proofs?} +Some students think proofs are lists of statements without hierarchical structure. +Some students have asked what lemma means. +Some students knew that lemmas were built for use in larger proofs. +Some students were interested to hear about Dr. Lamport's structure in proofs. + +\newpage +\section{What do students think it takes to make an argument valid?} +Some students, when prompted about rules of inference, felt that when all statement transformations were warranted, an argument was valid. +Some students stated that, when the target of the proof was true, the proof was valid, converse error. + + + + + +We organize our overview of results beginning from an ideal Hilbert-axiomatic style of proof approach, and moving through approximations as they become greater departures from it. +\begin{figure}[h] +\centering +\includegraphics[width=0.7\linewidth]{/home/theresesmith/Documents/2015Fall/Research/Thesis/valid} +\caption{Conceptualizations about validity of proofs} +\label{fig:validityThemes} +\end{figure} +\begin{table} + \caption{Critical factors for what a (valid) proof is} +\begin{tabular}{|c|c|c|} +\hline Lesser Conceptualization & Better Conceptualization & Critical Factor\\ \hline +\hline No Warrants & Some Warrants & Warrants\\ +\hline Some Appropriate Warrants & Fully Warranted & thoroughness\\ \hline +\end{tabular} + \end{table} + +\paragraph{Definition based reasoning} +Some students, and some teaching assistants in their teaching, are not organizing the approach to proof around definitions. +Instead some students and some teaching assistants are focusing on an intuitive approach, involving examples. +Some students use examples to infer definitions. +Some students use single examples as proof. + +Some students are not aware that proofs are illustrated with facts of, for the purposes of the class, less significance than the proof techniques. +Some students are not aware of the relevance of proof to their intended career. +These students do not see any point to learning more than a procedural approach to the proof material, as they believe it to be of no lasting significance to them. + +\paragraph{Generalization and transformation based reasoning} +Some students, and some instructors, do not emphasize that a single presentation can be seen as a representative of a group. For example, Mathematical Association of America\cite{} publishes a proof of the Pythagorean Theorem that uses rectangles to illustrate that, when they are square, the Pythagorean Theorem is being shown to be true, though of course, the rectangles need not always be square. The proof, having been established, does not rely upon the rectangles remaining in a square condition. + + + + + + + +\section{Combined Description} + +There are a couple of ways students work with exercises in proof, that are incomplete. + +Some students reason well with concrete entities, yet are confused with abstractions. These students are not appreciating the value of careful definitions, because they do not use them as tools, or the basis for reasoning. They are more comfortable with examples, because they are operating in a concrete world. + +Some students do not connect the world of concrete objects with the abstract, symbolic representation, but are making use of symbols. Some operations transforming symbolic expressions are performed correctly, but not all. The lack of understanding of the symbols combined with a procedural approach to producing a proof artifact, leaves these students personally unconvinced, and unmotivated to make use of proof when it would be helpful to them. + +Some students do understand application of facts, axioms and rules of inference, and are at home with careful definitions and symbolic concision. Some of these students also study math. + + +\newpage +\section{Diagram of Conceptualizations} + +\begin{figure}[h] +\centering +\includegraphics[width=0.95\linewidth]{./themes} +\caption{Themes from interview data} +\label{fig:themes} +\end{figure} +\newpage +\section{Outcome Space} +The outcomes were not arranged in a single progression. Rather, there were several means, listed below, by which students were able to construct the proof artifact required by the class. The students did not always find the artifact convincing. + +\begin{enumerate} +\item Concrete to Abstract -- generalize the argument, then the entities +\item Hilbert-style axiomatic/definitional proof +\item Abstract operations -- symbols rather than entities, structure of argument +\end{enumerate} + +The concrete to abstract path enabled students to reason with specific cases whose logic made sense to them, then make the step that the logical process itself was an entity that could be reused. The idea that other concrete entities could bear the same relationships, and be subject to the same reasoning constituted a step. The idea that analogies were being made, and that generalization was possible was another step. + +The reasoning by axioms and rules of inference path was known to some students. These students mentioned their appreciation of math, and in some cases their discomfort with philosophy, in connection with symbolization and application of rules of inference. + +One path was operation at the level of symbols, using procedures. This path is distinguished from that involving definitions, because some students, using definitions, were clear about appropriate operations to transform symbolic expressions, but students also sometimes were unsure about denotation and about appropriate operations. + +\section{Critical Factors} +On the path from concrete to structured proofs, called herein "generalize the argument, then the entities", one critical factor is that an argument about one set of concrete entities can be used on another set, having analogous relationships. + +Another critical factor is that, when an argument can be reused, sets of entities that stand in analogous relationships, the relationship can be generalized. When the relationship is generalized, the entities standing in that relationship can be given symbols. + +On the path that starts with symbols, students have not generalized from concrete to abstract entities, rather, they have entered the fray at the level of abstraction of symbols. Thus, a critical factor is to understand the operations appropriate to the symbols, which imbues application of the rules of inference with significance. Another critical factor is that these symbols can represent entities of interest. + + + + + +\section{Earlier Paper Material} + +\subsection{Categories of Experience of Entering Students} +Undergraduate students beginning study of the computing disciplines present +various degrees of preparedness\cite{smith2013categorizing}. Some had no experience, some had had +informal experience, and some had had formal classes. The formal classes +extended from using applications to building applications. Informal experience +ranged from editing configuration files, such as background colors, to full time +jobs extended over multiple summers. +After publishing this paper, we encountered more related information. For +example, consistent with the work of Almstrum\cite{almstrum1996investigating}, we found that, about implications, +some students, who do know that any statement must and can, be +either true or false, thought implications must be true. Some interview participants +enjoyed a modified Moore method\cite{cohen1982modified} geometry class in middle school, +and relished opportunities to create proofs (not yet published). Other students +were not so well prepared. +\subsection{Representation/Symbolization in Pumping Lemmas} +We found that some students may lack facility in notation. For example, in the +application of the pumping lemma, students are expected to understand the +role of $i$, in the context that a string $s$, having component substrings $x$, $y$ and $z$, +can be used to generate other strings, of the form $xy^iz$, where $i$ gives the number +of copies of the substring $y$. Moreover, students are expected to understand that +the subdivision of a string of length $p$, $\sigma_1^a\sigma_2^{p-a}$, where $a \in \{0,1,\ldots,p\}$ +uses $a$ as a parameter, a free variable, not one necessarily bound to a single instance +of a natural number, but a representation of a domain. An excerpt of the errors found on tests is shown in Table . Trigueros et +al. \cite[ p. 3]{jacobs2008developing} have observed that ``students are often unclear about the different +ways letters are used in mathematics''. We have seen this +lack of understanding in a situation in which it was proposed as evidence that +a single example, namely $\sigma_1^a\sigma_2^{p-a}$, formed a proof for a universally quantified +statement. +Some of our results were consistent with the framework described by Harel +and Sowder in 1998\cite{harel1998students}. We found students holding conceptualizations that +Harel and Sowder's 1998 model calls symbolization. Harel and Sowder have +identified another category of conceptualization, that correctly applied transformation +and axiomatic arguments. Some students expressed enthusiasm for +the power that inheres to building arguments with carefully specified component +ideas, in particular how the absence of ambiguity permitted arguments to +extend to great length while remaining valid. Not all of the students had developed +axiomatic conceptualizations of proof. About definitions, we collected +preliminary data on students' conceptualizations of definitions used in proofs. +Some students thought definitions were boring. Some students thought that +they could infer definitions from a few examples. Concerning executive function, +we found that some students do not state the premises clearly, and some +students did not keep track of their goal. About rules of inference, we found +Figure 5.3.1: Some categories / conceptualizations found among students of +introduction to the theory of computing, and published at FIE. +that some students apply invalid approaches to inference. + +\subsection{Abstract Model for Proof by Mathematical Induction and Recursion} +Far from finding agreement that (a) theorems are true as a consequence of +the definitions and the premise, and that (b) proofs serve to show how the +consequence is demonstrated from the premise, axioms and application of +rules of inference, instead we found a variety of notions about proof, including +the well-known procedural interpretation \cite{tall2008transition,weber2004traditional,tall2001symbols}, and the well-known empirical +misconception \cite{harel1998students}. The conceptualization that definitions are not necessarily +of interest compared with the procedures seemed different in kind from the +concept image / concept definition discoveries of R\"osken et al. \cite{rosken2007integrating}. +Interviews with students revealed that some students saw generation of a proof +by mathematic induction as a procedure to be followed, in which they should +produce a base case, and prove it, and should produce an induction step, and +prove that. This was consistent with Weber [?, p. 4-426] who has stated ``in +the studies that I conducted, it was more often the case that undergraduates +applied procedures that were not meaningful to them.'' He went on to give a +quotation from a participant [?, p. 4-426] ``And I prove something and I look at +it, and I thought, well, you know, it's been proved, but I still don't know that I +even agree with it [laughs]. I'm not convinced by my own proof!'' Some of the +students interviewed did not know why this procedure generated a convincing +argument. Polya[?] has written a problem involving all girls being blue-eyed; +a similar problem appears in Sipse \cite{sipser2012introduction} about all horses being the same color. +The purpose of this exercise is to make students aware that the truth of the +inductive step must apply when the base case appears as the premise. In some +cases, this point was not clear to the students. +Students' conceptualizations of proof by mathematical induction can support +their choice to apply recursive algorithms. One student reported success at +both mathematical induction and recursive algorithm application without ever +noticing any connection. This student opined that having learned recursion +with figures, and proof by mathematical induction without figures, that no +occasion for the information to spontaneously connect occurred. Students reporting +ability to implement assigned problems recursively, but not the ability +to understand proof by mathematical induction also reported that ability to +write recursive programs did not result in recognition of when recursive solutions +might be applicable in general. Students reporting ability to implement +assigned problems recursively, and also the ability to prove using mathematical +induction also reported preferring to implement recursive solutions in +problems as they arose. +Our work on students' choices of algorithmic approaches was consistent with +work by other researchers in computer science education\cite{booth1997phenomenography} on conceptualizations +of algorithms. Our work served to unify that of mathematician educators +with computer science educators, by providing a plausible explanation why +the conceptualizations of recursive algorithms that were found, might exist. +\subsection{Proofs by Induction} +Table 5.3.3: The Outcome Space for Proofs by Induction +Category Description +1Following procedure The method is learned, without understanding +2Understands base case The idea that a base case is proved by an existence +proof, often with a specific example +3Understands implication The idea that an implication is proved by +assuming the premise is not used +4Does not understand connection +Sees the implication and proves it well, but +does not anchor the succession to a base +case +5Does understand the argument +Understands the argument +6Knows why recursion +works +Can tailor the argument to explain recursive +algorithms +7Appreciates data structures +supporting recursion +Can see the benefit to algorithm from recursive +data structure +\subsection{Pumping Lemmas} +TABLE III. CATEGORIES\\ +understand inequality\\ +formulate correctly\\ +distinguish between particular and generic particular\\ +correctly apply universal quantifier\\ +recognize string as member of language set + +\section{Discussion} + \subsection{Importance} +Importance goes here, rather than in analysis\\ + +Programmers/developers who produce and/or verify software that is used in safety critical applications, such as medical equipment, self-driving cars, and defense-related equipment should be able to know that their software functions correctly. + +Programmers/developers who produce and/or verify software that is expected to perform work, such as search, efficiently, should be able to know that their algorithms are efficient. + +Computer science is the expected background preparation for people working in these careers. +Proof is the method that is used to ascertain, and to convince, that these goals have been achieved. +\subsection{Interpretation of Results} +As in mathematics, some students learn as procedure that which we would prefer that they understand. +Some procedural learning is insufficiently accompanied by an understanding as to which contexts to which it applies, and has become in some cases what Whitehead calls "inert knowledge". + +\subsection{More Discussion} +\paragraph{Helping Students Discern Abstraction} +Recall that variation theory holds that students cannot discern a thing unless +contrast is provided. Pang has pointed out that [], for persons aware of only +one language, ``speaking'' and ``speaking their language'' are conflated. Only +when the existence of a second language is known, does the idea of speaking +become separated from the idea of speaking a specific language. +(Here is a specialization (Hofstadter), formation of a new conjunct (Valiant), see Besold 2015) +Abstraction is important in computer science, and is worthy of investigation. +Inquiry into students' conceptualizations of formalization using symbols, symbolization, +has shown similar results among students of mathematics and of +computer science [?, ?]. Student populations contain the conceptualization that +proofs ought to be expressed using symbols, and some proof attempts show +that not all students are able to formalize meaningfully. Mathematics and computer +science pedagogies differ on the recommended style of variable names in +symbolization. In mathematics, there is a preference for single letter variable +names, and in computer science it is recognized that longer variable names assist +readers in understanding. In mathematics the use of single variable names +is preferred because it is thought to contribute to cultivating students' ability +to learn abstraction. If, in computer science education, we apply variation +Table 5.3.5: The Outcome Space for Proofs by Induction\\ +Category Description\\ + 1 Following procedure The method is learned, without understanding\\ + 2 Understands base case The idea that a base case is proved by an existence +proof, often with a specific example\\ +3 Understands implication The idea that an implication is proved by +assuming the premise is not used\\ +4 Does not understand connection +Sees the implication and proves it well, but +does not anchor the succession to a base +case\\ +5 Does understand the argument +Understands the argument\\ +6 Knows why recursion +works\\ +Can tailor the argument to explain recursive +algorithms\\ +7 Appreciates data structures +supporting recursion\\ +Can see the benefit to algorithm from recursive +data structure\\ +theory, we gain confidence in the idea that students may discern the process +of abstraction as we vary the names of the variables. We could imagine deriving +code from a requirement about a specific class, and using corresponding +variable names, and we could show the process of promoting the code into a +more general class in the inheritance hierarchy, changing the variable names to +correspond to the more general domain of objects. Thus we can borrow from +the approach used by mathematics education, but make it more explicit, taking +advantage of computer science's explicit treatment of inheritance hierarchies in +object oriented code. Seeking evidence of students' conception of abstraction, +we could examine overridden methods to see whether variable names in more +and less general implementations bear that relation to one another. +\paragraph{Helping Students Discern Abstraction} +\paragraph {Algebra} +In middle or high school algebra students became familiar with the use of letters in equations, +and solving equations which resulted in individual values, or no value, being attached to the letters. + +Ideally the ability to understand expressions, to formulate pre- and post conditions would be acquired. +As we have seen that this occurs sometimes, but does not always occur, +there may be benefit to some students to review this idea. +We might choose to emphasize abstraction in this process. + +\paragraph{Geometry} +In high school geometry, formal proofs of geometric properties are covered. +Students are exposed to a form for argument, and are given examples of use of rules of inference to perform logical deduction. +We have seen that sometimes this process is appreciated in enough generality to be recognized +as an example of argumentation. +We have seen as well, that some students found this process entirely specific to geometry, +doubting that it had broader application. + +\paragraph{Seeing a Broader Context} + +It may be that some students do not see a separation between the activity of formalization on the one hand, +and the application area of finding solutions to equations on the other. +It may be that some students do not see a separation between the activity of deducing using logic on the one hand, and the application area of learning geometric facts on the other. +It seems consistent with neglecting opportunities for abstraction, that these separations are not always seen, +Speciation, an idea which uses abstraction, providing a hierarchy of properties animals and plants might have, was not recognized early or universally. So, it is +not surprising that abstraction, which involves choice about which details to defer, and which to regard as significant, is not always obvious. +In the machine learning perspective, features can be learned. +What do I want to say, it takes some effort to recognize features? +There might be a way to formulate choice of features such that some better efficiency is gained by thinking of the features in that order vs. another order. +(Such as, we never have to think about some features for some parts of the tree.) +If we think about knowledge being organized in neural networks, such that abstraction has a physical manifestation, we can see that ideas between which there is little distance (by some measure, neurons, glia?) in the tree will more frequently elicit one another by linkages at the metabolic level. +At the neural level, modifications for efficiency are constantly taking place (Do we have this from Kandel and Squire?). +We might wish to exploit this in the way we teach, to exhibit the abstraction deliberately, to minimize the amount of neural connection remodeling that would occur in the process of providing an efficient neural connection remodeling that would occur in the process of providing an efficient neural representation. +Being able to learn by analogy testifies to the utility of having a neural representation that corresponds to abstraction. +Students who are working without hierarchical organization of concepts are at a disadvantage. +\paragraph{Mathematics tests in high school that involve proving} +What can we learn from students of computer science who excelled in reasoning to this level? + + +\section{Previously Published Work} + +Three papers in this area have been published to date: +\begin{itemize} + +\item CCSCNE: Categorizing the School Experience of Entering Computing +Students +\item FIE: Mathematization in Teaching Pumping Lemmas +\item Koli Calling: Computer Science Students' Concepts of Proof by Induction + +\end{itemize} +\section{ Categories of Experience of Entering Students} +Undergraduate students beginning study of the computing disciplines present +a various degrees of preparedness.\cite{reilly2014examination} Some interview participants enjoyed +a modified Moore method\cite{cohen1982modified} geometry class in middle school, and relished +opportunities to create proofs (not yet published). Other students are not so +well prepared. +After publishing this paper, more information relating to its topic has been +encountered. For example, consistent with the work of Almstrum \cite{almstrum1996investigating}, we have +found that, about implications, some students, who do know that any statement +must and can, be either true or false, think implications must be true. +\section{ Representation/Symbolization in Pumping Lemmas} +Some of our results to date are consistent with the framework described by +Harel and Sowder in 1998\cite{harel1998students}. We have found students holding conceptualizations +that Harel and Sowder's 1998 model\cite{harel1998students} calls symbolization: We have found +that some students may lack facility in notation. For example, in the application +of the pumping lemma, students are expected to understand the role of $i$, +in the context that a string $s$, having component substrings $x$, $y$ and $z$, can be +used to generate other strings, of the form $xy^iz$, where $i$ gives the number of +copies of the substring $y$. Moreover, students are expected to understand that +the subdivision of a string of length $p$, expressed as $\sigma_1^a\sigma_2^{p-a}$, where $a \in \{0,1,\ldots,p\}$ +uses $a$ as a parameter, a free variable, not one necessarily bound to a single instance +of a natural number, but a representation of a domain. We have seen this +lack of understanding in a situation in which it was proposed as evidence that +a single example, namely $\sigma_1^a\sigma_2^{p-a}$, formed a proof for a universally quantified +statement. An excerpt of the errors found on tests is shown in Table . + +Table : Some example errors\\ +Let x be empty\\ +$|xy| \leq p, so xy = 0^p$\\ +$|xy| \leq p; let x = 0^{p+r}, y = 0^{p+r}, 0 < r < p$\\ +Let's choose $|xy| = p$\\ +$0^{p+1}0^b1^p \neq 0^{p+1}1^p \therefore xy^2z \not\in \mathcal{L}$\\ +where $\mathcal{L} = \{0^i1^j, i \neq j\}$\\ +we choose $s = 0^{p+1}1^p$ within $|xy|$\\ +thus $\neq 0^p1^{p+1}$\\ +Let $x = 0^a, y = 0^b1^a$\\ +$x = 0^{p-h}, y = 0^h$\\ +$x = 0^i, y = 0^i, z = 0^i1^j$ + +Figure: Some categories / conceptualizations found among students of +introduction to the theory of computing, and published at FIE. + +Harel and Sowder identified a category of conceptualization that correctly +applied transformation and axiomatic arguments. Some students expressed +enthusiasm for the power that inheres to building arguments with carefully +specified component ideas, in particular how the absence of ambiguity permitted +arguments to extend to great length while remaining valid. Not all of the +students had developed axiomatic conceptualizations of proof. About definitions, +we have collected preliminary data on students' conceptualizations of +definitions used in proofs. Some students think definitions are boring. Some +students think that they can infer definitions from a few examples. Concerning +executive function, we have found that some students do not state the +premises clearly, and some students do not keep track of their goal. About +rules of inference, we have found that some students apply invalid approaches +to inference. +\section{ Abstract Model for Proof by Mathematical Induction and Recursion} +Interviews with students revealed that some students see generation of a proof +by mathematic induction as a procedure to be followed, in which they produce +a base case, and prove it, and produce an induction step, and prove that. Some +of the students interviewed did not know why this procedure generated a +convincing argument. Moore, as reported in Polya[] noted that some students +of mathematics formed the same conceptualization, that there is a procedure, +but it does not necessarily produce a convincing argument. Polya[] wrote +a problem involving all girls being blue-eyed; a similar problem appears in +Sipser\cite{sipser2012introduction} about all horses being the same color. The purpose of this exercise is +to make students aware that the truth of the inductive step must apply when +the base case appears as the premise. In some cases, this point was not clear to +the students. +Students' conceptualizations of proof by mathematical induction can support +their choosing to apply recursive algorithms. One student reported success at +both mathematical induction and recursive algorithm application without ever +noticing any connection. This student opined that having learned recursion +with figures, and proof by mathematical induction without figures, that no +occasion for the information to spontaneously connect occurred. Students reporting +ability to implement assigned problems recursively, but not the ability +to understand proof by mathematical induction also reported that ability to +write recursive programs did not result in recognition of when recursive solutions +might be applicable in general. Students reporting ability to implement +assigned problems recursively, and also the ability to prove using mathematical +induction also reported preferring to implement recursive solutions in +problems as they arose. +Our work on students' choices of algorithmic approaches is consistent with +work by other researchers in computer science education\cite{} on conceptualizations +of algorithms. Our work served to unify that of mathematician educators +with that of computer science educators, by providing a plausible explanation why +the conceptualizations of recursive algorithms that were found, might exist. + +Figure 4.0.2: Conceptualizations of proof by induction and recursion, published +in Koli Calling + +Index Element of Model +\begin{enumerate} + +\item Some students begin learning proof by mathematical induction as if it were +a procedure. +\item Some students learn two parts of this proof technique without seeing any +connection between the two. +\item Some students do not find the procedure to be a convincing argument. +\item Some students would not employ proof by mathematical induction to explore +whether a recursive algorithm would apply to a given problem. +\item Some students understand both proof by mathematical induction and also +recursion and had never noticed any similarity. + +\end{enumerate} +\section{Results of Combined Investigations} +There are some categories that are shared among the several contexts. +\section{Categories} +Categories found in one or more investigations + +Categories\\ +Definition of proof as convincing (to mathematicians) argument is not +always understood\\ +Definitions in general are not always recognized as significant building +blocks in arguments\\ +The idea of a false statement sometimes becomes troublesome when +negation is being learned.\\ +In particular, accepting that an implication may be false, can be troublesome. +Notation is sometimes difficult.\\ +Ideas presented relying on notation are not always connected with +ideas presented relying on figures.\\ +Warrants are not always recognized.\\ +Students do not always traverse levels of abstraction effectively.\\ +The applicability of valid argument forms to contexts of interest is not +always appreciated. +\section{ Critical Factors} +To determine critical factors, we can convert negative categories into achievement +levels. +\begin{tabular}{p{3cm}p{3cm}} +Categories & Achievement Levels\\ +The idea of a false statement +sometimes becomes troublesome +when negation is being +learned.&\\ +&True and false make sense, and +we can make arguments using +them.\\ +Definition of proof as convincing +argument is not always understood&\\ +Warrants are not always recognized.&\\ +&Proof can sometimes be obtained +through a series of warranted assertions.\\ +Definitions in general are not always +recognized as significant +building blocks in arguments&\\ +&Using agreed definitions and +valid rules of inference we can +sometimes explore the consequences +of definitions.\\ +Notation is sometimes difficult.&\\ +&Notation helps.\\ +Ideas presented relying on notation +are not always connected +with ideas presented relying on +figures.&\\ +&We might wish to help students +traverse multiple rendering of +ideas.\\ +Students do not always traverse +levels of abstraction effectively.&\\ +&We might wish to help students +traverse multiple levels of abstraction.\\ +The applicability of valid argument +forms to contexts of interest +is not always appreciated.&\\ +&We might wish to give exercise +with authentic (career related) +examples\\ + +\end{tabular} + +Using the achievement levels we can infer critical factors. +\begin{tabular}{p{3cm}p{3cm}} +Achievement Levels& Critical Factors\\ +True and false make sense, and +we can make arguments using +them.&\\ +& True and false apply to assertions.\\ +Proof can sometimes be obtained +through a series of warranted assertions. +& Proof is exploration and discovery.\\ +Using agreed definitions and +valid rules of inference we can +sometimes explore the consequences +of definitions.&\\ +& Efficiency but also abstraction +are aided by notation.\\ +Notation helps.&\\ +& Notation is one representation +and there are others. Ideas appear +in multiple guises.\\ +We might wish to help students +traverse multiple rendering of +ideas.&\\ +& When notation allows for multiple +interpretations, abstraction +above those multiple interpretations +has been achieved.\\ +We might wish to help students +traverse multiple levels of abstraction.&\\ +&Multiple levels of abstraction are +relevant at the same time.\\ +We might wish to give exercise +with authentic (career related) +examples.&\\ +& Authentic applications show the +use of this knowledge.\\ +\end{tabular} + + +\subsection{Abstraction} +Literature reports \cite{} students of CS have trouble with abstraction. +Taking abstraction to be the ability to select some details to ignore, +and thereby find a simpler model of an entity, we can transform the ideal +knowledge transfer experience into on disabled by a lack of ability to see this dimension. +The multiple-inheritance hierarchy that could be used to organize +definitions and relationships of ideas is less able. More entities will be +grouped together than effective use of the multiple inheritance hierarchy +would consider equivalent. +Another useful concept that students have been seen to underappreciate is the significance of careful definitions. +Abstraction hierarchies allow for efficiency in definitions. +A new entity can be defined as a specialization of an existing entity, and its differences +make up the new definition material. +In the absence of this multiple inheritance hierarchy, every definition in its full length +is attached to its entity. +Tie in with Mazur. For students holding the same granularity of refinement of +concepts, conversations would be easier, because there would be fewer disconnects as one participant expressed a thought on one degree of refinement far from that of another student. +If the ideas implying the refinement of the definition inheritance graph, being different from one +discussant to the next, are rare, and/or the meaning of the sentence does not depend upon it, these exchanges are not too disruptive or distressing. +On the other hand when two sets of refinement are very different, +and the meaning of the exchange depends upon the refinement in the speaker, that the hearer does not have, +then some degree of failure of communication will ensue. +Absence of abstraction converts tree of topics into sequence of topics. +Tree of proof examples (say of application of proof technique) into sequence of examples. +Might detract from recognizing what is a related example. +Would detract from plausible inference technique of ``related problem seen before''. +We have a goal for student programming that they should strive for segments of programs +(e.g., method implementations) to be small. One way of accomplishing this is to use abstraction, +such as combining instructions into a method, and calling the method. +If students have difficulty with abstraction, they might +have difficulty with choosing groups of instructions to represent a method. +Correspondingly, if they practice grouping instruction into methods, and using those methods, they would +be gaining practice relevant to using abstraction. +One way to cultivate abstraction is to pose a question of which one of several examples is different. +When several things are examples of one abstract idea and one is not, identifying the one that is different involves noticing the abstraction. +These questions could be instantiated using blocks of code. + +\subsection{Definitions} +Without abstraction the burdensomeness of definition is increased. This could contribute to the reluctance of students to embrace definitions. +\subsection{Symbolization} +Use of symbols is a kind of abstraction. +Symbolization is the syntax for simple, clear definitions as Gries\cite[p.205]{gries2012science}(Science of Programming) recommends for construction of programs. +Students will be hindered at this program derivation/development style if symbolization is a not-yet-acquired skill. +Program development/derivation should begin with a formulation of the requirements. +Students may arrive with some programming experience that is of a more intuitive, less +mathematically disciplined sort. +We have to ask how we desire to cultivate the abilities of such students. +Vygotsky discussed language acquisition by children, in which some children will have begun to invent +some terms for items in their environment, and will need to be guided to abandon neologisms for the naming generally agreed in their environment. +Kuhn discussed the reluctance of scientists who have been rewarded for operating in one +perspective on nature to adopt a different perspective. +Instructor may encounter a similar reluctance on the part of students +to adapt a scientifically/mathematically disciplined approach to programming, +especially if the students have experienced some success in their earlier work. +To win over such students, +demonstration of superior outcomes on problems, especially on problems that seem insoluble otherwise, +are more frequently convincing. +Happily, Professor Gries has provided such examples. +By showing superior relative efficacy of these approaches in an activity the students recognize as +desirable, instructors could motivate the students to learn symbolization. +\subsection{Structure} +sequence vs. sequence that has come about from combining parts. Refer to Leslie Lamport's structure for proofs. Combine with Gries' proofs for deriving code. The purpose for getting through Goguen and Malcolm is that it applies to imperative programs. + + + diff --git a/ch8.tex b/ch8.tex new file mode 100644 index 0000000..60c8eee --- /dev/null +++ b/ch8.tex @@ -0,0 +1,228 @@ +\chapter{Validity and Reliability} +strategies for trustworthy, valid, reliable +what about generalizability? %(e.g., to people with ASD) +\section{Interviews} +software programs that were used, to manage, organize data\\ +analyze as we go\\ +inductive and comparative\\ +precisely how the analysis was done\\ +thorough explanation of any strategies, such as discourse analysis +\section{Documents} +\section{Validity and Reliability in Proofs Using the Pumping Lemma +for Regular Languages} +Some support for the validity of the results comes from seeing several variations +of each proposed error type. We found in our data multiple versions of +unwarranted restrictions: choosing $x$ to be empty or choosing the length of $xy$ +to be $p$, and others. We found in literature warnings against attempts to prove +statements with universal qualifiers true by means of showing the existence +of examples \cite{devlin2012mathematical,Franklin}. These warnings suggest these errors have occurred before. +In textbooks \cite{epp2010discrete,rosen2003} we find single counterexamples for showing such a +statement false, and the method of exhaustion for showing a finite universal +statement to be true. Proof by contradiction for the purpose of showing such a +statement true, i.e., that any particular tentative counterexample contained an +inherent contradiction, is not itself universally accepted, due to not necessarily +being constructive \cite[p. 2]{bridges2007did}. We also found in our data, several versions +of misunderstanding inequalities. We found support in literature for errors of +misunderstanding how to work with inequalities, by students of this level\cite{Mattuck}. +\section{Proof by Induction} +We were encouraged by the overlap in description among interview participants. +The interviews were certainly not the same, but common elements, +specifically that there is a form to proofs by induction, appeared. Some students +referred to this form as steps, others as a procedure, or framework. Moreover, +degrees of understanding filled in a spectrum, from joyful deep understanding +to admissions of not understanding why the steps of proof by induction prove +anything, and conceptions in between. These included a supposition why a +proof of an induction step would, in combination with an established base case, +constitute a proof by induction, that its originator characterized as ``weird''. +\section{Domain, Range, Mapping, Relation, Function, Equivalence +Relation in Proofs} +\section{Definitions, Language, Reasoning in Proofs} +\section{Equivalence Class, Generic Particular, Abstraction in Proofs} +Using an analogy, I claim, is saying there is a set of relations among things $a_i$ that +we agree upon, furthermore, I might wish to teach that there is a corresponding +set of relations among things $b_i$. I might wish to say, use the relation we agree +upon for municipalities provide addresses for homes that can be used for +surface mail, and I might wish to teach that there is a corresponding provision +of addresses for items a computer programmer might wish to use for storage +and recall. We can note that addresses make use of a hierarchy of place names, +countries, states, cities, streets, street numbers, apartment numbers. We can +note that structured data types can correspondingly make use of instances and +fields and indices that can be arranged in a tree. +In the absence of abstraction, the surface mail address hierarchy might not pose +much more difficulty, but the data structure might, because the fields therein +are more subject to change than municipalities. In the absence of abstraction, +the comparison between one hierarchical arrangement with another would be +more difficult, because it is the structure of the abstraction itself, namely, the +choices of features regarded as significant throughout the tree, that is to be +recalled and used as a scaffold for the new information. +``An alternative pathway towards abstraction involves recognizing an analogy +between two structures in different domains, which then focuses one's attention +on the abstract structure they share. This new abstraction then becomes a +’concrete’ concept that one can study'' \cite [p 449]{}. +\section{Vertical Integration and Explanation} +It is accepted that, in discrete math, it is helpful to work problems. We may +inquire, what is it about working problems that helps? We can, at the neurophysiology +level, expect that long term potentiation of synapses, for the +synapses collocated with the long term memory for the concepts in the problem, +is being carried out, as the thinking about the problem occurs. We can +recall that a sense of reward, as might be gained from success at a problem, +or pleasantness in a problem statement, helps consolidate the memory for the +ideas that have been gained. We can recall that depression resulting from +avoidance of sadness at failure to solve a problem reduces the ability of the +hippocampus to support the formation of long term memory. We can, at the +cognitive neuroscience level, expect that the opportunity for like structures to +be recognized occurs, and analogies, are made, and the abstraction hierarchy of +concepts related to the problem is remodeled, extended, to more closely mirror +the mathematical definitions being used. We can, at the phenomenography +level, suppose that fine distinctions between concepts will be more likely to be +noted, because the mental structures that support these are forming. We can, +at the computer science education level, consider how to bring activity into +lecture, that poses the analogies and distinctions we wish the student to gain, +by varying the examples of the concepts such that a representative example +is contrasted with a non-example, in an ambience that fosters curiosity and +rewards progress. +\section{ Validation} +We draw a connection between epistemology and validation. Epistemology +is why we believe what we believe. Thus, it makes sense to apply our epistemological +framework to explain why we believe what we believe about our +results and interpretation. +Our epistemology is informed by the work of others over a wide range of disciplines: +Computer science education, mathematics education, and education +generally, especially phenomenography. Cognitive aspects, including memory +and attention, are shared by and form a bridge between phenomenography +and cognitive neuroscience. Neuroscience provides interesting relevant information. +Ira Black, MD, in [?, ?, [p 40] ``A satisfactory mechanistic description of any +well-framed cognitive process requires that we simultaneously explain it at +multiple levels of analysis. Different levels provide complementary insights +to characterization and causality that are unobtainable from any single line of +analysis.'' +\subsection{Validation at the Level of Computer Science Education} +Interviews with computer science educators, both instructors and teaching +assistants have provided a diversity of viewpoints, and generally support the +interpretations we have given. For example, one instructor, when asked what +students thought proofs were, said ``some kind of magic incantation'', and +teaching assistants have said ``students really struggle with this''. +\subsection{Validation at the Level of Mathematics Education} +The literature of mathematics education includes work on students' learning +about proof. Our work with computer science students has had the benefit +of some students who are dual majors of math and computer science, which +has allowed us to trace the similarities and differences of these cohorts of students. +The significance of definitions, the necessity and utility of proof, the role +played by interest in forming procedures and functions, the difference between +functional and procedural programming have differed in these three cohorts, +in so far as we have been able to examine. We did not explore the interest in +developing procedures/functions or procedural or functional programming in +mathematics majors who were not also computer science majors. + + + +\subsection{ Validation at the Level of Phenomenography/Variation Theory} +Variation theory supports our observation that comparing and contrasting fine +distinctions in material being taught aids the process of learning. We used +the difference between assignment and equality testing, manifest in the java +expression of ``=='' vs. ``=''. We compared a software procedure representation +with a mathematical formulation (the latter using only ``=''), for comprehensibility +by students. This helped us to see that barriers to student understanding +exist, for some students of computer science, at the level of formulation. It also +helped us see that the barrier between the internalization and interiorization +of Harel and Sowder might be less of a barrier in students of computer science +who are routinely conscious of the need to analyze procedures. +\subsection{Validation at the Level of Cognitive Neuroscience} +Many students have expressed an interest in learning from examples, and researchers studying students' acquisition of the ability to prove have observed a category for concepts called ``perceptual'' where students mistakenly believe or hope, that examples constitute a proof (of universality). Valiant points out two cases where examples are very effective in learning: +when on may employ elimination when the concept to be learned is a conjunction and an exemplar exhibits a variable in negative form, it is clear that that variable is not needed for set membership. +When a concept is a disjunction any variable that appears in positive form in a negative example is shown to be insufficient to guarantee membership. + +Valaint [p. 171] Humans do not argue readily from the contrapositive. +P.C. Wason 1983 Realism and rationality and the selection task. Thinking and Reasoning: Psychological Approaches Evans, ed., Routledge + + + +Valiant, in Circuits of the Mind [] that an ``important class that is not currently +known to be learnable is disjunctive normal form (or DNF for short)\ldots This +appears to be a most natural generalization of simple conjunctions from the +viewpoint of modeling human concepts. It can express the idea that examples +of a concept fall into a number of somewhat distinct categories, each corresponding +to noe of the conjunction. When discussing inductive learning we +have a \textit{hierarchical} context in mind. If we wish to learn DNF formulae, but do not +have an algorithm for learning these direction, we can nevertheless attempt to +learn these in stages. For example, to learn $x_1x_2 \land x_2x_3$ we could first learn the +simple conjunctions $x_1x_2$ and $x_2x_3$ separately in some fashion. Having learned +these we can learn the DNF when learning hierarchical in this way more is +required of the teacher or environment than in the simplest case of learning +by example. Somehow the subconcept $x_1x_2$ must be learned separately in supervised +or unsupervised mode. In the former case, for example, a teacher +may have to teach the name of this subconcept in unsupervised memorization +mode and then identify positive or negative examples of it so that it is learned +in supervised mode inductively. Alternatively, this subconcept may be learned +in unsupervised mode either by memorization or be correlational learning. `` +Valiant has written\cite{this is in a separate pdf} that the hippocampus is likely to be the location where the allocation of new memory locations is carried out. + +Valiant has observe that, given a set of concepts that can be hierarchically related, in the absence of hierarchy, when instead the concepts are flattened out, it is more unwieldy to make analogies, such as $A^B$ is analogous to $C$. +This is supportive of our interpretation of student data, in which we suggest that students who +find abstraction challenging, will in turn find remembering and using definitions more challenging, and will be at a disadvantage in terms of advancing to definition-based axiomatic reasoning. + + + + +\subsection{ Validation at the Level of Neurophysiology} +(Says who?) suggests that memory for events that are observed through one sensory modality are stored near the nervous tissue that process the input for that modality. +This is supportive of our interpretation of student data, in which we suggest that students who + learn proof by mathematic induction, represented symbolically, and recursive algorithms, represented pictorially, do not always ``see'' the analogy right away, because the memory traces are not activated at the same time. +When considering the two topics at the same time in discussion, both ideas are recalled, corresponding to metabolic activity in the memory (possibly tow different, separate, regions) facilitating formation of connection between the two ideas. +From Chapter 18 Migration in the Hippocampus, of Cellular Migration and Formation of Neuronal Connections: Comprehensive Developmental Neuroscience Vol 2, 2013, Elsevier ``the proliferative subgranular zone located at the border between the granular cell layer and the hilus, which serves as the major site for persistent neurogenesis in the adult hippocampus'' ``one of the more unique aspects of hippocampas development is the formation of the dentate gyrus, which involves formation of a specialized neural stem cell niche.'' ``hippocampus harbors neural circuitry essential for learning and memory {Lisman 1999} relating hippocampal circuitry to function neuron'' ``Cajal-Retzius cells \ldots somewhat penetrate the boundary but tend to avoid invading into olfactory cortex of olfactory bulb Bielle et al. 2005'', maybe +``signalling pathways \ldots regulate the redial glia-guided migration in the neocortex'' p.335 (not only during development) +0.339 nice graphic for germinative layers (was that supposed to be p.339?) +persistent neurogenesis in adult hippocampus Altman and Bayer 1990 Migration and Distribution percursors Comp Neurol subgranular zone Li et al. 2009 neurogenic zone Li and Pleasure 2005 Morphogensis of Dentat gyrus + + +% % % % % % % % % % % % % % % % % % % % % % +% % % % % % % % % % % % % % % % % % +\section{Validity and Reliability} +We checked for internal consistency and reinforcement, and for external compatibility +of our findings with existing educational literature in computer science +and in mathematics. We noted the phenomenological work of Gian-Carlo +Rota \cite{rota1997phenomenology} who has reported that memory for mathematical proof and its elements +is noticeably improved when a proof is deemed to be beautiful. We were encouraged +by the overlap in description among interview participants. In the +literature of mathematics education, we found researchers [?] reporting quite +similar conceptions of proof by mathematical induction in students of mathematics. +In the literature of computer science education we found research \cite{booth1997phenomenography} +on a different topic, but with similar results. Booth reported categories of +conceptions of recursion similar to our categories of conception of proof by +mathematical induction. +\section{Researcher Bias and Assumptions} +Researcher Bias and Assumptions +strategies for trustworthy, valid, reliable +what about generalizability? %(e.g., to people with ASD) +\subsection{Proofs Using the Pumping Lemma for Regular Languages} +The author believes diagrams aid the abstraction process. The researchers +tend to believe that students want to learn, and will try to comprehend and to +become able to apply the material, and that the limitations temporarily present +in the student can be overcome by explanation and practice. +\subsection{Proofs by Induction} +\subsection{Domain, Range, Mapping, Relation, Function, Equivalence Relation +in Proofs} +\subsection{Definitions, Language, Reasoning in Proofs} +\subsection{Equivalence Class, Generic Particular, Abstraction in Proofs} + +\subsection{Assessing Validity} + +The results have bridged papers in computer science education, by Professor Booth\cite{}, and mathematics education, by \cite{}. + +The results have been consistent with results of others in mathematics education. + +% % % % % % % % % % % % % % % % % % % % % % % % % % % +% % % % % % % % % % % % % % % % % % % % % % % % % % % % +\section{Validity} +By choosing a varied population we hoped to obtain transferable results. + +We compared our results with existing publications. + +We performed a little triangulation by using multiple views into the student population: interviews and tests. We also compared the results from this with information obtained in tutoring and larger help sessions. We consulted faculty, who had experience with teaching this material, and who had experience with students who were supposed to have learned this material in prerequisites. + +% % % % % % % % % % % % % % % % % % % % % % % +\subsection{Assessing Validity} + +The results have bridged papers in computer science education, by Professor Booth\cite{}\cite{booth1997phenomenography}?, and mathematics education, by \cite{}. + +The results have been consistent with results of others in mathematics education. diff --git a/ch9.tex b/ch9.tex new file mode 100644 index 0000000..0945d42 --- /dev/null +++ b/ch9.tex @@ -0,0 +1,1152 @@ +\chapter{Related Work} +Maybe I want to put this in the order of definition, relationships, specialization, symbolization, analogy, generalization/abstraction +\section{Goal Definition} +Schoenfeld gives this expression of a goal for instructors teaching proof: He states that mathematics literature includes ``knowledge and perspectives of world-class mathematicians vs. more or less ordinary PhDs''\cite[p. 74]{schoenfeld1998reflections}. Do we have such characterization for computer scientists? If so, what are these characteristics that are relevant for computer science students, and what projection do these have into students' conceptualizations? + + \section{Methods} +Archavi et al.\cite[p. 4]{arcavi1998teaching} report using microgenetic analysis, which they describe as having roots in both cognitive science and ethnography. +``Schoenfeld, Smith and Arcavi\cite{schoenfeld1993learning} describe it as striving 'for explanations that are both locally and globally consistent, accounting for as much observed detail as possible and not contradicting any other related explanations'''. +Schoenfeld is, among other categorizations, a cognitive scientist, and uses this knowledge to inform his teaching.Archavi et al.\cite[p. 4]{arcavi1998teaching} . + +Research on teaching and learning about proof in mathematics education has +produced an extensive literature. Only a small sampling is mentioned below. +Mathematics educators, including Keith Weber[?], Harel and Sowder in +1998[?], and David Tall[?] have studied students' learning of proof in the mathematics +curriculum. Leron, in 1983, [?] has described the structural method +for proof construction, attributing it to recent ideas from computer science. +Lamport, in 1995, [?] in work on proof construction, has given one approach +that computer science students might find compatible with their background. +Velleman, in 2006, has written software and a textbook [?] about proving with +a structured approach. Weber has reported the success of several approaches +to pedagogy [?]. +Barnard [?] has commented upon students negating statements with quantifiers. +Edwards and Ward [?, p. 223] have discussed the role of definitions for undergraduate +mathematics courses, stating ``the enculturation of college mathematics +students into the field of mathematics includes their acceptance and +understanding of the role of mathematical definitions''. Bills and Tall [?] have +distinguished student understanding of definitions that is sufficient that the +student can use them in proofs. +Harel and Sowder [?] and Harel and Brown [?] have conducted qualitative +research on mathematics students' conceptualization of proofs. They have developed +three main categories, each with several subcategories. Evidence from +our studies is consistent with the presence of these categories of conceptualizations +in the population of CS(E) students. +Tall[?, ?] has also categorized mathematics students' understanding of proof. +He has studied the development of cognitive abilities used in proof, starting, +as did Piaget,[?] with abilities believed present at birth. +Yang and Lin have modeled reading comprehension.[?] +Leron[?] has written about encouraging students to attend to proof structure +by teaching with generic proofs (proofs that use a generic particular). +Mejia-Ramos et al.[?] have built a model for proof comprehension. They have +observed that students who are assessed on appreciation of structural and +other appropriate features of a proof, rather than on rote reproduction, are +more likely to develop a deeper understanding of proof. +Knipping and Reid[41] have examined proof in mathematics education. +Weber[?, ?, ?, ?, ?, ?, ?, ?, ?] has investigated students' approaches to and difficulties +with proof. When studying student proof attempts in group theory, Weber +has found that some typical students' inabilities to construct proofs arise despite +having adequate factual and procedural knowledge, the ability to apply that +knowledge in a productive manner was lacking. [?] More specifically applying +the knowledge was seen to include selecting among facts, guided by knowledge +of which were important, for those most likely to be useful. [?] Alcock +and Weber,[?] have studied students' understanding of warrants, the support +for the use of a particular inference. Weber has published a framework for describing +the processes that undergraduate students use to construct proofs. [?] +Almstrum[?] has investigated the understanding of undergraduate computer +science students of problems related to logic, compared to problems only +weakly related to logic, and has shown that some students have trouble with +the notion of truth or falsity. +Healy and Hoyles[?] have reported on algebra students' preferences for the +content of convincing arguments, and their distinction between preferences +for ascertaining vs. preferences about what was likely to be well-received on +assessments. +{\.I}mamo{\u g}lu[?, ?] has studied the conceptualizations of proof of students who +were preparing to become mathematics and science teachers, in their freshman +and senior years. +Knuth has applied qualitative research to the conceptualizations of proof by +high school mathematics teachers [?, ?]. +Because our work with proof also has explored the consequences for the student +in terms of algorithm choice, including recursive algorithms with proof +by mathematical induction, the work of Booth[?], who has used phenomenography +to develop a model of students' understanding of recursive algorithms +is related. +Zhang and Wildemuth[?] have described qualitative analysis of content. +\section{ Proofs Using the Pumping Lemma for Regular Languages} +Mattuck[36] states ``analysis replaces the equalities of calculus with inequalities: +certainty with uncertainty. This represents for students a step up in +maturity.''[page xiii] and ``these are things which I find that many of my students +don't seem to know, or don't know explicitly. They subtract inequalities +\ldots ``. +\subsection{Quantifiers} +In 2010 Pillay [44] asserted that ``there has been no research into the actual +learning difficulties experienced by students with the different topics'' in formal +languages and automata theory. Of the pumping lemmas, Pillay states ``A +majority of the students made logical errors when proving that a language +is regular and using the Pumping Lemma to show that a language is nonregular. +These could be attributed to a lack of problem-solving skills and an +understanding of the Pumping Lemma.'' Devlin[18] observes that quantifiers +can appear daunting to the uninitiated, and that statements containing multiple +quantifiers can be difficult to understand. +\subsection{ Symbols} +H\"uttel and N{\o}rmark[45] described a successful method for improving both +student activity level in the course and final grades, which combines peer +assessment with creation of notes that can be used during the exam. (``The +incentive was that their answers to text (CHECK) questions would be available for them +to use at the written exam. No other textual aids would be allowed at the +exam.''[p. 4]) The better performance on the exam is welcome; whether it is +due to having notes compared to closed book, or having performed the review +might not be certain. +According to Arnoux and Finkel[46], it is not unusual for students to acquire +mathematical knowledge without attaching meaning to it, and leaving them +unable to solve some problems. They go on to report that Paivio proved +that ``double coding (verbal and visual)'' facilitated remembering. They also +report that different parts of the brain are used to process verbal and visual +information, and therefore more of the brain is involved when both verbal and +pictorial communication is used. They prefer multi-modal representations. +Xing[47] writes about aiding students comprehension of proofs being aided by +graphs. She reports ``students feel that Pumping Lemma(PL) is so abstract to +grasp that using it to prove that a language is non-regular is a daunting task.'' +She shows a graphically laid out proof that a given language is not regular. This +graph has the advantage over a traditional proof, i.e., a sequence of statements, +that the dependencies of states on axioms or intermediate results are plainly +shown by graph edges. +Simon et al.[43] ask ``Is it possible that students plug and chug in computing, not +really understanding the concepts as we would like them to?'' and go on to say +``We posit that the need exists for computing instructors to design assessments +more directly targeting understanding, not just doing, computing. And, of +course, to adopt teaching approaches that support student development of +these skills.'' +Mazur[25] developed peer instruction to address students' propensity to practice +a plug-and-chug approach to problems. This approach has been applied +to computer science teaching, including theory of computation, by several researchers +including Simon, Zingaro, Porter, Bailey-Lee and others[48, 49, 50, +51, 27]. +\subsection{Teaching Pumping Lemmas} +In 2003 Weidmann[39] wrote a dissertation on teaching Automata Theory to +students at the college level. She found that past performance in prerequisite +theory courses was a statistically significant indicator for success in their college +level course. She described a theoretical framework called ``pedagogical +positivism'', a stance between logical positivism and constructivism, allowing +the notion of a teaching method best suited to a group of students to learn Automata +Theory. She interviewed a teacher with ``several'' years of experience +teaching this course (p. 5), who ``admitted that she did not have a better way +to teach abstract thinking other than repeated exposure'' (p. 98). +In chapter 5, Discussion, Conclusions and Implications, of this dissertation[39], +the suggestion ``Instead of simply providing the solution to a problem in class, +or stating the intuitive leap that makes the problem easy to solve, the students +should be exposed to the iterative thought process that lead to the intuition +that created the solution.''(p. 201) appears. One suggestion is ``Learning objectives +should be set to focus on familiarity with formalisms and rigorous +mathematical notations” (p. 224) and another suggestion is “Include programming +projects as part of the required coursework''(p. 224). The combination +of these brings to mind the suggestion of Harel and Papert[40]: ``constructing +personally designed pieces of instructional software'', and the thought that the +students might dwell more effectively on the notion of abstraction as they tried +to teach someone else about it. +\section{ Proof by Induction} +Kinnunen and Simon [7] describe an example applying phenomenography to +computing education research, listing several recent examples, and also providing +a detailed description of a mainly data- but also theory-driven refinement +of categories. +Berglund, Eckerdal and Thun\'e [16, 3, 4] have applied phenomenography to +computing education research, obtaining classifications by judicious grouping +of student conceptions derived from interview data. Eckerdal et al. [4] describe +how the results using phenomenography showed additional insights beyond +other methods. +Jones and Herbst [6] considered which theoretical frameworks might be most +useful for studying student teacher interactions in the context of learning about +proofs. Bussey et al. [2] illustrated student teacher interactions in the space of +learning, and the objects of learning, in variation theory, modified from the +model of Rundgren and Tibell [13]. +Reid and Petocz [12] used phenomenography to study students' conceptions +of statistics. Their purposes included to ``enable teachers to develop curricula +that focus on enhancing the student learning environment and guiding +student conceptions of statistics.'' They asked students to describe how they +understood statistics and then organised student responses into a hierarchy of +conceptions. They used interviews to understand individual students, and the +group of interviews to show the variations they found. They found the students with the most superficial understanding to be carrying out steps without +knowing their meaning. +Krantz [8] describes proof by induction, giving several examples in this book +of proof techniques for computer science. +\section{Domain, Range, Mapping, Relation, Function, Equivalence Relation in Proofs} +Marilyn Carlson, \cite{carlson1998cross}shows that we can easily expect too much from our students in terms of what they understand of functions. This has significance for what we think are adequate examples to use for proof by mathematic induction, for example. +\section{ Definitions, Language, Reasoning in Proofs} +Weber, Alcock, Knuth +\subsection{Procedural vs. Understanding} +Is it that Tall and bifurcation are about learning the procedural vs. understanding approach to dealing with proof? +There are indications\cite[p. 18]{loewenberg2003mathematical} that mathematics teachers in grade school and high school who were mathematics majors themselves learned a procedural approach to mathematics and "lacked an understanding of the meanings of the computational procedures or of the solutions. Their knowledge was often fragmented, and they did not integrate ideasthat could have been connected (e.g., whole-number division, fractions, decimals, or division in algebraic expressions.)" +\subsection{Recall of Relevant Information vs. Inert Knowledge} +Bransford et al.\cite[p. 296]{bransford2000designs} attempt to address the problem identified by as inert knowledge (in the sense of Whitehead\cite{whitehead1959aims}). They situated class activity in a problem solving environment, and they showed\cite{van1992jasper} that this instruction had better results for students' ability to transfer skills to new word problems than traditional instruction. + +Lehrer et al. \cite[p. 334]{lehrer2000inter} found that "at least in some circumstances, giving children models may be less helpful than fostering their propensity to construct, evaluate, and revise models of their own to solve problems that they consider personally meaningful." + +\section{Abstraction} +Lesh and Doerr\cite{lesh2000symbolizing} used model-eliciting to engage students in the creation of a combination of meaningful descriptions, explanations and procedures. These models were recognized as tools to be shared and reused, consequently the idea of generalization was implicit. Lesh and Doerr argue that by illuminating the idea of a tool that may be reused, they divide the problem of teaching generalization into two parts: making a general model, and discerning its domain of applicability. + + +Kemmerer\cite{kemmerer} + +According to Huang et al.\cite{huang2015highest}, a large body of research suggests that an abstract cognitive processing style produces greater creativity. Empirically, decades of work have shown that both abstract thinking and creativity are consistently linked to right-hemispheric activation in the brain (e.g., Fink et al., 1996\cite{fink1996brain} and Mihov et al., 2010\cite{Mihov2010442}). +Miron-Spektor et al.\cite{Miron-Spektor20111065} have shown that observing anger communicated through sarcasm enhances complex thinking and solving of creative problems. + +(We want to know, do they understand deduction, abstraction, where are they on van Hiele levels ) + +According to Gray and Tall \cite[p. 117]{gray1994duality}, Hiebert and Lefevre observed ``a connected web \ldots a network in which the linking relationships are as prominent as the discrete pieces of information \ldots a unit of conceptual knowledge cannot be an isolated piece of information; +by definition is it part of conceptual knowledge only if the holder recognizes its relationship to other pieces of information ``\cite[p. 3-4]{hiebert2013conceptual} +conceptual knowledge is harder to assess than other kinds of knowledge. + +\section{Diagrams in Proof} +Gibson\cite{gibson1998students} examined students' use of diagrams in proofs, and found that diagrams helped link students' ideas to mathematization, namely, to representation in symbols, and also to support variation, in the sense of the critical difference between what Harel and Sowder\cite{harel1998students} call perceptual and transformational conceptualizations. +\section{Equivalence Class, Generic Particular, Abstraction in Proofs} +\section{Computer Science Education} +Thun\'e and Eckerdahl\cite{thune2009variation} have applied variation theory has been applied to the teaching of computer science. + + +\section{Educational Psychology} +\subsection{What do students need to construct?} + +Archavi et al.\cite[p. 13]{arcavi1998teaching} ``I'd like to have you doing some mathematics and I will do everything I can --- including using grading --- as a device for having you do that.'' + +\section{Phenomenography, Variation Theory} + +Marton and Booth\cite{marton1997learning} have written + +{\aa}kerlind \cite{aakerlind2012variation} has written on how + +Runesson\cite{runesson2005beyond} has applied variation theory to math + +\section{Constructivism} + + + +Vygotsky in Language and Thought said we do as individuals build up thoughts and then becoming socialized with shared language, some accommodation would need to be enforced onto the child. [p.17] the psychological problem is to become convinced that always, necessarily a given picture has to appear as one of a multiple of possible graphs of the same category (i.e. only as a representative of a class \ldots must be grasped not in a final fixed state but rather \textit{in construction} the point moving) + +Vygotsky\cite[p. 49]{vygotsky1978mind} noted that "one child selected a picture of an onion to recall the word 'dinner'. When asked why she chose the picture, she gave the perfectly satisfactory answer, 'Because i eat an onion'. However, she was unable to recall the word 'dinner' during the experiment. This example shows that the ability to form elementary associations is not sufficient to ensure that the associative relation will fulfill the \textit{instrumental} function necessary to produce recall." + +\subsection{What do students need to construct?} + +Archavi et al.\cite[p. 10]{arcavi1998teaching} ``To be successful, students must know both the appropriate heuristics and the mathematics required to solve the problem. +\subsection{Intuition} +Students have some knowledge constructed already, and it is not all conscious. + +overconfidence --- counter by ``search for reasons it might be wrong'' Koriat et al., 1980\\ +confidence --- doesn't correlate with correctness\\ +be as to conform Tweney Doherty Mynatt 1981\\ +``renouce several of his funcamental beliefs with regard to reality'' [p. 39]\\ +$$ Combine desire to gain points having taken the place of desire to learn, with propensity to learn how to take tests rather than how to believe, and obtain ``How we answer the tests, or, what we really think'' $$ +Piaget (Piaget-Beth 1966 [p. 195] ) ontogenetic construction of evidence a new domain integrates former domain as subdomain\\ +(n heast?) intuition tends to survive even when contradicted by systematic formal instruction [p. 47]\\ +Polanyi 1969 [p. 143-144]\\ +\ldots in the structure of tacit knowledge we have found a mechanism which can produce discoveries by steps we cannot specify this mechanism may then account for scientific intuition \ldots not the supreme immediate knowledge called intuition by Leibnitz or Spinoza or Husserl, but a work-a-day skill for scientific guessing with a chance of guessing right.\\ +Polanyi sees a deep analogy between integrative capacity +$$ there we have ``unsupervised'' specialization network formation during consolidation, perhaps $$ ``Where to turn for a logic by which such tacit powers can achieve and uphold true conclusions'' Polanyi 1967 [p. 137]\\ +$$I'm thinking about conscious / unconscious$$ +$$ When we do something consciously we can be checking, when we do something unconsciously, we might not be $$ +Fischbein [p.59] ``Inferential affirmatory intuition may have an inductive or deductive structures. After one has found that a certain number of elements (objects, substances, individual, mathematical entities, etc.) have certain properties in common one tends \textit{intuitively} to generalize and to affirm that the \textit{whole} category of elements possesses that property. This is not a mere logical operation. +The generalization appears more of less suddenly with a feeling of confidence. +This is a fundamental source of hypotheses in science. +According to Poincar\'e ``generalization by induction copied, so to speak, from the proedures of experimental sciences'' is one of the basic categories of intuition (Poincar\'e 1920 [p. 20]).\\ +\cite[p. 67]{fischbein1987intuition}(check) ``One morning walking on the bluff, the idea came to me with just the same characteristics of brevity, suddenness and immediate certainty that the arithmetical transformation of indeterminate ternary indefinite forms were identical to those of the non-Euclidean geometry Poincar\'e 1913 [p. 388]''\\ +David Tall mathematician and psychological analyst, moment of insight ``never felt that he made 'conjectures'; what he say were 'truths' evidenced by strong resonances in his mind. Even though they often later proved to be false, at the time he felt much emotion vested in their truth \ldots intense intuitive certainties. Yet at the same time his contact with them often seemed tenuous and trasient; initially he had to write them down, even though they might be imperfect, before they vanished like ghosts in the night (Tall 1980 [p. 33])\\ +$$ being unconscious seems to go with consolidation. Either unconscious because attending to something else like walking on a bluff, or asleep, being unconscious is relevant to these integration occurring and then moving into consciousness $$ + +$$''Really wants to know'' implies an openness to change the pre-determined ideas, and ``complyig with requriements'' does not imply readiness to revise $$\\ +\cite[p. 68]{Fischbein} citing Feller ``experienced player absorbs a complicated situation at a glance and is unable to account rationally for his intuition''\\ +$$ it (the part of the brain doing the reasoning) is functioning without conscious oversight (the neurons that did that when the capability was new have been deemed extraneous and removed)$$) +$$Brooks -- the first system is done carefully with all consciousness like the beginning chessplayer in Feller, the second system has some unwarranted conviction and the third system has mostly warranted $$\\ +\cite[p. 69]{Fischbein} Felix Kelin (1898) trained intuition\\ +Suppes 1966 train the intuition for finding an writing mathematical proofs''\\ +\cite[p. 72]{Fischbein} categorical syllogism type AAA seems easiest for which, EAE, AII 65\%, EIO +(These are categorical syllogism types. See www.philosophypages.com/lg/e07a.htm) +\cite[p. 77]{Fischbein} +AAA and modus ponens come earliest and are class inclusion, maybe $\bar{p} \rightarrow q$ never develop\\ +re \cite[p. 81]{Fischbein}, $$ people have data stored to supply their intuition and it our be wrong education involves opening it up to conscious inspection, fixing it, and restoring the rapid unconscious operation $$\\ +\cite[p. 106]{Fischbein} citing \cite[p. 228]{Wertheimer 1961} ``These thoughts did not come in any verbal formulation. I very rarely think in words at all. T thought comes, and I may try to express it in words afterwards''. Einstein\\ +\cite[p. 119]{Fischbein} A total fusion of the generality of a principle and a particular directly graspable (in this case figural) expression of it. It is this kind of fusion which is the essence of intuition.\\ +\cite[p. 120]{Fischbein} specific, directly convincing example and the general principle derived through similarity and proportionality from the particular case.\\ +\cite[p. 129]{Fischbein} Analogy frequently intervenes in mathematical reasoning, Polya writes about great analogies \\ +138 1985 software by David Tall\\ +\cite[p. 144]{Fischbein}ways in which people process concepts Smith Meliss 1981\\ +\cite[p. 147]{Fischbein} ``For many students the concepts of parallelogram, square and rectangle are not organized hierarchically. They represent classes of quadrilaterals of the same generality''. +$$ some programmers before unified method were guilty of writing code this way, with wasteful effect. Moreover, Liskov Substitutability Principle was enunciated to help people know how to populate hierarchies when they were learning to do so. Students who are not organizing their concepts hierarchically are similarly disadvantaged. As I believe this hierarchical situation is consolidated during sleep or relaxation, ti becomes a research question$$ +\cite[p. 159]{Fischbein} analogies already similar diagram post concept\\ +\cite[p. 165]{Fischbein} diagram relies on intervening structure (conceptual structure) else it does not communicate\\ +stability of intuition, Ajzen? 1983 epistemic freezing\\ +\cite[p. 214]{Fischbein} concept of intuitive loading --- have to know students first before knowing how to teach them + + +Intuition in Science and Mathematics An Educational Approach Efraim Fischbein 1987 Reidel Publish +Westcott combines theoretical analysis with experimental findings. +Andrea di Sessa building a theory of intuition +Bergson 1952 essence of lining changing phenomena +Kant intellectual (does not exist) and sensible intuition +1980 [p. 268] + +Poincar\'e useful +Hahn 1956 source of misconception +to use or to eliminate? +Berne professional quality work without awareness says Westcott 1968 [p.42-46] +immediacy --- is that because crosses into conscious unconscious\\ +consistency, brevity of expression $\rightarrow$ bearty +if the result of the brain's consolidation of knowledge, info, into uncouscious knowledge, usable, available for recall +going into intuition, what you taught us for the test, or what we really think +Fischbein p. 9 ``One may not be aware of the existence of such an explicit representation but it continues to act tacitly and to influence ways of reasoning. + +Seymour Papert 1980 apparently says something about intuition + +Brouwer, Weil, Kline 1980 [pp 306-327] + +The sum of the angles of a triangle is equal to two right angles'' +Connect bewteen intuitino and reasoning +\subsection{Social Constructivism} +Archavi et al.\cite[p. 6]{arcavi1998teaching} ``Students' mathematical activity takes place in an inherently social milieu.'' +\subsection{Tall: Set-befores and Met-befores} +McGowan and Tall \cite[p. 172]{ (2010 Jour. Math. Behav.)} ``If learning defaults to the goal of learning how, it can be successful. However, if it is accompanied by a lack of conceptual meaning so that mistakes occur, it can become fragile and more likely to fail in the longer term. At this stage the problems may proliferate as the student becomes confused as to which rule to use, where to use it, and how to interpret it. + +Tall and Mejia-Ramos \cite[p. 138]{2010, Explanation and Proof in Mathmatics, Springer} ``Here proof develops through generalized arithmetic and algebraic manipulation'', +different kinds of warrants for truth $$ so assess student by asking what kind of warrant$$ see Pinto and Tall (1999 and 2002) build on met-befores. +\begin{figure}[tbph] +\centering +\includegraphics[width=0.7\linewidth]{chp7p1} +\caption{How proof develops, Tall Mejia-Ramos} +\label{fig:chp7p1} +\end{figure} + +\subsection{Harel and Sowder} + + \cite[p. 237]{harel1998students}Rather than gradually refining students' conception of what constitutes evidence and justification in mathematics, we impose on them proof methods and implication rules that in many cases are utterly extraneous to what convinces them. +Editors Schoenfeld et al.\cite{kaput1998research} describe that Harel and Sowder\cite{harel1998students} ``characterize students' cognitive schemes of proof''. + +The subdivisions in the 1998 version of categories of conceptualizations \cite{harel1998students}, specifically intuitive -- axiomatic, structural and axiomatizing, +matter much in computer science, because intuitive -- axiomatic could be thought to be less used in computer science than in math, program's content could be less intuitive than Euclidean geometry, more subject to checking by assertion checking or debugger examination. + + \cite[p. 268]{harel1998students} contextual proof scheme: --students have learned to work in a context, e.g., $\mathbb{R}^n$, and so, interpret statements that have greater generality as restricted to be in the context they have learned ``he or shee has not yet abstracted the concept \ldots beyond this specific context''. Compare this with Pang's (is it Pong?) observation that for students who know only one language, ``speaking'' and ``speaking that language'' are concepts that are undifferentiated. + + \cite[p. 274]{harel1998students} ``An important distinction between the structured proof scheme and the intuitive proof scheme is the ability to separate the abstract statements of mathematics (e.g., $1+1=2$) from their corresponding quantitative observations (e.g., 1 apple + 1 apple = 2 apples) or the axiomatically -- based observations from their corresponding visual phenomena \ldots ``, ``axiomatic proof scheme is epistemologically an extension of transformational proof scheme. One might mistakenly think of the axiomatic proof scheme is the ability to reason formally \ldots ``. + + \subsection{Pirie and Kieren Model of Mathematical Understanding} + \cite{meel1998honors} + Verify these are due to Pirie and Kieren rather than to Meel. + + \paragraph{Primitive Knowing} + This is brought by the student, and is also known as intuitive knowledge, situated knowledge, prior knowledge and informal knowledge. + \paragraph{Image Making} + any mental image not necessarily pictorial + \paragraph{Image Having} + mental picture / objects, concept image, frame, knowledge representation structure, students' alternative frameworks + \paragraph{Property Noticing} + unselfconscious knowing, can notice distinctions combinations connections between mental objects + \paragraph{Formalizing} + abstract (this is a verb) common qualities from classes of images, classlike mental objects built from noticed properties, description of these class-like mental objects results in production of full mathematical definitions + \paragraph{Observing} + ability to consider one's own formal thinking, organize personal thought processes, recognize ramifications, + \paragraph{Structuring} + axiomatic system, conceive proofs of properties associated with a concept + \paragraph{Inventising} + create new questions, develop new concepts + \paragraph{folding back} + reorganizing lower level understanding to accommodate new information + + +\subsection{van Hiele Levels} +Abstraction is before deduction +\subsection{Performance Levels} +Baranchik and Cherkas\cite{baranchik1998supplementary} found three levels of understanding in a population taking algebra exams: +\begin{enumerate} +\item Early skills --- arithmetic and elementary algebra +\item Later Skills --- subsequent algebra and a variety of skills involving methematical abstraction, and +\item Formalism --- either devising a solution strategy or reformulating a problem into a standard form that permits a solution using early or later skills +\end{enumerate} +\subsection{Student Centered} +Carlson\cite{carlson1998cross} has concluded that ``\ldots an individual's view of the function concept evolves over a period of many years and requires an effort of 'sense making' to understand an orchestrate individual function components to work in concert.'' +\subsection{Use of Diagrams} +Gibson\cite{kaput1998research} states ``Diagrams aided students' thinking by corresponding more closely to the part of their understanding with which they were operating at the time and by reducing the burden that proving placed on their thinking.'' +\cite[p. 205]{kaput1998research} The nature of internal representations, however, is unclear because they are not observable.: +$$ nature of internal representations can be broad, and we can perhaps influence the nature of internal representations, which are ultimately neural nets, by how we teach, and nature of internal representations is such that some, e.g., perceptual, are nto as helpful as others, e.g., transformational. Get the superior colliculus involved, see the motion Ties in with variation theory. Also visualization parts of brain.(B17?) $$ + +Winn, B, (get the citation from Gibson article in Kaput RCME 1998)( Charts, graphs and diagrams in Ed. materials Psych Illus Basic Research Vol 1 Springer 1987 pp. 152-198) has a spectrum for internal representations from pictures to works, the word end is called abstract. + +Zimmerman, Visual thinking in Calculus Visualization Teaching Learning Math 1991 +Gibson\cite[p. 132]{kaput1998research} ``There is no doubt that diagrams play a heuristic role in motivating and understanding proofs'' +Tall 1991 Intuition and rigor, role of visualization in teaching learning mathematics +Gibson\cite[p. 288]{kaput1998research} ``When student used visual language I inferred that they were operating with the visual part of their understanding'' +Gibson\cite[p. 289]{kaput1998research} ``Students indicated that diagrams helped them understand information by appealing to their natural thinking. They said that diagrams seemed to coincide with the way their 'minds work' and that information represented visually seemed easier or clearer than verbal/symbolic representations.'' +more concrete than verbal/symbolic +Gibson\cite[p. 290]{kaput1998research} ``used it to help me see what would be happening'' +$$ executive parts of brain is engaging visual parts of brain$$ +easier than holding the mental image is look at the drawn image +Gibson\cite[p. 291]{kaput1998research}''When I read the definitions you can't think about the whole thing at once, but when you have a picture you can'' +Gibson\cite[p. 294]{kaput1998research}''Because students did not usually think of their criteria in terms of formal definitions, their ability to decide whether their criteria had been met was hindered when they worked with information represented in only verbal/symbolic form.'' +``They could obtain ideas more readily from diagrams than they could from verbal/symbolic representations'' +Gibson\cite[p. 297]{kaput1998research} Why always keep the picture in your mind when you can have it on the paper, allowing you to focus more on how to get to the end of the proof instead of always having to recall the picture in each individual step?'' +$$visual rather than mirror area is possible$$ +Gibson\cite[p. 298]{kaput1998research} ``students sometimes used diagrams to help them express their ideas'' symbolically +$$compare proofs without words$$ +Gibson\cite[p. 298]{kaput1998research} ``diagrams helped Laura write out her ideas by helping her connect her ideas to verbal/symbolic representations of these ideas'' +Gibson\cite[p. 299]{kaput1998research}''you need to down load that picture on here so that you can touch it and then allow your brain to think about the words you need to say'' +visualization does not always help, Gibson quoted some sources +Gibson\cite[p. 302]{kaput1998research} ``when attempting to solve unfamiliar problems, students can benefit from using diagrams'' +Moore\cite[p. 262]{moore1994making} ``The students' ability to use the definitions in the proofs depended on their knowledge of the formal definitions, which in turn depended on their informal concept images. The students often needed to develop their concept images through examples, diagrams, graphs and others means before they could understand the formal verbal or symbolic definitions'' %[p. 262], Moore R Making the transition to formal proof Ed Studeies in Math 1994. +Gibson\cite[p. 303]{kaput1998research}''That students would operate in this manner (with the visual part of their concept images) and that such behavior might be of benefit is reasonable when one considers the nature of the concepts in the proofs together with the students' experiences as visual beings and the physiology of their brains''. + + +\section{Cognitive Science} +Archavi et al.\cite[p. 6]{arcavi1998teaching} Mathematics requires abstraction, and problems should inspire generalization and specialization. + + + +\subsection{Intrinsic Reward} +Archavi et al.\cite[p. 9]{arcavi1998teaching} Good problems are ``\ldots non-routine and interesting mathematical tasks, which students want and like to solve, and for which they lack readily accessible means to achieve a solution''. +\subsection{What do students need to construct?} + +Archavi et al.\cite[p. 13]{arcavi1998teaching} `` There were occasions later in the course in which the whole-class discussion also dealt with issues of mathematical elegance and aesthetics.'' + + +Leslie Valiant\cite[p. 103]{valiant2000circuits} points out that representations, for models of cognition, are not all equally learnable. +(in polynomially many steps, p. 104) +Easily learnable representations (of concepts) ``include Boolean conjunctions (e.g., $x_1 \land x_5 \land \bar{x_y}$) and Boolean disjunctions (e.g., $x_1 \lor \bar{x_3} \lor x_8$) \ldots An important class that is not currently learnable is disjunctive normal form (or DNF for short)'', (e.g., $x_1\bar{x_2}x_3 \lor x_1x_2 \lor x_2x_4x_7$), describes a concept whose membership can be attained in one of three ways, in two of which $x_2$ must b true, but in the other of which $x_2$ may be false, so long as $x_1$ and $x_3$ are true. +He goes on to observe these may be learned in stages, stating ``more is required of the teacher or environment than in the simplest case of learning by example'' [p. 104] +He uses the idea later clarified by Marton and Pang\cite{} stating ``a teacher may have to teach the name of this subconcept and then identify positive and negative examples of it'' [p. 104]. +`` In this context, learning theory can be thought of as defining the granularity with which learning can proceed without intervention \ldots the largest chunks of information that can be learned feasibly without their having to be broken up into smaller chunks'' [p. 104] +(Combine this with the approximately 7 chunks in short term memory?) + +Generalization and analogy are directly addressed in mathematics teaching by assigning students to ``search for connections and extensions of problems''\cite{santos1998instructional}. +\subsection{Analogical Reasoning} +Gentner and Smith\cite{gentner2012analogical} define analogical reasoning as "the ability to perceive and use relational similarity between two situations and events", and have stated that analogical reasoning is fundamental to human cognition. +They state that \cite[p. 131]{gentner2012analogical} ``Analogy is often the most effective way for people to learn a new relational abstraction; this makes it highly valuable in education.'' +Because we wish to obtain the value inherent in reasoning by analogy, we note that it depends upon recognition of relationships, and abstraction, to compare relationships at a level divested of some specifics. +Abstraction, for students of computer science, has been observed to be difficult to learn\cite{or2004cognitive} in that context. +Nevertheless, application of proverbs, such as "Don't cry wolf.", is routinely expected in education of children\cite{lutzer1988comprehension}. +Or-Bach and Lavy show empirical data and provide insight into the difficulties of computer science students who have trouble extracting common features from a problem statement that emphasizes differences, and promoting those to a more general class, while maintaining the differences in the more specific classes. +The relationship from one class to a related class in an inheritance hierarchy, motivated as it has been by code reuse, is more stereotyped than the relationships in proverbs, which are not restricted to generalization/specialization. So, we should be careful about generalizing the difficulty students of computer science have with abstraction. +Gentner and Smith go on to say\cite[p. 131]{gentner2012analogical} that analogical reasoning is characterized by retrieval, in which a current topic in working memory may remind a person of a prior analogous situation in long term memory; mapping, which involves aligning the representations and projecting inferences from one analog to another; and evaluation, which judges the success of the alignment of the representations and inferences. +Thus we see that the relationships are key in analogical reasoning, compared with being stereotyped in establishing inheritance hierarchies. +Gentner and Smith\cite[p. 133]{gentner2012analogical} remark that "Another benefit of analogy is \textit{abstraction}: that is, we may derive a more general understanding based on abstracting the common relational pattern." and "analogies can also call attention to certain differences between the analogs." +Though we might wish to have people readily retrieve knowledge that would, by analogy, be helpful to solving a current problem, Gick and Holyoak\cite{gick1980analogical} showed that people do not always retrieve the knowledge they have, rendering it, at least temporarily and for this purpose, what Alfred North Whitehead called "inert knowledge"\cite{whitehead1959aims}. +Gentner and Toupin \cite{gentner1986systematicity} have observed, however that, older children (and not younger children) benefited from systematicity: a summary statement of the structure of the relationships. There is a shift that can occur from focussing on objects to focusing on relatiohships, called a "relational shift", which has been the subject of research\cite{gentner1988metaphor,rattermann1998more,bulloch2009makes}. +Dunbar\cite{dunbar2000scientists} outlines three important strategies that scientists use: attention to unexpected findings, analogic reasoning, and distributed reasoning. Dunbar states\cite[p. 54]{dunbar2000scientists} "our analyses suggest that analogy is a very powerful way of filling in gaps in current knowledge and suggesting experimental strategies that scientists should use" and "If scientific reasoning is viewed as a search in a problem space, then analogy allows the scientist to leap to different parts of the space rather than slowly searching through it until they find a solution". + +Day and Gentner\cite{day2007nonintentional} showed in +Day and Gentner\cite[p. 41]{day2007nonintentional} +"Gentner and Medina proposed that +schemas and other abstractions are often derived via a +process of repeated analogizing over instances (see also +Cheng \& Holyoak, 1985)." + +\textbf{This, schemas and abstractions, earned a double question mark. Maybe that means it should be reported in more length.} +Day and Gentner\cite[p. 41]{day2007nonintentional}"The goal of this research was to investigate an important open question: Can a single prior instance influence how a new episode is understood, and if so, does it do +so by using a structurally sensitive mapping process, as +in analogy?" +Day and Gentner\cite[p. 42]{day2007nonintentional}"The results are consistent with the claim that individuals +may use a single prior instance as a source for nonintentional inference based on structural commonalities. The +pattern of inferences is what would be expected if participants were structurally aligning the two representations +and drawing inferences about the target from relationally +similar aspects of the base. Participants' responses that the +inferred information had actually been stated in the target +story suggest that these inferences were not deliberately +considered and evaluated, but rather were spontaneously +incorporated into the target representations as they were +being created." + +\subsection{Generalization} +Generalization is thought to result when multiple instances of analogies, sharing the same structure of relationships, have been considered. *who was I reading before kowatari?" + +Ball states\cite[p. 38]{loewenberg2003mathematical} "Generalization involves searching for patterns, structures, and relationships in data or mathematical symbols. These patterns, structure, and relationships transcend the particulars of the data or symbols and point to more--general conclusions that can be made about all data or symbols in a particular class. Hypothesizing and testing generalizations about observations or data is a critical part of problem solving." + +She continues \cite[p. 38]{loewenberg2003mathematical} "In one of the simpler common exercises designed to develop young students' capabilities to generalize, students are presented with a series of numbers and are asked to predict what the next number in the series will be. \ldots Representational practice play an important role in generalizing. For example, being able to represent an odd number as $2k+1$ shows the general structure of an odd number. \ldots Representing the structure using symbolic notation premits a direct view of the general form." + +Lesh and Doerr\cite[p. 379]{lesh2000symbolizing} encourage students to construct models, that may include "a combination of spoken words, written symbols, pictures or diagrams, or references to other models or real-life experiences \ldots in any case, the representation tends to organize and simplify the situation so that additional information can be noticed, or so that attention can be direct toward underlying patterns and regularities, which may, in turn, drive changes in conceptions." + +Bowers\cite[p 390]{bower2000postscript} summarizes ideas on generalizing saying: "Bransford et al.\cite{bransford2000designs} describe several studies to support the claim that 'people's representations of problems and experiences have strong effects on the degree to which they will transfer their knowledge to new settings'. Similarly, Lesh and Doerr\cite{lesh2000symbolizing} argue that the models students produce when engaging in model-eliciting problems are not just solutions to the problem at hand, but instead stand as more generalized conceptual tools that can be 'shared and reused in other situations' ". + +Huth et al.\cite{huth2012continuous} + A continuous semantic space describes the representation + + % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % + + + $$ One reason we delve into this is that we want to know something about to what degree different factors that might possibly assist learning are significant. For example, how important is it to note the beauty of a proof, and what is the significance of the order in which a proof is presented (for example, lemmas first), and how quickly might we expect students to grasp a hierarchy of abstractions. We learn possibly surprising things, such as, if we provide a fragrance during learning a proof with ideas about spatial locations, and we provide that same fragrance during the early part of sleep, the memory will be consolidated more effectively, as demonstrated by subsequent recall during an awake state.$$ + + Cerf et al. \cite{cerf2014studying} opine "early neuron activity observed here could represent the early stages of the formation of a thought or recollection, the states at which we may not yet be fully aware of the content of the thought" + + \subsection{Cognitive Neuroscience} + Cognitive neuroscience provides evidence for believing that suspense, and concern for characters, is useful in helping students selectively attend to, and remember at an abstracted level, the material they are seeing. + For example, + Bezdek et al. \cite{Bezdek2015338} have measured brain responses corresponding to attention, and have shown that attention is modulated by the emotional flow of a narrative as it unfolds over time, and that suspense is associated with increased central processing (of the visual field) and decreased peripheral processing. Moreover they have reason to believe that this attention does produce downstream consequences, reflecting encoding of content at a level abstracted from visual features. They have brain metabolism imaging showing decreases in activity that has been associated with mind-wandering\cite{Christoff20098719}. + Kosslyn and K\"onig \cite[p. 56--57]{kosslyn1992wet} describe some layout of lower level functions in the brain, "The ventral (object-properties-encoding) system in the temporal lobes not only registers key properties of shapes, but also encodes color and texture; this information is matched to that of objects stored in visual memory. This temporal-lobe memory stores information in a visual code, which cannot be accessed by input from other sensory modalities. \ldots The outputs from the \ldots encoding systems come together at an \textit{associative memory} (which relies on tissue in various places in the brain) \ldots once the appropriate information is accessed, one knows the name of the object, categories to which it belongs, sounds it makes, and so forth. \ldots there is ample evidence that the frontal lobe plays a critical role in this process" + Kosslyn and K\"onig \cite[p. 78]{kosslyn1992wet} "For example, if a caterpillar is still against a twig, it may be very difficult to notice. But if it is moving, we may identify it immediately. Computing motion relations appears to be qualitatively distinct from computing the organization of portions of static images, and distinct regions of the brain apparently encode motion (particularly areas MT and MST). There appears to be a distinct \textit{motion relations subsystem}. The motion relations subsystem extracts key aspects of motion fields, and operations concurrently with the preprocessing subsystem." + $$ knowing whether two (simultaneously presented) parts of a proposed presentation will require attention from two systems able to operate concurrently, or will make conflicting demands upon one attention window is useful$$. + + + Kosslyn and K\"onig \cite[p. 102]{kosslyn1992wet} "the frontal lobe clearly has a role in setting up plans. More important, the frontal lobe clearly has a role in formulating and testing hypotheses."$$needed for creating proofs$$. + + Kosslyn and K\"onig \cite[p. 104]{kosslyn1992wet}"a subsystem that \textit{engages} attention. \ldots the thalamus. The thalamus is a kind of switching station, connecting many parts of the cortex." + + Kosslyn and K\"onig \cite[p. 112]{kosslyn1992wet} "Visual object agnosia is often divided into two types Patients who are diagnosed as having \textit{apperceptive} agnosia have difficulty putting together visual information to form an integrated perception on an object. Some such patients describe the world as fragmented or chaotic. These patients cannot determine whether two objects are the same or different, let alone identify an object they see. However, even these patients are not blind. Patients who are diagnosed as having \textit{associative agnosia}, in contrast, have difficulty associating the perceptual input with previously stored information. Patients who have 'pure' associative agnosia can discriminate between and properly compare shapes, even though they cannot identify the shapes \ldots could tell whether objects were the same or different, but not what they were. In short, a problem appreciating the shape of an object is apperceptive; a problem identifying the object while being able to distinguish its shape is associative." + $$ it would be nice to diagnose student difficulties to this degree, especially if an treatment could be associated with the diagnosis. Moreover, there could be a strong analogy here. Students could recognize two applications of rules of inference as being the same without being able to identify which rule of inference it is. This suggests a clicker question about rule applications, as to whether they are the same or not, or, choose the rule application that is different. $$. + + Kosslyn and K\"onig \cite[p. 114]{kosslyn1992wet} "Prosopagnosia is particularly puzzling because at least some of these patients apparently recognize faces unconsciously, and never become aware that they have done so; patients with prosopagnosia showed changes in the electrical properties of their skin (i.e., increased electrodemal skin conductance responses) when they were viewing familiar faces, compared to unfamiliar ones, even when they claimed to have no idea whom they were looking at. The stimulus must be matching a stored memory of a face in the pattern activiation subsystem (at least to some degree), but processing sops early -- and the persons is never aware that a match was made. + + Kosslyn and K\"onig \cite[p. 118]{kosslyn1992wet} There are processes that activate stored visual information to generate visual mental images. + + Posner for systems involved in attention + + Kosslyn and K\"onig \cite[p. 124]{kosslyn1992wet} "one of the most intriguing aspects of the neglect syndrome is that it appears to affect consciousness itself." + + Kosslyn and K\"onig \cite[p. 132]{kosslyn1992wet} "Patricia Goldman-Rakic and her colleagues showed that the frontal lobes contain a short-term spatial memory." + + Kosslyn and K\"onig \cite[p. 136]{kosslyn1992wet} "the (mental) image is not like a picture; it is facing almost as soon as it is generated."(Fink, Pinker, Farah, Chambers, Reisberg) + + Kosslyn and K\"onig \cite[p. 147]{kosslyn1992wet} "In either case, instructions somehow must be provided to the attention shifting subsystems; if the image is truly novel, the instructions cannot be previously stored. Thus, it is of interest that there are rich connections from the frontal lobes (which presumably direct the process), not only to parts of the parietal lobes known to be involved in attention, but also to the subcortical structures involved in shifting attention." Goldman-Rakic, posner, 1987, 1988, petersen 1990 + + $$Kosslyn et al. have inferred an organization of processing in the brain, and we as instructors could think about how we are deploying the learning task over this architecture. We could think about what path information has follow, to be learned to the extent that it can be called into future use. That is, while some instruction could produce inert knowledge, the goal is usable knowledge.$$ + + Kosslyn and K\"onig \cite[p. 152--153]{kosslyn1992wet} "By inferring that images occur in the same visual buffer that is used in perception, we expect that the properties of the buffer that affect perception also should affect imagery. If so, then the inability to maintain patterns in images for very long may be another consequence of this common mechanism. That is, in perception one does not want an image to linger; one wants to 'clear the buffer' every time the eyes move. Indeed, if images did not fade rapidly, they would smear and become overlaid. \ldots Thus, patterns in the visual buffer are transient in both perception and imagery." + + Kosslyn and K\"onig \cite[p. 154]{kosslyn1992wet} "A symbolic use of imagery involves the same subsystems used in other kinds of imagery reasoning; one must generate the image and retain it long enough to operate on it and 'see' the results. But there is one critical difference between this kind of symbolic imagery and the other sorts: One now must decide how to convert abstract material to particular patterns in the image. For example, one could visualize relative intelligence not only as dots on a line, but also as a set of circles" + + Kosslyn and K\"onig \cite[p. 163]{kosslyn1992wet} both hemispheres can generate images (posterior of brain), instructions come from frontal lobes. Left hemisphere naturally, right hemisphere with training. Kosslyn and K\"onig \cite[p. 164]{kosslyn1992wet} both hemispheres can generate images, but in different ways. + + Kosslyn and K\"onig \cite[p. 165]{kosslyn1992wet} image transformations require contributions from both hemispheres + + Kosslyn and K\"onig \cite[p. 168]{kosslyn1992wet} "Learning to read these (already familiar) words is learning to use an additional route into associative memory to access the information that is stored with words. The problem is, that we initially learned to access the relevant memories on the basis of hearing sounds, \ldots How are we able to use a pattern of lines to access these memories?" + + $$subvocalization is an inferior way to accomplish this$$ + + + + + + + Kosslyn and K\"onig \cite[p. 193]{kosslyn1992wet} "With repeated use, the entire pattern of lines becomes an entry in the pattern activation subsystem and the pattern recognized there is associated with a word in associative memory" + + $$repetition of relationships between items allows us to claim a pattern, a pattern suggests the thought of generalization, the symbolic representation of the pattern makes generalization more efficiently notated, maybe increases awareness of the possibility of generalization, and the ability to generalize is used in transfer of knowledge to further applications, counteracting inert knowledge$$ + + Kosslyn and K\"onig \cite[p. 204]{kosslyn1992wet} "the information that allows one to understand a word must be in associative memory, and possibly is stored only in the left hemisphere. (The left hemisphere is typically the site of the most language processing, and hence it would not be surprising if representations of word meaning were stored primarily in this hemisphere.) \ldots the left hemisphere associative memory \ldots presumably implements the word shape/sound associations." + + Kosslyn and K\"onig \cite[p. 207]{kosslyn1992wet} writing about a form of dyslexia that has provided insight, describe ideas of Coltheart\cite{schmalz2015getting} "He hypothesized that only words that name visible objects or properties are stored in the right hemisphere, \ldots " + + Kosslyn and K\"onig \cite[p. 214]{kosslyn1992wet} "Sounds are represented initially in a cortical structure in the inner part of the superior (upper) temporal lobes. Heschl's gyrus \ldots is the auditory analog to area V1; indeed, this structure is often called A1 (to indicate that it is the first cortical auditory area). As in vision, the raw auditory input is organized and represented in the auditory buffer prior to high-level processing. Ulrich Neisser posited that such a buffer serves as an 'echoic memory';" rather than being organized as visual input, where spatially adjacent cells have spatially adjacent receptive fields, instead it is organized so that spatially adjacent cells receive input at different sound pitches/frequencies. + + Kosslyn and K\"onig \cite[p. 215--216]{kosslyn1992wet} "Recall that in vision there are two subcortical pathways from the eyes to the brain, the geniculo-striate and the tecto-pulvinar; the tecto-pulvinar pathway (eye, superior colliculus, pulvinar, cortext) draws attention to potential regions of interest. The inferior colliculus projects to the deep and superior colliculus play a similar role in audition. \ldots the auditory receptive fields of neurons in the superior colliculus shift with changes in eye position, allowing the auditory and visual maps to remain aligned. (see, for example Maddox et al.,\cite{maddox2014directing}) Hence, one tupically pays attention to a single object, registering its appearance and sounds at the same time." + + Kosslyn and K\"onig \cite[p. 219--220]{kosslyn1992wet} "visual preprocessing subsystem becomes 'tuned' by experience to encode useful visual patterns \ldots the separate auditory areas are also connected with reciprocal connections \ldots the reasoning we used to infer than experience tunes the visual preprocessing subsystem also leads us to expect that stimulus properties that distinguish between words will be noted downstream, and feedback will reinforce the encoding of those properties in the auditory preprocessing subsystem" + + Kosslyn and K\"onig \cite[p. 220--221]{kosslyn1992wet} "\textit {categorical perception} \ldots lies at the heart of what is accomplished by the auditory preprocessing subsystem \ldots the same categories are extracted when a word is spoken by different people -- and these categories help one to understand the words spoken under different circumstances." + + $$ + Kandel talks about removing some extraneous (i.e., those that might be redundant, maybe less often on) connections, do I think this is having the effect of categorization/generalization? + Choosing consciously to de-emphasize consideration of details at a high level, and unconsciously removing less-often exercised distinctions could have a similar effect. + $$ + Kosslyn and K\"onig \cite[p. 225]{kosslyn1992wet} "We are led to infer than the representations of the sounds of individual words depend on temporal--parietal cortex" + + Kosslyn and K\"onig \cite[p. 227]{kosslyn1992wet} "If we assume that unimodal memories are stored in the subsystem that encodes them", which is done by Squire (1987)\cite{squire1987memory}(check this, there is a google book) + + + + David and Squire reviewed protein synthesis connected with memory formation\cite{davis1984protein} " Evidence from learning curves, examination of short-term retention, and posttraining drug injection indicate that initial acquisition is not dependent on such synthesis, but it appears that protein synthesis, during or shortly after training, is an essential step in the formation of long-term memory." + + Kosslyn and K\"onig \cite[p. 230]{kosslyn1992wet} "it is possible that semantic information is organized along these lines, with appearance-based meanings segregated from use-based meanings". + + Kosslyn and K\"onig \cite[p. 343]{kosslyn1992wet} "We inferred in Chapters 3 and 4 that unimodal visual information is probably stored in the inferior temporal lobe (in the object-properties-encoding subsystem), and we inferred in Chapter 6 that unimodal auditory information is probably stored in temporal-parietal cortex." + + Kosslyn and K\"onig \cite[p. 344]{kosslyn1992wet} "information in associative memory can be activated by input from any perceptual modality". Associations can be established between representations in perceptual memory and in associative memory. "memory formation subsystems rely on anatomical structures \ldots the principal members of this set being the \textit{hippocampus} (and related cortex), the \textit{limbic thalamus}, and the \textit{basal forebrain}." + + Kosslyn and K\"onig \cite[p. 345]{kosslyn1992wet} "the hippocampus receives input from a number of other structures (the septum and the hypothalamus, via the fornix; the anterior thalamic nucleus and the subcallosal area, via the cingulum; and the amygdala). \ldots The hypothalamus appears to be involved in motivation, and the amygdala appears to have a role in emotion; clearly both factors affect what we remember. \ldots The hippocampus plays a critical role in the storage of new perceptual representations. \ldots also plays a critical role in storing associations between representations. (Mishkin and Appenzeller 1987, Squire 1987)" Long term potentiation is a phenomenon of hippocampal cells in neural microcircuits involved in storing associations between representations. + + Kosslyn and K\"onig \cite[p. 346]{kosslyn1992wet} "many of the thalamic nuclei appear to be involved in attentional processes (Posner and others) \ldots The basal forebrain \ldots in turn issues a signal that new representations and/or associations should be stored.(Mishkin and Appenzeller 1987) This is a biochemical signal, consisting of the release of \textit{acetylcholine}." + + Kosslyn and K\"onig \cite[p. 347]{kosslyn1992wet} "we shall decompose the memory formation subsystem into two more precisely characterized subsystems, \ldots these subsystems are involved in initiating the learning sequence, and in changing selected connections strengths in particular neural networks, respectively." + + Kosslyn and K\"onig \cite[p. 347]{kosslyn1992wet} "the \textit{striatum} plays a critical role in skill acquisition \ldots the striatum receives information from cortical perceptual areas". + + Kosslyn and K\"onig \cite[p. 349--350]{kosslyn1992wet} "If novel stimuli are perceived, \ldots when a match is not obtained, this information is sent to the frontal lobes and provides input to the print-now sybsystem; recall that perceptual encoding subsystems have anatomical projects into the frontal lobe (Goldman-Rakic, 1987) Thus, the perceptual encoding subsystems send outputs to the associative memory \ldots Structural changes are initiated that will allow the systems later to reconstitute the pattern of activation evoked by the novel stimulus" + + Kosslyn and K\"onig \cite[p. 351]{kosslyn1992wet} "The key to storing new information in memory is the ability to change the 'strengths' of connections among neurons in just the right way. This \ldots has been documented in actual neural networks (Kandel and Schwartz, 1985, Shepherd 1988)" + + Kosslyn and K\"onig \cite[p. 353]{kosslyn1992wet} "These changes (in synaptic connections) apparently begin in the hippocampus \ldots this phenomenon is called long term potentiation. \ldots it can last hours, days, weeks, or even longer -- depending on \ldots as well as various properties of the stimulus." + + $$ It is the accumulation of surface area from vesicles delivering neurotransmitter at the presynaptic cell in the synaptic cleft that creates microenvironments that are more effective (NMDA activated/molecule of neurotransmitter delivered) in activating the postsynatic neuron, since the corresponding membrane that is used to restore the number of vesicles is taken from smooth area.$$ + + Kosslyn and K\"onig \cite[p. 358--359]{kosslyn1992wet} "The idea that associative memory hooks back into unimodal perceptual representations is consistent with a range of clinical findings. \ldots Squire suggests that the perceptual systems that encode information may actually store much of it.(Squire 87) \ldots We speculate that associative memory depends in part on the superior, posterior temporal lobe, if only because patients with lesions in this area often appear to have disrupted associations." + + Kosslyn and K\"onig \cite[p. 361]{kosslyn1992wet} "When an object is later perceived and input enters associative memory, the relevant associations are activated." + + Kosslyn and K\"onig \cite[p. 370--371]{kosslyn1992wet} "We often store new information even if it has no obvious relevance to any goal or problem at hand. This is called \textit{incidental} memory.\ldots if one pays attention to a stimulus, it is likely to be stored 'automatically,' with no decision to do so. \ldots one tries to memorize the information, and is more likely to remembers it than if the effort were not made. This sort of memory is called \textit{intentional} memory. \ldots the longer the information is attended to, the more likely it is that the memory formation subsystems eventually will store it in memory \ldots if the property lookup subsystems access more information about the to-be-remembered material, memory will be improved. \ldots called a \textit{depth of processing} effect" + + Kosslyn and K\"onig \cite[p. 372]{kosslyn1992wet} "one can store information relatively effectively by inventing distinctive \textit{retrieval cues}. \ldots Allan Paivio reviews a large amount of evidence that we remember information better when we use a 'dual code' (visual and verbal) than when we store it in only a single way (Paivio 1971)" + + Kosslyn and K\"onig \cite[p. 373]{kosslyn1992wet} "when one becomes an expert in any domain, one often cannot report how one performs the task. Much, if not most, of the information in memory cannot be directly accessed and communicated" + + $$ it is not in conscious memory anymore$$ + Lisman and Sternberg\cite{lisman2013habit} talk about Habit and nonhabit systems for unconscious and conscious behavior: Implications for multitasking. + + Peter Graf and Daniel Schacter implicit memory + + Kosslyn and K\"onig \cite[p. 375]{kosslyn1992wet} "There is considerable evidence that priming tasks and explicit memory tasks rely on distinct processing subsystems \ldots certain drugs impair both recall and recognition in explicit memory tasks, but do not affect the magnitude of priming." + + Kosslyn and K\"onig \cite[p. 376]{kosslyn1992wet} In priming, "The words apparently were processed to some level within the system, even when the patient was fully unconscious." + + Kosslyn and K\"onig \cite[p. 377]{kosslyn1992wet} "priming has two components, only one of which is perceptual" There is an advantage to having the priming and the recall be in the same sensory modality, only for the right hemisphere. " Graf and Schacter also showed that implicit memory for associations between words is modality-specific. + + $$ to make the most of the priming effect, the students should have practice writing responses to stimuli, like test questions. For memorization type test questions, that are answered by handwriting, note-taking in class, of the same item, should help.$$ + + Kosslyn and K\"onig \cite[p. 380]{kosslyn1992wet} "Mishkin suggests that a subcortical structure called the \textit{substantia nigra} is critically involved in the 'reinforcement' process that strengthens connections between perceptual states and responses." + Stimulus/response learning, striatum, dopamine. Is this what is used in flash cards? This kind of learning is restricted, [p. 383]"the response can only be evoked by the appropriate stimulus" + + Kosslyn and K\"onig \cite[p. 387]{kosslyn1992wet} "material in \textit{working memory} is used to aid reasoning processes (Baddeley 1986). Reasoning processes only can operate on information in short-term memory, but relatively little information can be stored in short-term memory." + $$ so lemmas are good$$ + + Kosslyn and K\"onig \cite[p. 387-388]{kosslyn1992wet} " We interpret the short-term memory structures Patricia Goldman-Rakic reports in the frontal lobe (Goldman-Rakic 1987, 1988) as extension of the perceptual encoding subsystems, which serve to make perceptual information immediately available to the decision processes; according to this view, it is debatable whether one want to conceive of the information as actually being stored -- as opposed to monitored -- in the frontal lobe. + Working memory, then, corresponds to the activated information in the long-term memories, the information in short-term memories, and the decision processes that manage which information is activated in the long-term memories and retained in the short-term memories(Kosslyn 1991)" + + Kosslyn and K\"onig \cite[p. 398]{kosslyn1992wet} "recall that Goldman-Rakic provides evidence that perceptual information ultimately projects to the frontal lobe(Goldman-Rakic 1987, 1988)" + + Kosslyn and K\"onig \cite[p. 398--399]{kosslyn1992wet}explicit memory formation uses acetylcholine, modifying the strengths of connections in the appropriate networks, implemented in part in the hippocampus and related cortex + + + + + + + + Squire and Dede\cite{} + Martin\cite{martin2015grapes}"some of the latest functional + neuroimaging findings on the organization of object concepts + in the human brain. I argue that these data provide strong + support for viewing concepts as the products of highly inter- + active neural circuits grounded in the action, perception, and + emotion systems. The nodes of these circuits are defined by + regions representing specific object properties (e.g., form, color, and motion) and thus are property-specific, rather than + strictly modality-specific. How these circuits are modified + by external and internal environmental demands, the distinction between representational content and format, and the + grounding of abstract social concepts are also discussed." + + $$we have modality specific long term, and we have association area for other than single modality, we have consolidation and reconsolidation, do we have spatial arrays of concepts$$ + \subsection{Brain Imaging} + Bachmann\cite{bachmann2015brain} discusses "brain-imaging markers of neural correlates of consciousness" + $$when we are learning a skill we can be conscious of exercising that skill, and later, we can become less conscious of specifically how we exercise that skill. Is the part of the brain that is conscious moving? Is the location of the memory moving? Could be both. Don't some motor skills move to the cerebellum, and aren't there problems with this for dyslexics? What's going on when something suddenly appears in consciousness? I think the metabolic activity brings the consciousness to the place where the memory is. But in these kind of answers popping into consciousness (Poincar\'e?) isn't it a new synthesis that pops into consciousness?$$ + + Luck and LeClerc \cite{luck2014potentiation} wrote about the Potentiation of Associative Memory by Emotions: An Event-Related FMRI Study, + + Brain imaging provides evidence for believing that creativity, (generating novel ideas, such as proofs) can be improved by training and takes time corresponding to reorganizing intercortical interactions\cite{kowatari2009neural}. (Look here kowatari more, there is something about predominance of right prefrontal over left.) + According to Huang et al.\cite{huang2015highest}, a large body of research suggests that an abstract cognitive processing style produces greater creativity. Empirically, decades of work have shown that both abstract thinking and creativity are consistently linked to right-hemispheric activation in the brain (e.g., Fink et al., 1996\cite{fink1996brain} and Mihov et al., 2010\cite{Mihov2010442}) + . + + Squire tells us \cite{squire2015conscious} "findings suggest that fMRI activity in the medial temporal lobe reflects processes related to the formation of long-term memory" + + Chambers et al.~\cite[p. 1045]{chambers2003developmental}, citing Gurden et al, Mulder et al., Robinson and Kolb, and Hyman and Melenka~\cite{gurden1999integrity,mulder1997short,hyman2001addiction} state "Dopamine transmission in nucleus accumbens and prefrontal cortex regions projecting to the nucleus accumbens has been implicated in mechanisms of learning and plasticity, including changes in long-term potentiation and morphology of neuronal dendritic trees." + + \subsection{Brain structure} + + \begin{quote} + Who can trace out the secret threads by which our concepts are united?\\ + Hermann von Helmholtz + \end{quote}\cite{kounios2015eureka} + + Takeuchi et al. \cite{takeuchi2010training} Training of working memory impacts structural connectivity + + Melby-Lerv{\aa}g \cite{melby2013working} "current findings cast doubt on both the clinical relevance of working memory training programs and their utility as methods of enhancing cognitive functioning in typically developing children and healthy adults. " + + Rutishauser et al.\cite[p. 104-105]{fried2014single} medial temporal lobe "lesion subjects showed reduced (but above chance) recognition memory performance but, strikingly, has a complete lack of performance improvement for items shown together with task-irrelevant novel attributes. In contrast, normal control subjects had a substantial gain in memory performance for these items (Kishiyama et al., 2004\cite{kishiyama2004restorff}). Together, this indicates that the 'von Restorff effect' (Wallace, 1965\cite{wallace1965review}; Kinsbourne \& George, 1974\cite{kinsbourne1974mechanism}; Hunt, 1995\cite{hunt1995subtlety}; Parker et al., 1998\cite{parker1998restorff}) is driven by neuronal mechanisms that reside in the MTL. \ldots Novelty responses are thus a sensitive measure to quantify learning and plasticity. \ldots We identified a subpopulation of single neurons in the hippocampus and the amygdala that showed striking differences in their spiking response. \ldots the same cell would indicate the novelty of a stimulus regardless of which category the stimulus was from. \ldots These cells \ldots also show changes in firing rate as a function of repeated presentation even when subjects are only passively viewing stimuli without an explicit memory task (Perdreira et al., 2010\cite{pedreira2010responses})" + + Rutishauser et al.\cite[p. 106]{rutishauser2014single} "it seems that there are at least two distinct classes of novelty-sensitive single neurons in the human MTL: abstract and visually tuned. The first class of untuned general novelty detectors could serve to signal the significance of stimuli during the acquisition of new memories (Lisman \& Otmakova, 2001\cite{lisman2001storage}). It has been suggested that such neurons trigger dopaminergic release through projections to the ventral tegmental area (Lisman \& Grace, 2005\cite{lisman2005hippocampal})" + + Mormann et al.\cite[p. 131--133]{mormann2014visual} reports "Another seminal study described neurons representing a specific semantic concept in the human MTL (Quian Quiroga et al., 2005). \ldots A problem in determining the precise turning curves of semantic neurons in the MTL is to find a suitable parameterization of the stimulus space \ldots compounded in human studies by the short duration of any one experiment in any one patient." + + Ouchi et al.\cite{ouchi2013reduced} "Adult neurogenesis is known to be important in hippocampus-dependent memory" + + Ojemann\cite[p. 262]{ojemann2014human} has demonstrated that lateral temporal neurons are involved in recent memory, making use of attention to increase the success of consolidation of memory of items competing with distractions. "The evolutionary changes in the brain orgainzation for recent memory involve an expansion of the cortical component with relative conservation of the medial temporal -- hippocampal component. \ldots A substantial literature has established the importance of the temporal lobe in learning. \ldots neurons with changes during \ldots memory were significantly more likely to have associative learning changes." + + Kowatari et al.\cite{kowatari2009neural} state "In the experts, creativity was quantitatively correlated with the degree of dominance of the right prefrontal cortex over that of the left, \ldots Our results supported the hypothesis that training increases creativity via reorganized intercortical interactions." + + Waisman et al.\cite{waisman2014brain} observe that "various studies demonstrate that when complexity of the (arithmetic) problems rises, more brain areas simultaneously support the solving process", citing Zamarian et al.\cite{zamarian2009neuroscience}. + + Waisman et al.\cite{waisman2014brain} investigated "cortical activity associated with solving problems that require translation between symbolic and graphical representations". + + Waisman et al.\cite[p.691]{waisman2014brain} stated that the "posterior parietal cortex is know to be activated when mental representations are manipulated (Zacks 2008)\cite{zacks2008neuroimaging}. + + Deng et al.\cite{deng2010new} report that "Neurons born in the subventricular zone(SVZ) differentiate and integrate into the local neural network as granule cells of the dentate gyrus." + + Knutson et al.\cite{knutson2001anticipation} state that a region in the nucleus accumbens codes for expected positive incentive value, and + \cite[p. 4]{knutson2001anticipation} it is "an apparently lateralized response of the right nucleus accumbens." + + Chambers et al.~\cite{chambers2003developmental} explained that "Adolescent neurodevelopment occurs in brain regions associated with motivation, impulsivity, and addiction. Adolescent impulsivity and/or novelty seeking as a transitional trait behavior can be explained in part by maturational changes in frontal cortical and subcortical monoaminergic systems. These developmental processes may advantagiously promote learning drives" + + $$ these systems that we are trying to use to shepherd information from the place it begins (sensory to MTL) to the right prefrontal cortex, from where it can be retrieved for creative application to problem solving, are developing$$ + + \begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{./l73f1.jpeg} + \caption{In this figure reprinted from Chambers\cite{chambers2003developmental}, (I plan to do something, either redraw or ask permission) we see how sensory input, new information, is delivered to hippocampus. Other sources have shown us that new neurons are created in or near hippocampus that are a response to new information arriving and related to memory for the new information. We have seen how presence of dopamine, from striatum and VTA assist the consolidation of new memory into longer term memory. We have seen that for monomodal information, the long term memory is stored in cortex near where input is provided by that modality (visual cortex, auditory cortex) and for multimodal information, the long term memory is stored in association cortex. We have seen that information stored in association cortex is more readily retrieved, as any of the associated modalities can help retrieve it. We have seen that this consolidation requires protein and is facilitated by sleep, (I forget which of REM or slow wave sleep.) We have seen how reconsolidation can occur, assisted by nucleus accumbens, and can result in information accessible to the prefrontal cortex, on the right side. We have seen how anticipation of positive reward activates the nucleus accumbens on the right side. Could it be that anticipation of positive reward occurs in REM sleep, I wonder.} + \label{fig:poster23} + \end{figure} + + Anderson et al.~\cite[p. 53]{anderson2011cognitive} state "There is some reason to suspect that the angular gyrus (ANG) may also be engaged to serve the metacognitive activities of monitoring and reflecting." (on non-routine problem solving). They go on to say "Regions close to the right ANG have been found to play a variety of metacognitive functions, citing a review by Decety \& Lamm\cite{decety2007role}. + + Anderson et al.~\cite[p. 54]{anderson2011cognitive} state "Another region that is potentially involved in metacognition is Brodmann Area 10 or frontopolar cortex (FPC), particularly its lateral portion, (citing Fletcher and Henson\cite{fletcher2001frontal}). A number of converging lines of research suggest that this region of the brain may be critical in the ability to extend knowledge." + Anderson et al.~\cite[p. 58]{anderson2011cognitive} state "The left ANG is often distinguished from the right in many theories including the triple code, but the pattern of ANG effects in this experiment is basically the same in the two hemispheres." + Anderson et al.~\cite[p. 62]{anderson2011cognitive} state "In every case (brain areas related to metacognition), the patterns are roughly bilaterally symmetric." + + + \subsection{Brain function} + + + + R. Quian Quiroga\cite{quiroga2012concept} opines that concept cells are the building blocks of declarative memory functions. + + Suthana et al.\cite{suthana2012memory} report on Memory enhancement and deep-brain stimulation of the entorhinal area. + + Imamoglu (fix the accents) et al.\cite{imamoglu2012changes} discuss changes in functional connectivity support conscious object recognition. + + Murayama and Kitagami\cite{murayama2014consolidation}dopaminergic memory consolidation effect can result from extrinsic reward. + + $$ + so, give a little quiz at the end of lecture, covering the main points, and hand out tickets in exchange for handing in quizzes. Then, tickets can be handed in with homework to count for points. So they are paid at the time they are thinking about quiz contents, and that is expected to help with consolidation of the material on the quiz.$$ + + Born and Wilhelm\cite{born2012system} discuss System consolidation of memory during sleep + + Diekelmann et al.\cite{diekelmann2012offline} describe that Offline consolidation of memory varies with time in slow wave sleep and can be accelerated by cuing memory reactivations. + + Taylor et al.\cite{tayler2013reactivation} describe Reactivation of neural ensembles during the retrieval of recent and remote memory. + + Cowansage et al.\cite{cowansage2014direct} describe the Direct reactivation of a coherent neocortical memory of context + + Lustenberger et al.\cite{lustenberger2012triangular} discuss a triangular relationship between sleep spindle activity, general cognitive ability and the efficiency of declarative learning. + + Roux and Uhlhaas\cite{roux2014working} consider working memory and neural oscillations, questioning whether alpha--gamma versus theta--gamma codes for distinct WM information. + + Walker and Stickgold\cite{walker2014sleep} consider Sleep, memory and plasticity. + + Tonnoni and Cirelli\cite{tononi2014sleep} discuss Sleep and the price of plasticity: from synaptic and cellular homeostasis to memory consolidation and integration. + + Rutishauser et al.\cite[p. 107]{rutishauser2014single} "Neurons coded this information very reliably: The decoder (a function of a population of neurons) could tell (for correct trials) whether the stimulus was new or old on a single trial basis with an accuracy of 75\% \ldots (using) a single previously identified novelty/familiarity neuron. Performance increased to 93\% if six neurons were considered. \ldots for 75\% of error trials, the decoder predicted what the correct response would have been (but which was not given by the subject). \ldots a simple decoder outperform(s) the patient \ldots The neurons have better memory than the patient demonstrated behaviorally," + + Rutishauser et al.\cite[p. 111]{rutishauser2014single} "Many factors modulate the probability that a memory for a stimulus will be formed. Examples include attention, motivation, and saliency of the stimulus (Paller \& Wagner, 2002\cite{paller2002observing}). Structurally, the modification of synaptic circuits by plasticity mechanisms is thought to underlie memory formation (Martin et al., 2000\cite{martin2000synaptic}) + + Rutishauser et al.\cite[p. 112]{rutishauser2014single} "findings from animal literature indicate that theta oscillations and the timing of neuronal activity relative to the ongoing theta oscillations have a strong influence on plasticity as well as learning, suggesting the possibility that the two are functionally linked by theta oscillations. \ldots The power of theta oscillations measured on the scalp \ldots can be predictive of whether a memory is formed or not (Klimesch et al., 1996\cite{klimesch1996theta}; Sederberg et al., 2003\cite{sederberg2003theta}) \ldots what is relevant for whether a memory was formed or not is whether the preferred phase of a particular neuron was followed faithfully and not the absolute phase \ldots what was predictive (of whether a memory was formed or not) was whether the spikes that were fired were phase locked to ongoing theta or not." + + Rutishauser et al.\cite[p. 113]{rutishauser2014single} "the spike field coherence at the time of learning was already indicative of whether a memory was later strong or weak." + + Mormann et al.\cite[p. 140]{mormann2014visual} state "The process of encoding episodic memories consists of associating pieces of semantic information (what happened where with whom involved and so on) in a defined temporal order. Lesion studies in humans have shown that structures in the MTL are essential for the encoding of episodic memories (Squire et al., 2004; Squire et al., 2007; Squire, 2009; Milner et al. 1968, Scoville \& Millner 1957). Representations of semantic information at the single unit level are frequently found in these very structures and thus might provide a unique opportunity to investigate how our brain links pieces of semantic information together into episodic memories (Quiroga, 2012). \ldots Episodic memories are always context dependent whereas semantic memories are context invariant and can emerge via generalization of recurring context-dependent experiences (Buzsaki, 2005)." + + Mormann et al.\cite[p. 142--143]{mormann2014visual} state "Earlier notions that the amygdala might be specialized to elicit or mediate fear responses (LeDoux, 1996) have been supplemented by more abstract accounts whereby the amygdala processes ambiguity or unpredictability in the environment (Herry et al., 2007) and mediates an organism's vigilance and arousal (Davis and Whalen, 2001). \ldots In humans, neuroimaging studies of the amygdala argue for a broad role in processing stimuli that are strongly rewarding or punishing (Sander et al., 2003; Ohman et al., 2007) \ldots In human fMRI memory studies, increased blood flow in the amygdala during encoding was found to correlate with improved memory formation (e.g, Canli et al., 2000). In addition, the phase locking of human amygdala neurons to ongoing theta oscillations was found to predict memory formation (Rutishauser et al., 2011) \ldots there might be a distinction between the hippocampus and the amygdala in terms of the extent to which unconscious information reaches those areas. If indeed unconscious information can reach the amygdala but not the hippocampus and surrounding structures" + + Paz and Pare\cite{paz2013physiological}" in emotionally + arousing conditions, whether positively or negatively valenced, + the amygdala allows incoming information to be processed + more efficiently in distributed cerebral networks." + + $$ This is just corroborating that infectious enthusiasm for a subject, on the part of the instructor, helps students learn.$$ + + Schwabe et al. \cite{schwabe2014reconsolidation} there is reconsolidation + + Patel et al.\cite[p. 205]{patel2014human} "Functions such as reward processing, motivations, and learning have since been attribted to basal ganglia circuits." + + Patel et al.\cite[p. 207]{patel2014human} "Examined impact of emotional valance and cACC responsitveness to complext attnetion tasks \dots Examined reward properties of dopaminergic neurons using virtual financial reward" + + Patel et al.\cite[p. 208--209]{patel2014human} "when there is a differentce in expected and actual outcome -- a prediction error signal -- midbrain dopaminergic neurons rapidly fire at the onset of the unexpected reward. \ldots This feature is thought to drive reward-based learning and adaptive behavior. \ldots It is thought that phasic dopaminergic activity is the neural substrate of this type (classical conditioning) of learning (Schultz, 1998) \ldots dopamine release in the striatum" + + $$ So, deliver unexpected rewards. Maybe some clicker questions have greater value.$$ + + Patel et al.\cite[p. 210]{patel2014human} "the ventral striatum has become a focal point in studies of reinforcement learning, \ldots phasically active neurons, thought to be the medium spiny neurons that make up about 95\% of striatal neurons, are more relevant to strengthiening functional circuits diring instrumental conditioning and procedural learning (Graybiel 2008, Jog 1999)" anticipation of rewards, including secondary rewards (monetary) + + + Patel et al.\cite[p. 212]{patel2014human} "NAcc activity reliably encodes the anticipation of reward proportional to reward magnitude" + + Patel et al.\cite[p. 213--214]{patel2014human} "each subregion of the ACC is predomintely involved with distinct roles, such as motivation and cognition (Paus, 2001). Notably these areas are not homogeneous and demonstrate some overlap in function. \ldots The portion of the ACC implicated in reward processing and cognition is the dACC. \ldots The vmPFC is strongly connected to the limbic system, which is a group of brain structures that are implicated in several functions such as emotion, motivation, and memory." + + Ojemann\cite[p. 268]{ojemann2014human} states "there are also 'subconscious' or 'implicit' memory processes, processes of which the subject is unaware that change performance. One such process is repetition priming, a shortening of reaction time with repeated presentation of the same item. Changes in lateral temporal cortical single neuron activity related to this, \ldots that study included recordings throughout lateral temporal cortex, neurons with those significant implicit memory changes were all in superior temporal gyrus or superior portion of middle gyrus, significantly more superior and posterior than neurons with recent memory processes \ldots implicit memory then involves neural networks in posterior superior temporal cortex, largely separate from those for recent memory" + + Rutishauser et al.\cite[p. 348]{rutishauser2014next} state "Different timescales of memory formation have been described at the neuronal level." + + Rutishauser et al.\cite[p. 348]{rutishauser2014next} "It has remained very difficult to directly link the mechanisms of synaptic plasticity to memories" + %$$ Hebbian by deposition of membrane, increasing the folds per volume, because membrane harvesting for vesicle retrieval is from flat$$ + + Rutishauser et al.\cite[p. 348]{rutishauser2014next} "We are able to recall memories that were established years or even decades ago, but the processes by which such remote call(sic) works remain largely unknown." + %$$ it is one cell activating another, and glial cells bringing in blood to the region in response to activated neuron. Remember, it was Wilder Penfield stimulating neurons that brought back remote memories$$ + Rutishauser et al.\cite[p. 348]{rutishauser2014next} "emotions are likely to play a key role in memory formation (Cahill et al. 1995, Fanselow \& Gale 2004, Phelps, 2004) + + + Rutishauser et al.\cite[p. 351]{rutishauser2014next} "There is ample evidence that multiple tasks show sleep-dependent enhancement (Stickgold, 2005)" + + There is a journal Neurobiology of Learning and Memory.(single neuron book p 182) + + Patel et al.\cite[p. 211]{patel2014human} "Knutson and colleagues further demonstrated that NAcc activation increases proportional to the magnitude of the anticipated monetary reward (Knutson et al, 2001) + + According to Kowatari et al.\cite[p.1679]{kowatari2009neural}, Carlsson et al.\cite{carlsson2000neurobiology} "reported that both hemispheres were involved in highly creative subjects." Kowatari et al. \cite[p.1679]{kowatari2009neural} "found that professional training reorganized brain activation patterns, which was correlated with increased creativity." + Kowatari et al. \cite[p.1682]{kowatari2009neural} "In the expert group, a right and left hemispheric difference was obvious; only the right prefrontal cortex (PFC) and parietal cortex (PC) were activated in the expert group, whereas in the novice group, bilateral PFC and PC were activated." + Kowatari et al. \cite[p.1682]{kowatari2009neural} "This results indicated that the direct or indirect interaction between the right and left PFC might contribute to producing highly original designs in the expert group." + + Kowatari et al. \cite[p.1683]{kowatari2009neural} "Based on these observations, we postulated that \ldots brain regions that are involved in yielding high creativity indices shifted from the PC to the PFC." + + Deng et al.\cite[p. 341]{deng2010new} report that "the adult born dentate granule cells (DGCs) exhibit stronger synaptic plasticity than mature DGCs, as indicated by their lower threshold for the induction of long term potentiation (LTP) and their higher LTP amplitude. and, citing Toni et al.\cite{toni2008neurons}, say "structural modification of dendritic spines and axonal boutons continues to occur as the just-born DGCs become older" Toni et al.\cite{toni2008neurons} report that neurons born in the adult dentate gyrus form functional synapses with target cells. + + Deng et al.\cite[p. 343]{deng2010new} report, citing Kee et al. \cite{kee2007preferential} that "learning by a mouse when a set of adult-born DGC was at least 4-6 weeks of age led to preferential activation of these cells during memory retrieval" during the learned task "when the DGCs were 10 weeks old." + + Trouche et al. \cite{trouche2009recruitment} state that recruitment of adult-generated neurons into functional hippocampal networks contributes to updating and strengthening of spatial memory. + + Deng et al.\cite[p. 343]{deng2010new} surmise that finding suggest that, compared with their mature counterparts, adult-born DGCs may be specifically activated by an animal's experiences and thus can make unique contributions to learning and memory. + + Deng et al.\cite[p. 344]{deng2010new} opine that neurogenesis allows plasticity to be mostly localized to newborn immature DGCs, preserving the information that is represented by mature DGCs. %dentate granule cells + + Deng et al.\cite[p. 348]{deng2010new} report, citing Kitamura et al.\cite{kitamura2009adult} "a recent study in mice suggested that adult neurogenesis facilitated memory reorganization that led to a gradual reduction of the hippocampus-dependence of memories and the permanent storage of these memories in extra-hippocampal regions. + + Diekelmann and Born\cite{diekelmann2010memory} state that "Sleep has been identified as a state that optimizes the consolidation of newly acquired information in memory, depending on the specific conditions of learning and timing of sleep. Consolidation during sleep promotes both quantitative and qualitative changes of memory representations. Through specific patterns of neuromodulator activity and electric field potential oscillations, slow-wave sleep (SWS) and rapid eye movement (REM) sleep support system consolidation and synaptic consolidation, respectively. During SWS, slow oscillations, spindles and ripples -- at minimum cholinergic activity -- coordinated the re-activation and redistribution of hippocampus-dependent memories to neocortical sites, whereas during REM sleep, local increases in plasticity-related immediate-early gene activity -- at high cholinergic and theta activity -- might favour the subsequent synaptic consolidations of memories in the cortex." + + Diekelmann and Born\cite{diekelmann2010memory} state that, among its functions, "sleep's role in the establishment of memories seems to be particularly important". promoting primarily the consolidation of memory. + They tell us that "Consolidation refers to a process that transforms new and initially labile memories encoded in the awake state into more stable representations that become integrated into the network of pre-existing long-term memories.", involving active re-processing of 'fresh' memories within the neuronal networks that were used for encoding them. + + Diekelmann and Born\cite{diekelmann2010memory} , citing Stickgold et al., and Walker et al.\cite{stickgold2000visual.walker2003dissociable} state that "For optimal benefit on procedural memory consolidation, sleep does not need to occur immediately but should happen on the same day as initial training." + + Chambers et al.~\cite[p. 1044]{chambers2003developmental}, when discussing events activating loops within primary motivation circuity, state "These events may also facilitate mechanisms of neuroplasticity among nucleus accumbens neurons, and their afferents." + + Chambers et al.~\cite[p. 1045]{chambers2003developmental}, citing Masterman et al.~\cite{masterman1997frontal}, stated "dopamine release into the nucleus accumbens is associated with motivational stimuli, subjective reward, premotor cognition(thought), and learning of new behaviors" + + Chambers et al.~\cite[p. 1045]{chambers2003developmental}, citing Waelit et al.~\cite{waelti2001dopamine}, stated "Rewards delivered in intermittent, random, or unexpected fashions have greater capacity over repeated trials to maintain dopamine cell firing and reward-conditioned behavior." + + Chambers et al.~\cite[p. 1045]{chambers2003developmental} state that "well-learned motivated behaviors or habits performed under expected contingencies become less dependent on nucleus accumbens dopamine release." + + Chambers et al.~\cite[p. 1045]{chambers2003developmental}, citing Yates~\cite{yates1990theories} "In adolescence, the prefrontal cortex has not yet maximized a variety of cognitive functions \ldots Measures of prefrontal cortex function, including working memory, complex problem solving, abstract thinking, and sustained logical thinking, improve markedly during adolescence. + + Wittmann et al.~\cite{wittmann2005reward}show that activation of dopaminergic midbrain is associated with enhanced hippocampus-dependent long term memory formation. + + Wittmann et al.~\cite{wittmann2005reward} state that reward anticipation reliably elicits a dopaminergic response. They hypothesize that the known improved dopamine driven synaptic plasticity and long-term potentiation is associated with better memory consolidation in the hippocampus. Their findings are consistent with they hypothesis that activation of dopaminergic midbrain regions enhances hippocampus-dependent memory formation, possibly by enhancing consolidation. They have shown that activity of the ventral tegmental area and medial substantia nigra accompanied hippocampal activity related to memory formation, in that both structures were activated by novelty and in relation to subsequent free recall performance. The areas that respond to signals related to reward are the dopaminergic areas when the response is reward prediction and the mesial frontal cortex after learning the contingency between the predicting stimulus and the reward; there is a shift with learning.\cite{knutson2003region}. Their findings support their hypothesis that the hippocampus is a major site for the neuromodulatory influence of reward on long-term memory formation. + + Lee et al.~\cite{lee2007strategic} reported on neuroanatomical correlates of converting between symbolic algebra and a pictorial representation. They found that for conversion in either direction, the active areas include the both left frontal gyri, intraparietal sulci bilaterally, which are linked to working memory and quantitative processing. They also found that using the symbolic method activated the posterior superior parietal lobules and the precuneus, in contrast to the pictorial method. They conclude that the symbolic and pictorial strategies impose different attentional demands. + + Lee et al.~\cite{lee2007strategic}, citing Anderson et al.~\cite{anderson2003information}, observe that algebraic transformation is subserved by the left posterior parietal region and the left dorsal lateral prefrontal cortex. Lee et al.~\cite{lee2007strategic}, citing Sohn et al.~\cite{sohn2004behavioral}, who found that "anterior prefrontal activation + was greater in the story condition and posterior parietal + activation was greater in the equation condition". + + $$ then creativity is found in the same or nearby location to the storytelling way, rather than the symbolic representation way$$ + + Lee et al.~\cite[p. 167]{lee2007strategic} report the symbolic method was associated with activation in the left precuneus and bilateral posterior superior parietal lobules. This finding suggest the symbolic condition recruited attentional processes more extensively than did the model method. Also activated were various loci in the visual processing area and in the basal ganglia. The model condition did not activate any areas beyond those activated by the symbolic ". According to Lee et al.~\cite[p. 167]{lee2007strategic}, both the precuneus and the posterior superior parietal lobules are associated with attentional processes. + $$so, maybe it takes more attention to work with symbols. After all, they are more concise$$ + + Lee et al.~\cite[p. 168]{lee2007strategic} citing Owen et al.~\cite{owen2005n} say that dorsolateral prefrontal, overlapping middle frontal is involved in reorganizing material into pre-existing knowledge structures. + + $$ thinking about proof might use this $$ + + Lee et al.~\cite[p. 169]{lee2007strategic} found that "occipital areas were activated in the algebraic condition. This suggests participants spent more time viewing the questions in the algebraic conditions.\ldots activation in the posterior superior parietal lobules might be related" + + Wittmann et al.~\cite{wittmann2007anticipation} found that the "hippocampus differed from the response profile of SN/VTA in responding to expected and 'unexpected' novelty". Their results demonstrate parallels between the processing of novelty and reward in the SN/VTA. Their fMRI analysis revealed that cues predicting novel images elicited significantly higher SN/VTA activation than cues predicting familiar stimuli.[p. 198] + Wittmann et al.~\cite[p. 200]{wittmann2007anticipation} "Irrespective of whether the dopaminergic midbrain drives the hippocampus or vice versa, coactivation of the hippocampus and SN/VTA could be associated with increased dopaminergic input to the hippocampus during anticipation. This, in turn, could induce a state that enhances learning for upcoming novel stimuli" + + Keller and Menon~\cite{keller2009gender} studied brain activation during mathematical cognition, and compared men and women. They found that the same brain areas were used: right intr-parietal sulcus areas and angular gyrus regions, ventral stream of right lingual and parahippocampal gyri. "Females had greater regional density and greater regional volume where males showed greater fMRI activation. \ldots Our findings provide evidence for gender differences in the functional and structural organization of the right hemisphere brain areas involved in mathematical cognition. Together with the lack of behavioral differences, our results point to more efficient use of neural processing resources in females." + Keller and Menon~\cite[p. 348]{keller2009gender}stated "Gender differences were all localized to the right posterior regions of the brain." + + Diekelmann et al.~\cite[p. 116]{diekelmann2010memory} observes that "a great number of studies indicate that sleep supports consolidation of memory in all major memory systems \ldots There is growing evidence that explicit encoding, even in procedural tasks, involves a dialogue between the prefrontal cortex and the hippocampus, citing \cite{schendan2003fmri}, which also integrates intentional and motivational aspects \ldots Sleep changes memory representations quantitatively and qualitatively. \ldots a strengthening of associations \ldots qualitative changes in memory representations." + + $Isay$ In order to encourage the prefrontal cortex involvement, we should be explicit about motivation for choosing one inference rule over another as the demonstration / pedagogical proofs are exhibited.$$ + + Diekelmann et al.~\cite[p. 116]{diekelmann2010memory} observes that "subjects learned single relations between different objects which, unknown to the subject, relied upon an embedded hierarchy, citing \cite{ellenbogen2007human}. When learning was followed by sleep, subjects at a re-test were better at inferring the relationship between the most distant object, which had not been learned before. Likewise, after sleep subjects more easily solved a logical calculus problem that they were unable to solve before sleep or after corresponding intervals of wakefulness citing \cite{wagner2004sleep}. Of note, sleep facilitated the gain of insight into the problem only if adequate encoding of the task was ensured before sleep." + $$ need the definition of adequate encoding. Does this use of encoding refer to placing the representation into, say, hippocampus?$$ + Diekelmann et al.~\cite[p. 116]{diekelmann2010memory} "sleep can re-organize newly encoded memory representations, enabling generation of new assoications and the extraction of invariant features" + $$ here is generalization, abstraction, we want cs students to learn$$ + Diekelmann et al.~\cite[p. 116]{diekelmann2010memory} "from complex stimuli, and therby easing novel inferences and insights. Re-organization of memory representations during sleep also promotes the transformation of implicit into explicit knowledge \ldots procedural and declarative memory systems interact during sleep-dependent consolidation." + They also observe that once implicit memory has become explicit, subjects no longer showed improvement in implicit procedural skill. + $$I'm connecting explicit with conscious. Once the subject is conscious of (interiorized after internalized, using Harel and Sowder's 1998 scheme, thinking about what you are doing as you do it) the procedure, they carry it out consciously, which could be more slowly. Maybe eventually they will become unconscious of how they carry out this skill, maybe the slowing process of conscious execution will drop away$$ + + (what has Stickgold been learning about sleep, memory, lately?) + + Diekelmann et al.~\cite[p. 117]{diekelmann2010memory} "It is assumed that the re-activations during system consolidation stimulate the redistribution of hippocampal memories to neocortical storage sites" + + (probably there is more recent on redistribution) + Diekelmann et al.~\cite[p. 117]{diekelmann2010memory} "In addition to system consolidation, consolidation involves strengthening of memory representation at the synaptic level." + + $$Maybe this is so that when the memories are moved farther out from the hippocampus, there is a stronger trail to it$$ + + Diekelmann et al.~\cite[p. 121--122]{diekelmann2010memory} In the active system consolidation view, "It is assumed that in the waking brain events are initially encoded in parallel in neocortical networks and in the hippocampus. During subsequent periods of SWS the newly acquired memory traces are repeatedly re-activated and thereby become gradually redistributed such that connections within the neocortex are strengthened, forming more persistent memory representations. Re-activation of the new representations gradually adapt them to pre-existing neocortical 'knowledge networks', thereby promoting the extraction of invariant repeating features and qualitative changes in the memory representations." + + Diekelmann et al.~\cite[p. 122]{diekelmann2010memory}, citing Hasselmo et al.\cite{} suggest that "acetylcholine serves as a switch between modes of brain activity, from encoding during wakefulness to consolidation during SWS" + + Diekelmann et al.~\cite[p. 122]{diekelmann2010memory}, citing Wagner and Born \cite{wagner2008memory} observes that glucocorticoids (cortisol in humans) block the hippocampal information flow to the neocortex, and if the level of glucocorticoids is artificially increased during SWS, the consolidation of declarative memories is blocked. + + $Isay>$ so, we need to find out whether students who play video games on the way to retiring are decreasing or increasing their cortisol in the process.$$ + + + There is evidence that some games help reduce cortisol "The impact of playing computer games on cortisol concentration of saliva before and after the game showed that the amount of saliva plasma after playing the game has dropped significantly." \cite{aliyari2015effects}, casual video games decrease stress\cite{russoniello2009effectiveness} and there is evidence that Tetris in particular reduces stress\cite{mercer2015stress} and there is evidence that excessive use of violent video games by some young men \cite{eickhoff2015excessive} can negatively impact their cognitive effectiveness. Maass et al. conducted a study on 117 university students; Maass et al. state "The more time spent on media the poorer cognitive performance is. This association has mainly been found for general-audience, violent, and action-loaded contents but not for educational contents. \ldots A significant univariate difference was found for high- vs. low-arousing contents in general (independent of type of media), the high-arousing content leading to poorer ability to concentrate after media use. The expected mediating and moderating effects are not supported. The study yields evidence that short-term mechanisms might play a role in explaining the negative correlations between media use and cognitive performance." \cite{maass2015does} + + $Isay>$ might wish to advise students who play video games on the way to retiring to, close to retiring, use those that reduce stress$$ + + Diekelmann et al.~\cite[p. 122]{diekelmann2010memory} report "The concept of a redistribution of memories during sleep has been corroborated by human brain imaging studies (82,83,149,159,158) Interestingly, in these studies, hippocampus-dependent memories were particularly redistributed to medial prefrontal cortex regions (82,83,122)." + + $$ if it is the case that when students. trying to understand some math in computer science, but opting to memorize, given the time available (Is this what David Tall's bifurcation is about?) form memories that are not hippocampus-dependent (procedural memories are less hippocampus dependent)? If so, is it then also the case that they are less likely to be conveyed to the medial prefrontal cortex? Is the intervention then that instructors provide better explicit descriptions, give exercises to write something in code, which we hope is a bridge from internalized/implicit to interiorized/explicit, declarative, and avail ourselves of emotional support by evaluating the beauty, to aid in recruiting hippocampus-dependent memory formation? $$ + + Diekelmann et al.~\cite[p. 122]{diekelmann2010memory} state that "These regions not only have a key role in the recall and binding of these memories once the are stored for the long term, citing Frankland and Bontempi \cite{frankland2005organization}, \ldots prefrontal-hippocampal system might provide a selection mechanism that determines which memory enters sleep-dependent consolidation." + + Diekelmann et al.~\cite[p. 123]{diekelmann2010memory} state that the REM time interval upregulation of genes related to plasticity is dependent upon the learning experience in prior wakefulness, and is localized to the brain regions involved in prior learning, citing Ribeiro \cite{ribeiro2007novel,ribeiro2002induction}. + + \paragraph{Steps} + \begin{enumerate} + \item the input is a demonstration of a proof that explicitly describes the motivation for choosing each successive inference rule after another, and explicitly describes the motivation for choosing each lemma, i.e., why was that part of the proof handled separately, (e.g., we know we can, and we know it will be useful, but something about how we suspect it will be useful) Moreover, because we know emotional content is helpful in consolidation of memory during sleep, we remark upon such beauty as we may find in the proof. + Note that it is important to be, in the unfolding of time, orderly. + \item sensory input appears in sensory acquisition (accompany with pleasant scent\cite{born2012system}, and relevance to future plans\cite{born2012system}) + \item sensory input conveyed to medial temporal lobe, where it is sometimes seen with single neuron instrumentation + \item unexpected novelty stimulates dopamine, differently from expected novelty (as in exploration) + \item reward stimulates dopamine, or, if prediction of reward is learned, the stimulus role is transferred to the prediction + \item dopamine can come from SN/VTA + \item dopaminergic midbrain is associated with enhanced hippocampus-dependent long-term memory formation \cite{wittmann2005reward}, i.e., rewards help form long term memory, and it occurs in some sleep phase, maybe REM or slow wave + \item LTP is divided into early and late, and dopamine contributes to late~\cite{wittmann2005reward} + \item dopamine is also used for long term depression, which is also learning + \item new neurons are generated~\cite{deng2010new} related to new hippocampus memories + + \item explicit (vs. only implicit) learning favors access to sleep-dependent consolidation\cite[p. 115]{diekelmann2010memory} + \item motivational tagging of memories, might signal behavioral effort and relevance and mediate preferential consolidation\cite[p. 116]{diekelmann2010memory} + \item if video games are played just before retiring, they should probably not be violent. Conversely, if violent video games are played, something else, such as Tetris, should be used after the violent ones, prior to retiring. + \item sleep deprivation is expected to be detrimental to learning + \item sleep occurring 3 hours after learning was more effective than sleep delayed by more than 10 hours.\cite{gais2006sleep,talamini2008sleep,walker2003dissociable} + \item use same scent as in class, during SWS + \item slow oscillations typically seen in slow wave sleep (earlier part of sleep) have a causal role in the consolidation of hippocampus-dependent memories~\cite[p. 119]{diekelmann2010memory} + \item ripples typically seen in slow wave sleep (earlier part of sleep) have a causal role in the consolidation of memories~\cite[p. 119]{diekelmann2010memory} + \item it is not a particular sleep stage per se that mediate memory consolidation, but rather the neurophysiological mechanisms associated with those sleep stages~\cite[p. 116]{diekelmann2010memory} + \item re-activation of encoded memories occurs during slow wave sleep, in the order the remembered material was experienced Maquet\cite{maquet2000experience} cited in Diekelmann\cite[p. 117]{diekelmann2010memory} + \item theta oscillations, associated with REM sleep, have been found specifically over the right prefrontal cortex to be correlated with the consolidation of emotional memories\cite{nishida2009rem} + \item practice retrieval\cite{Bridge01082015}, better after sleep, can disrupt decoding if before sleep (check with Bridge 2015) + \item once attention to an item of knowledge has been rewarded, subsequent attention to that item is involuntary \cite{sali2014role} + \item consolidation occurs, differentiated by number of modalities, could be inert knowledge, as Whitehead~\cite{whitehead1959aims}, or retrievable, preferably. The number of related modalities, the more easily retrieved. + \item Retrieval allows for reconsolidation.\cite{sandrini2015modulating} (check it)\cite{schwabe2014reconsolidation}(check it) \cite{forcato2013role}(check it) + \cite{walker2003dissociable} (check it) + \item dopamine, nucleus accumbens helps reconsolidation occur with connection to right pre-frontal cortex \cite{knutson2001anticipation} and this is helped by anticipation of positive reward + \item right pre-frontal cortex is what experts use to be creative \cite{kowatari2009neural}, so we want to shepherd our taught material here, so that it is readily retrievable for inventing proofs + \end{enumerate} + + Chou et al.~\cite[p. 726]{chou2011sex} observes "the analytic brain for mathematical and logical cognition comprises the inferior frontal gyrus, parietal cortex and supramarginal gyrus", citing Dehaene et al, 1998k Goel et al., 1998, Zago et al., 2001. They measured, using fractional anisotropy (FA), microstructure of white matter that differed significantly in several areas, between men and women. + $$Of these, at least the bilateral precuneus has been identified as of interest in mental activity related to mathematical proofs.$$ + They state ~\cite[p. 731]{chou2011sex} "the interaction analysis of dispositional measures by sex demonstrated that FA of the WM \ldots underlying occipital gyrus and postcentral gyrus was negatively associated with systematic quotient (SQ)in females.\ldots males exhibited larger FA in the WM of hippocampus whereas females showed larger FA in WM of parahippocampal gyrus \ldots females typically hold an advantage in tasks related to declarative memory, in which the parahippocampal gyrus has been implicated, such as in the retrieval and recognition of longterm \ldots memories." + + Lisman et al.\cite{lisman2011neohebbian} report that "For novel information and motivational events such as rewards this signal at hippocampal CA1 synapses is mediated by the neuromodulator, dopamine." They summarize a consequence of the Hebb framework "if cell A represented object A and cell B represented object B, the co-occurrence of the two object would, by the Hebb rule, strengthen the synaptic linkage between these cells. This link would subsequently be evident when only object A was presented because it would lead to the firing of cell B, thus bringing object B to mind by association." + + Lisman et al.\cite[p. 537]{lisman2011neohebbian} state "Two types of experiments demonstrate that dopamine can strengthen the synaptic potentiation produced by learning itself." + %PPT pedunculopontine tegmentum + Lisman et al.\cite[p. 540]{lisman2011neohebbian} state "Thus, novelty, reward stimuli and aversive stimuli are all able to activate the dopamine system \ldots in humans. + + Lisman et al.\cite[p. 540]{lisman2011neohebbian} state "This reward-related memory enhancement was associated with a coactivation of SN/VTA, striatum, and hippocampus, as detected by fMRI (\cite{adcock2006reward,wittmann2005reward}) Memory enhancement after long retention intervals (e.g. 24h) has been consistently found (\cite{krebs2009personality,wittmann2011behavioral}). Moreover, the enhancement was greater at late timepoints than at early intervals (i.e. 3 wks vs 20 min)(47) + + $$ using novelty, reward (or punishment, i.e., if there are bad test grades, maybe they can be used), make these memories.$$ + + Lisman et al.\cite[p. 540]{lisman2011neohebbian}point out that it is necessary to be able to encode and consolidate after a single exposure. + + \begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{./lismanNeoHebbian} + \caption{connectivity in medial temporal lobs and hippocampus ventral tegmentum loop processing info about object and spatial context. Allows perirhinal cortical info about novelity to general dopamine response} + \label{fig:lismanNeoHebbian} + \end{figure} + Lisman et al.\cite[p. 542]{lisman2011neohebbian} summarize a model, citing Frey and Morris~\cite{frey1997synaptic} "weak stimulation induces on ly early long term potentiation (LTP). By contrast, stronger stimulation produces the dompamine-dependent protein synthesis that allows late LTP.\ldots the memory for event sthat occur before or after the dopamine release would depend not only on their own properties, but also on whether they fell within the penumbra of a dopamine-releasing stimulus." + + $$Music that gives "chills" gives dopamine, so if we could play something like the prelude to the StarWars IV before class, students would be primed. Some national anthems might be chill inducing, such as the French, Marseillaise (lyrics?) How long is this penumbra? It could be different for each person. for rodents, 1/2 hour$$ + + Lisman et al.\cite[p. 542]{lisman2011neohebbian} "novel photographs of natural scenes ('strong events', such as those one would expect to see in the magazine National Geographic)" had a penumbra of at least 5 minutes. + + $$so, have some slides with nat geo pictures, at least every 5 minutes, new every time$$ + + Lisman et al.\cite[p. 542]{lisman2011neohebbian} "Cholinergic\cite{sarter2005unraveling} and noradrenergic\cite{frey2008synaptic} projections to Medial temporal lobes can also modulate Long term potentiation and long-term memory. \ldots Reward-related SN/VTA activation improves memory for the rewarded stimulus but not for the non-rewarded stimuli given in close temporal proximity \cite{wittmann2011behavioral} implying either a very short or a very stimulus-specific penumbra. This is at odds with the observation that novelty-related activation of the SN/VTA has a long (ca 30 min) penumbra that affect memory for unrelated information (e.g., exposure to novel scenes can affect memory for words)\cite{fenker2008novel} One possible resolution is that the duration or stimulus-specificity of the penumbra depends on the type of motivational event that triggers dopamine release." + + Lisman et al.\cite[p. 544]{lisman2011neohebbian} "the ability to recollect newly acquired information could be intrinsically rewarding. In fact, the study of human learning has revealed an interesting puzzle; long-term retention is not helped by simple re-exposure to recently learned material but is greatly helped by retesting even when subjects already know the answer \cite{karpicke2008critical}. One interesting possibility is that retesting provides an opportunity to generate intrinsic reward signals, thereby enhancing long-term persistence of newly learned material." + + Mains et al.~\cite{Mains01072015}"Embedding three (clicker) questions within a + 30 min lecture increased students' knowledge + immediately after the lecture and 2 weeks later. We + hypothesise that this increase was due to forced + information retrieval by students during the learning + process, a form of the testing effect." + + Bridge and Voss \cite{Bridge01082015} "Cueing with actively retrieved objects facilitated memory of associated objects, which was associated with unique patterns of viewing behavior during study and enhanced ERP correlates of retrieval during test, relative to other reminder cues that were not actively retrieved. Active short-term retrieval therefore enhanced binding of retrieved elements with others, thus creating powerful memory cues for entire episodes." + + $$students may make their own flash cards to practice retrieval, but it appears a more effective strategy would have multiple differing cues$$ + + Rottschy e al.\cite[p. 830]{rottschy2012modelling} define "working memory subsumes the capability to memorize, retrieve and utilize information for a limited period of time". + + Rottschy e al.\cite[p. 836]{rottschy2012modelling} "experiments using non-verbal material showed significantly higher convergence in the left (pre-)motor area and bilateral dorsal pre motor cortex." + + Rottschy e al.\cite[p. 843]{rottschy2012modelling} "selective attention system (Shulman et al.) \ldots is right-dominant and \ldots includes the temporo-parietal junction. \ldots apparent overlap between a distributed central executive for working memory, (and) the attention system" + + $$we can get their attention, for example by music that gives chills, and it will bring blood circulation to those areas, so, working memory will be supplied with circulation$$ + + + + Wittman et al.\cite{wittmann2011behavioral}"Recent functional imaging studies link reward-related activation of the midbrain substantia nigra –ventral tegmental area + (SN/VTA), the site of origin of ascending dopaminergic projections, with improved long-term episodic memory. Here, + we investigated in two behavioral experiments how (1) the contingency between item properties and reward, (2) the magnitude of reward, (3) the uncertainty of outcomes, and (4) the contextual availability of reward affect long-term memory. + We show that episodic memory is enhanced only when rewards are specifically predicted by the semantic identity of the + stimuli and changes nonlinearly with increasing reward magnitude. These effects are specific to reward and do not occur in + relation to outcome uncertainty alone. These behavioral specifications are relevant for the functional interpretation of how + reward-related activation of the SN/VTA, and more generally dopaminergic neuromodulation, contribute to long-term + memory." + + Abraham et al.\cite[p. 1906]{abraham2012creativity} investigates a specific aspect of creativity that they call conceptual expansion. They found that this activity selectively involved the anterior inferior frontal gyrus, the temporal poles and the lateral frontopolar cortex. These findings "go against \ldots dominance of the right hemisphere during creating thinking, and indicate \ldots anterior cingulate cortex \ldots (for) abstract facets of cognitive control." + + Abraham et al.\cite[p. 1907]{abraham2012creativity} explain that conceptual expansion "refers to the ability to widen the conceptual structures of acquired concepts, a process that is especially critical in the formulation of novel ideas", citing Ward~\cite{ward1994structured}. + Abraham et al.\cite[p. 1910 -- 1911]{abraham2012creativity} found that the regions involved were left anterior inferior frontal gyrus, lateral frontopolar cortex, temporal poles, posterior regions in the inferior frontal gyrus, the middle frontal gyrus, the anterior cingulate cortex, the dorsomedial prefrontal cortex and the inferior parietal lobule. The "activation pattern is strongly lateralized to the left hemisphere." For working memory, "the overall brain activation pattern as a function of working memory was stronger in the right hemisphere" + + \begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{./frontopolar-cortex} + \caption{left frontal polar cortex playing a particularly relevant role in concept expansion, is thought to mediate cognitive control at the most abstract level of information processing. The left dorsolateral pre frontal cortex, and the dorsomedial prefrontal cortex (BA8/9 and 8) also showed stronger brain activity} + \label{fig:frontopolar-cortex} + \end{figure} + + \begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{./inferiorfrontalgyrus} + \caption{Conceptual expension was associated with greater brain activity in left anterior inferior frontal gyrus (right is pictured)} + \label{fig:inferiorfrontalgyrus} + \end{figure} + + \begin{figure} + \centering + \includegraphics[width=0.9\linewidth]{./gr1} + \caption{The inferior frontal gyrus, temporal poles and frontopolar cortex are involved in coceptual expansion. The roles of the anterior cingulate cortex and the dorsolateralprefrontal cortex were found to be most responsive in conceptual expansion, and active in divergent thinking.} + \label{fig:gr1} + \end{figure} + + Abraham et al.\cite[p. 1912]{abraham2012creativity} In a measure intended to isolate cognitive control processes, results showed the dorsolateral prefrontal cortex and superior parietal lobule bilaterally, and "only the right dorsolateral prefrontal cortex and anterior cingulate were found to be involved." + + $$we are seeing that being creative calls upon left side structures, and when we get specifically to being creative with symbolic and diagrammatic representations, we may call upon also the right sides. $$ + + Abraham et al.\cite[p. 1913]{abraham2012creativity} "The roles of the anterior cingulate cortex and the dorsolateral pre-frontal cortex are particularly noteworthy given the patterns of activation in these regions in the current study. Not only were they found to be more activated during divergent thinking compared to working memory, more importantly, they were also found to be most responsive as a function of conceptual expansion. \ldots the posterior aspect of the dorsomedial pre frontal cortex was also activated as a function of conceptual expansion. \ldots As this region has been discussed with reference to concepts that are central to hypothetical reasoning, such as constructive processes in cognition~\cite{abraham2008thinking} which involve flexible recombination of representations from memory~\cite{schacter1998cognitive} and evaluative judgment~\cite{zysset2003functional}, the dorsomedial prefrontal cortex may prove to be highly relevant structure for select aspects of creative thinking. \ldots speaks against the ubiquitous idea the right brain is more 'creative' than the left. \ldots in the current study, we have explored the deliberate problem solving mode of creating thinking under time constraints. There is, however, another vast dimension of creative thinking where idea generation occurs spontaneously, effortlessly, and/or in a state of defocused attention~\cite{|} In fact, creating idea generation is far less likely to result from deliberate cogitation during real everyday problem solving, but instead, it occur spontaneously and unpredictably. This unconscious non-deliberate spectrum of creating thinking \ldots is less amenable to well-controlled investigation. " + + Born and Wilhelm~\cite[p. 192]{born2012system} "Experimental evidence for these three central implication is provided: It has been shown that reactivation of memories during slow-wave sleep(SWS) plays a causal role for consolidation, that sleep and specifically SWS consolidates preferentially memories with relevance for future plans, and that sleep produces qualitative change in memory representations such that extraction of explicit and conscious knowledge from implicitly learned materials is facilitated." + + $$In procedural memory we don't need to know why, there might not be any, (for example, remember the melody) but for some things they are accompanied by why. Is declarative everything other than procedural? What about implicit vs. explicit? These both are compatible with "why". There are times when we can use knowing why to save on what would otherwise need to be remembered. Does it have a name? Is it named in David Tall's article with bi-furcation in the name?$$ + + Born and Wilhelm~\cite[p. 195]{born2012system} "Via the olfactory system odour stimulation acquires immediate access to the hippocampus. \ldots we found that the odour when re-exposed during SWS after learning induced a distinct activation of the left hippocampus, i.e. the odour served as a cue that reactivated the new memories for the card locations encoded in the left hippocampus, thereby enhancing these memories \ldots hippocampal networks are particularly sensitive in SWS to inputs capable of reactivating memories." + + Born and Wilhelm~\cite[p. 197]{born2012system} "explicit encoding favours access to sleep-dependent memory consolidation (\cite{robertson2004awareness}). Involvement of the prefrontal-hippocampal system underlying explicit encoding has been proposed as prerequisite for consolidation to occur during sleep(\cite{marshall2007contribution}). \ldots emotionality of the encoded events can increase the memory benefit from sleep (\cite{kuriyama2004sleep,wagner2006brief})." + + Wagner et al. \cite{wagner2006brief} investigated memory after a four hour interval of sleep. "Sleep following learning compared with wakefulness enhanced memory for emotional texts after 4 years (p = .001). No such + enhancement was observed for neutral texts (p = .571)." + + Born and Wilhelm~\cite[p. 197]{born2012system} "Processing of anticipatory aspects of behaviour such as expaectancies and plans is particularly linked to executive functions of the prefrontal cortex that regulates activation of memory representations during anticipated retrieval and accommodates specifically the intentional and prospective aspects of a memory representation~\cite{polyn2008memory} \ldots prefrontal tagging of memories explicitly encoded under control of the prefrontal-hippocampal system could be decisive for the selectivity in off-line memory consolidation" + + Born and Wilhelm~\cite[p. 199]{born2012system} "there is convergent evidence \ldots that the system consolidation process during sleep supports the extraction of invariant and repeating features in newly encoded memories, and in this way, the conversion of implicit into an explicit and conscious form of memory \ldots more than twice as many subjects of the sleep group gained insight into the hidden structure as compared with the wake control group \ldots subjects who had slept after \ldots training were distinctly more able to deliberately generate the sequence underlying \ldots than the subjects who had stayed awake" + + Born and Wilhelm~\cite[p. 201]{born2012system} "sleep appears to prime the transformation of implicitly encoded information into explicit knowledge, i.e., something that is not conscious before sleep enters consciousness through sleep". + + Dudai~\cite[p. 229]{dudai2012restless} defines declarative memory as that which requires conscious awareness for retrieval (facts, events), and nondeclarative can be retrieved in absence of conscious awareness (habit, skill). + + Dudai~\cite[p. 231]{dudai2012restless} reminds "university students can improve their memory bye practicing self-testing, because retrieval practice is a powerful mnemonic enhancer", citing Karpicke and Roediger~\cite{karpicke2008critical}. + + Forcato et al.~\cite[p. 1]{forcato2013role} observe "the reconsolidation process alllows new information to be integrated into the background of the original memory; second it strengthens the original memory. \ldots at least one labilization-reconsolidation process strengthens a memory via evaluation 5 days after its re-stabilization. \ldots this effect is not triggered by retrieval only. \ldots repeated labilization-reconsolidation processes made the memory more resistant to interference during re-stabilzation." + + Forcato et al.~\cite[p. 1]{forcato2013role} "reconsolidation does not represent recapitulation of initiali consolidation, but rather, if refers to the functional role of this process: to stabilize memories." + + Forcato et al.~\cite[p. 2]{forcato2013role} "when the reminder only included contextual cues (context reminder), the memory was evoked but not labilized." + + A reminder has the effect of labilization which allows reconsolidation. "We found that just one labilization-reconsolidation process was enough to strengthen a memory that was evaluated 5 days following its re-stabilization. \ldots Memory persistence is increased by repeated triggering of labilization-reconsolidation." + + Wirebring et al. \cite{}"Repeated testing is known to produce superior long-term retention of the to-be-learned material compared with repeated encoding and + other learning techniques, much because it fosters repeated memory retrieval. This study demonstrates that repeated memory retrieval + might strengthen memory by inducing more differentiated or elaborated memory representations in the parietal cortex, and at the same + time reducing demands on prefrontal-cortex-mediated cognitive control processes during retrieval. The findings contrast with recent + demonstrations that repeated encoding induces less differentiated or elaborated memory representations. Together, this study suggests + a potential neurocognitive explanation of why repeated retrieval is more beneficial for long-term retention than repeated encoding, a + phenomenon known as the testing effect." + + \subsection{Educational Neuroscience} + + \section{Systems Biology} + be sure to get the Kandel, Dudai 2014 review + + \section{Physiologically Informed Constructivism} + Research has shown the progression of an idea, from a short term representation in the medial temporal lobe, to a consolidated memory in an area related to the single sensory modality with which that idea was received, to a representation in association cortex when multiple sensory modalities are involved, to a reconfiguration in right prefrontal cortex when an idea is used creatively. + How we as instructors shepherd these representations in the minds of our students can be suggested by cognitive neuroscience. One example is a deeper understanding of the utility, for memory and attention, to intrinsically rewarding learning activities. Another example is the application of multiple sensory modalities, such as representations in figures, text and mathematical symbols, and also pseudocode. Yet another is the deliberate construction of pseudo-monetary rewards, of unpredictable value, in the immediate aftermath of + instruction of a new idea. (This derives its effect from the dopamine response to the monetary reward, which is augmented by not knowing the amount.) + + We can expect information stored in the cortex near a single sensory modality to be retrieved when a similar situation recurs. When multiple modalities are involved there are more ways to arrive at increased metabolism reactivating this memory, bringing it into consciousness. + + Music is rewarding. The areas of the brain that are rewarded by memory are the same ones that help us remember. (Blood Zatorre salimpoor) We can reward the students / administer dopamine to help them remember. We have from Blood and Zatorre~\cite{blood2001intensely} that music so intensely pleasurable that it creates "chills" is correlated with activity in nucleus accumbens, which we also know, from (whom?) advances consolidation of memory representations in medial temporal cortex into longer term memory. %Here I am thinking how REM sleep is seen to be helpful to consolidation of memory, and I am thinking about the "subject matter" of REM sleep, and wondering whether a method more time-efficient than sleep could be developed + + $$ bagpipe music generates chills$$ + + We want the students to construct an understanding of the material, for example, the correctness or resource utilization of an algorithm, and to be able to creatively apply the information they have to construct a proof of it. + + The material first arrives in the student's awareness through some sensory modality, and we wish the information to be remembered, not only as inert knowledge, but as information that enters consciousness in response to a situation in which it is usefully employed in a proof. + + Lisman and Grace\cite{lisman2005hippocampal} describes the hippocampal--ventral-tegmental area loop, controlling the entry of information into long term memory, facilitated by dopamine(DA). One stimulus for production of DA is the arrival of an unexpected reward \cite{schultz2000neuronal}, another is novelty\cite{kafkas2015striatal} (check this). Instructors can provide unexpected rewards with, for example, increased points for clicker questions. Other ways to provoke DA release, in the part of the brain that produces memories, is with music.\cite{salimpoor2015predictions} (check that this is the right article). Lisman and Grace\cite{lisman2005hippocampal} describe reactions that they state "provide a basis for the dopaminergic modulation of early long term potentiation (LTP)", which is a change to the signaling behavior of neurons in the brain. They continue "It follows that novelty itself should enhance LTP." Moreover they claim\cite[p. 707]{lisman2005hippocampal} "There is reasonable evidence from animal experiments that DA enhances learning, as would be expected from its enhancement of LTP." and \cite[p. 708]{lisman2005hippocampal}"The spiny cells in the accumbens are a likely site for combining novelty signals and goal-dependent motivational signals." and \cite[p. 709]{lisman2005hippocampal} "reasonable working hypothesis that \ldots combines novelty signals with information about saliency and goals \ldots thereby enhance the entry of the information into memory." \cite[p. 709]{lisman2005hippocampal} "without dopamine, late LTP does not occur and early LTP decays within about an hour." + + Wittmann et al.\cite{wittmann2005reward}"Long=term potentiation in the hippocampus can be enhanced and prolonged by dopaminergic inputs from midbrain structures such as the substantia nigra. This improved synaptic plasticity is hypothesize to be associated with better memory consolidation in the hippocampus." They say that reward anticipation reliably elicits a dopaminergic response. They hypothesize that "activation of dopaminergic midbrain regions enhances hippocampus-dependent memory formation, possibly by enhancing consolidation." Wittmann et al.\cite[p. 464--465]{wittmann2005reward}"supports our hypothesis that the hippocampus is a major site for the neuromodulatory influence of reward on long-term memory formation \ldots supports the hypothesis that dopaminergic neuromodulation enhances hippocampus-dependent memory formation \ldots It is likely that a greater proportion of subsequently recallable items will undergo hippocampus-dependent consolidation than of subsequently recognizable items. \ldots these results provide evidence for a relationship between activation of dopaminergic areas and hippocampus-dependent long-term memory formation." + + Here I want to diagram a sequence of activities mapped onto the brain areas, showing the progression of memory from the medial temporal lobes with new dentate granular cells, followed by consolidation in one sensory cortext or association cortext followed by reconsolidation into prefrontal and parietal followed by prefrontal from where it can be used creatively in the construction of proofs. It would be good if I could cite references for each milestone, and associate with conceptualizations, such as those in Harel and Sowder and Tall. + + % % % % % % % % % % % % % % % % + + \subsection{Intuition} + help and obstacle\\ along with obstacles arising from intuition there exist epistemological obstacles Bachelard 1938 Brosseau 1983 preventing acquisiton of new knowledge. There exist didactic obstacles. + epistemological obstacles + \subsection{Met-befores} + Tall\\ + McGowan Tall\cite{Metaphor or met-before 2010 Jour Math Behavior}, The idea met-before (formerly met afore) emphasize that a metaphor relates new knowledge (the 'target') in terms of existing knowledge (the 'source') developed from previous experience, so that new ideas can be related to familiar knowledge already in the grasp of the learner. + + Small example of a met-before: Integrated circuits are available at many levels of integhration, from singletons of transistors to tens of millions. + One simple circuit function ins the counter. The number of cluck edges since the last reset, modulo the number given by $2^n$, where $n$ is the number of bits in the counter, is represented digitally, that is, by a voltage level whose domain has been partitioned into that representing 1 and that representing 0. A counter may reset immediately (so to speak) upon the reset signal. This kind is called asynchronous reset. The synchronous reset kind resets after a clock edge occurs during a reset input. + Having, for the purposes of this example, set the context this way, now consider this problem, from Santos-Trigueros\cite{[p. 74]{}} + ``Nine counters with digits from 1 through 9 are placed on a table.'' + Had we not just been discussing counters in another setting, this sentence might have been understood as intended, more quickly. That is, the context can serve as a distraction, to be overcome. It can help the instructor to realize that students arrive in class, not only lacking wished-for preparation, but also bringing unhelpful contexts. + \subsection{Harel and Sowder} + \subsection{van Hiele Levels} + \subsection{Student Centered} + something about students' perspectives are not always well-matched to their needs + + Students might have in mind material they would like to learn, and there may be also a lack of appreciation for material in required courses + Students may have a rate at which they would like to learn --- points at which they would like to pause and integrate new material with things they already know. + \subsection{Attention} + Lindquist \cite{lindquist2013mind} describes Mind wandering during lectures: Observations of the prevalence and correlates of attentional lapses, and their relationships with task characteristics and memory. + + Brosch et al.\cite{brosch2013impact} examined the impact of emotion on perception, attention, memory, and decision-making. + + Sali et al.\cite{sali2014role} show that "Previously rewarded stimuli involuntarily capture attention." + + \subsection{Memory} + Ojemann\cite[p. 257]{ojemann2014human} " \textit{episodic, explicit} or \textit{declarative} memory, memory for the specific event (specific name, word) that occurs at encoding " + + Ojemann\cite[p. 257]{ojemann2014human} "Our memory paradigm requires storage over a short period and thus a measure of \textit{recent} or \textit{short-term} memory. In the functional neuroimaging literature memory for this duration is often referred to as \textit{working} memory. + + Ojemann\cite[p. 257--258]{ojemann2014human} "Lateral temporal cortex \ldots models of brain stubstrate for recent verbal memory \ldots during the encoding phase." + + \subsection{Social Constructivism} + Attempts at communication, as in conversations about material, are regarded + as helpful to learning. + + McGowan Tall 2013 Jour Math Behav + ``One student wrote that she knew her answer was correct (it was actually incorrect) because the other members of her group agreed with her. These students consistently evaluated both the numerical expression 'minus a number squared' and a quadratic function with a negative-valued input incorrectly throughout the remaining twelve weeks of the semester. This cautions us to realize that cooperative leaning amongst students who are failing to make sense of the mathematics may reinforce their problematic conceptions rather than reconstruct them'' [p. 533] + + Though it is easy to assume that communication between practitioners is carried out verbally, there are examples of proofs without words \cite{nelson1993proofs}. + + D\"orfler\cite[p. 129]{dorfler2000means} proposes that by discussion, abstraction can be promoted "the abstract terms might serve the purpose of talking about a variety of concrete, even physical experiences such as describing observations \ldots This abstracted manner of talking then acquires some independence from the experiences and experiential phenomena referred to, so that the abstract objects gain discursive existence. First, the abstract description lends 'meaning' to the experiences. Later, the abstract objects derive their 'meaning' from their taken-to-be representations or applications." + + D\"orfler\cite[p. 129]{dorfler2000means} summarizes "our experiences with material objects are schematized in an image schema that is projected metaphorically to terms such as \textit{abstract object}. \ldots At times, these image schemas might even be exteriorized by symbolic expressions that, in turn, can serve as generic terms. \ldots A cognitively oriented explanation for the failure to be inducted into the mathematical discourse is, therefore, the lack of image schemata on which to base the discursive extension \ldots this lack might results from an absence of pertinent experiences \ldots there can be differences in the abilities of each individual to schematize his or her experiences and to make metaphoric use of words." + + + + \subsection{Beliefs about Diagrams} %after social constructivism, because people attempt to communicate with diagrams + helpful, hindering, post-conceptual (i.e., they refer to existing concepts, maybe do not convey new ones), + Hilbert's ``who does not'' with a, b, c\\ + perceptual to transformative\\ + animation + \subsection{Semiotics} + Because sybmolization supports generalization\cite{loewenberg2003mathematical} and operations in mathematics\cite{schoenfeld1998reflections}, and because symbols are used also in efficient communication with others, symbolization is a skill our students need. + + Van Oers\cite[p. 133--134]{van2000appropriation} emphasizes the role of the adoption of symbol use, as students learn mathematics, stating "Mathematics as a discipline is now generally conceived of as an activity in which constructive representation, with the help of symbols, plays a decisive role" citing Bishop, Freudenthal and Kaput. + + Van Oers\cite[p. 133--134]{van2000appropriation} summarizes: "According to Freudentahl, mathematics is basically an activity of mathematizing: that is, organizing a (concrete empirical or abstract mental) domain, representing it with the hop of symbols \ldots experimenting with symbolic means". Freudenthal\cite[p. 10]{freudenthal1973mathematics} describes some of the history of symbol use: "Another algebraic idea is symbolism, the use of signs which do not belong to everyday language, to indicate variables. 'Think of a number' is how the problems are introduced in old narrative algebra. In Diaphantus' work the word 'number' becomes more and more a computation symbol. This continues in Indian and Arabian mathematics. The \textit{cossists} of the late Middle Ages has a whole system of symbols for the unknown and its powers \ldots " + + Van Oers\cite[p. 135]{van2000appropriation} states that van Hiele "emphasized the importance of symbols in mathematics for grasping the mathematical meaning. \ldots appropriating the meaning of symbols is primarily a communicative process" requiring a mutual understanding of the meaning. + + Van Oers\cite[p. 136]{van2000appropriation} states: "Symbols are indispensable as means for coding the results of thinking. More importantly, however, symbols also function as ways of organizing in the course of thinking". He goes on to report " According to empirical investigations of the development of mathematical thinking in pupils, the failure of meaningful appropriation of mathematical symbols has turned out to be one of the main problems in mathematics learning.", citing Hughes, 1986 and Walkerdine, 1988, also Miles and Miles 1992. + + Van Oers\cite[p. 170]{van2000appropriation} states: "The analysis of symbolizing in a mathematical context has led us to the realization that symbol use is intrinsically related to meaning, negotiation of meaning, and communication." + + Nemirovsky and Monk described symbolizing\cite[p. 177--178]{nemirovskymonk} "Conceiving of symbolizing as the creation of a space in which the absent is made present and ready at hand elicits at least two major issues: (a) the nature of such a space, and (b) the ways in which the absent is made present and ready at hand". + They observe \cite[p. 178]{nemirovskymonk} "our play as children is a crucial activity through which each one of us has practiced and learned to symbolize", citing Piaget 1962, Slade and Wolf 1994 and Winnicott, 1971/1992. + Nemirovsky and Monk give an example \cite[p. 204]{nemirovskymonk} "Lin shifted her attention from being immersed in creating something \ldots to reflecting on it as a particular manner of doing things". They go on to say, "Symbolizing is making possible the sudden and unanticipated encounter with past experience that can radically transform the 'here and now' of the symbolizer. + + $$ sudden, unanticipated, coming into consciousness is a relevant idea $$. + + Nemirovsky and Monk state\cite[p. 212]{nemirovskymonk} "Insights that 'come' or 'happen' to us is a way of saying that we often experience what we become as surprising and unexpected." + + Bransford et al.\cite{bransford2000designs} mention "a common problem of expertise, namely, that things become so intuitively obvious that one forgets the difficulties that novices have in grasping new ideas". + + $$ consider that procedures to which we have become so accustomed that we do not need conscious attention (e.g., shifting gears for a car or bike) could be represented more efficiently in neurons, see Kandel and Squire on Memory and Attention\cite{squire2000memory} and Squire \cite{squire2015conscious}$$ \ No newline at end of file diff --git a/chp7p1.png b/chp7p1.png new file mode 100644 index 0000000..6d950eb Binary files /dev/null and b/chp7p1.png differ diff --git a/frontmatter.tex b/frontmatter.tex new file mode 100644 index 0000000..00069ec --- /dev/null +++ b/frontmatter.tex @@ -0,0 +1,118 @@ +%%%% Unless you have more than two associate advisors, or more than two previous degrees, there is no need to edit this file. If you do fall into one of the latter categories, the set-up below should be transparent enough for suitable adjustments to be made. + +\frontmatter + +%%%Title page 1 +\thispagestyle{empty} +\begin{center} +{\LARGE +{\bf\mythesistitle} +} +\vspace{.6in} + +\myname, Ph.D.\\ +University of Connecticut, \myyear + +\vspace{.6in} + +{\large\bf ABSTRACT} +\end{center} + +\input{abstract.tex} + +\newpage + +%%%%Title page 2 +\thispagestyle{empty} +\begin{center} +{\LARGE +{\bf\mythesistitle} +} +\vspace{.6in} + +\myname + +\vspace{.6in} + +\degreethree \\ +\degreetwo \\ +\degreeone + +\vfill +A Dissertation \\ +Submitted in Partial Fulfillment of the \\ +Requirements for the Degree of \\ +Doctor of Philosophy \\ +at the \\ +University of Connecticut + +\vspace{.25in} + +\myyear + +\end{center} +\newpage + + + +%%%%%%%% Copyright Page +\setcounter{page}{1} +\thispagestyle{empty} +\phantom{skip} +\vspace{.5in} +\begin{center} +Copyright by + +\vspace{1in} +\myname + +\vspace{4.5in} +\myyear +\end{center} +\newpage + + +%%%%%%%%%%%%% Approval Page +\thispagestyle{plain} + +\begin{center} +{\large\bf APPROVAL PAGE} + +\vspace{.5in} +Doctor of Philosophy Dissertation + +\vspace{.5in} +{\LARGE\bf\mythesistitle} + +\vspace{.5in} +Presented by\\ +\myname, \degreeoneshort, \degreetwoshort, \degreethreeshort +\vspace{.75in} +\end{center} + +\begin{center} +\begin{minipage}{4.5in} +Major Advisor \hfill$\underset{\hbox{\majoradvisor}}{\rule{3in}{1pt}}$\\[15pt] + +Associate Advisor \hfill$\underset{\hbox{\associateone}}{\rule{3in}{1pt}}$\\[15pt] + +Associate Advisor \hfill$\underset{\hbox{\associatetwo}}{\rule{3in}{1pt}}$ +\end{minipage} + +\vspace{1in} +University of Connecticut\\ +\myyear +\end{center} + + +\newpage + +%%%%%%%%%%%%% Acknowledgments Page +\thispagestyle{plain} + +\begin{center} +{\large\bf ACKNOWLEDGMENTS} +\vspace{1in} +\end{center} + +\input{acknowledgments.tex} \ No newline at end of file diff --git a/incomingAlgos.tex b/incomingAlgos.tex new file mode 100644 index 0000000..afa412b --- /dev/null +++ b/incomingAlgos.tex @@ -0,0 +1,67 @@ +Product: +an assessment instrument/list of questions for incoming to algorithms, +in which we expect to see proofs about resource utilization + +Recall proof by mathematic induction:\\ +There is a proposition, $p$, that we want to show to be true for some domain (i.e., set) $D$. +There is some correspondence between the elements of $D$ and the natural numbers. +When the corresponding natural number, k, is at some value, say $k_0$ for which we can readily show that p is true, we take advantage of that ease, and prove $p(k_0)$, that is to say, prove the proposition p is true for the case $k_0$.\\ +Next we need to have a link, from one case to another. Consider a sequence, i.e., the idea "next" makes sense. Then, the implication "$p$ is true of k implies that $p$ is true of next(k) provides a link. We have a successor function for the natural numbers; the next natural number is obtained by adding 1. Consider the implication "$p$ is true of k implies that $p$ is true of $k+1$. +We can combine a base case, $p(k_0)$ with a linking implication, $p(k) \implies p(k+1)$, where the context in which the linking implication is true includes $k_0$, to show that $p$ is true of all the elements of the domain that are greater than or equal to $k_0$. +The above considerations make useful the following two part procedure. +Find a base case and prove it. +Find a linking implication and prove it, for a domain including the base case. + + +\begin{enumerate} + +\item Proofs of Termination +\begin{enumerate} +\item for ($i=0;i<10;i++$)\{\\ + disp(i);\\ +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item for ($i=0;i>10;i--$)\{\\ + disp(i);\\ +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item for ($i=n;i>0;i--$)\{\\ + disp(i);\\ +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item +i=n; +while ($i>n$)\{\\ + disp(i);\\ + i--; +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item +i=n; +while ($$)\{\\ + disp(i);\\ + update(condition); +\}\\ +Assuming there is no problem with disp or update, how do we prove that this loop terminates? +\end{enumerate} + +\item Proofs by Loop Invariant \\ +Consider the following situation:\\ +There is a proposition, $p$, that we want to show to be true for some domain (i.e., set) $D$, \textbf{and we will process elements of that domain using a loop}. +There is some correspondence between the elements of $D$ and the natural numbers. +When the corresponding natural number, k, is at some value, say $k_0$ for which we can readily show that p is true, we take advantage of that ease, and prove $p(k_0)$, that is to say, prove the proposition p is true for the case $k_0$. \textbf{We will choose our loop variable's first value to be $k_0$.}\\ +Next we need to have a link, from one case to another. Consider a sequence, i.e., the idea "next" makes sense. Then, the implication "$p$ is true of k implies that $p$ is true of next(k) provides a link. We have a successor function for the natural numbers; the next natural number is obtained by adding 1. Consider the implication "$p$ is true of k implies that $p$ is true of \textbf{next($k$). The loop specification produces a sequence, defining "next".} +We can combine a base case, $p(k_0)$ with a linking implication, $p(k) \implies p($next($k)$, where the context in which the linking implication is true includes $k_0$, to show that $p$ is true of all the elements of the domain that are \textbf{next after} or equal to $k_0$. +The above considerations make useful the following two part procedure. +Find a base case and prove it. +Find a linking implication and prove it, for a domain including the base case. + +In the specific situation of proof by loop invariant, these procedure steps are called:\\ +Prove that the property is true before the loop starts. +Prove that what happens in the loop does not, at the end of any single loop iteration, change the property to false. + +\item + +\end{enumerate} + + \ No newline at end of file diff --git a/incomingDiscrete.tex b/incomingDiscrete.tex new file mode 100644 index 0000000..fd80ea2 --- /dev/null +++ b/incomingDiscrete.tex @@ -0,0 +1,239 @@ +Product: +an assessment list of questions for incoming to discrete math + +\begin{enumerate} + +\item Matching symbolic representations with pseudocode + +%Stick breaking:\\ +%Start with a unit length.\\ % stick.\\ +%This unit serves as "what is in stock".\\ +%Every time a fractional part is required, a random fraction of the remaining %stock is taken.// %the stick is broken, one piece will be provided as output of the process, and the remainder will be held for future breaking.\\ +%When it is desired to have $p$ fractions, adding to length 1, $p-1$ iterations will satisfy this.\\ + +\begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./pic8} +\label{fig:pic8} +\end{figure} + +\[ + \sum_{i=0}^k \frac{1}{2^i} +\] + + +let num = rand()*10;\\ +let stock = 1;\\ +let amount = 0;\\ +let frac = 1/2;\\ +getRandomFraction()\{\\ +while (num $>0$)\{\\ +stock = stock*frac;\\ +amount = stock+amount;\\ +num = num-1;\\ +\}\\ +return amount;\\ +\} + + + +let num = rand()*10;\\ +let stock =1;\\ +let amount = 0;\\ +let frac = 1/2;\\ +getRandomFraction()\{\\ +frac=rand(); \\ +amount = stock*frac;\\ +stock = stock - amount;\\ +return amount;\\ +\}\\ + + + + + + + +\newpage +\item Matching figures/diagrams with symbolic representations\\ +Show which equation goes with which diagram, if they can be matched. +\begin{enumerate} + + +\item \begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./pic2GNUPaint} +\caption{} +\label{fig:pic2} +\end{figure} + +\item \begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./pic4} +\caption{} +\label{fig:pic4} +\end{figure} +\end{enumerate} + +\begin{enumerate} + +\item $b^2 + ab = (b+a/2)^2 - (a/2)^2$ + +\item $(a+b)^2 + (a-b)^2 = 2(a^2 + b^2)$ + + +\end{enumerate} + +\newpage +\item Matching figures/diagrams with pseudocode +\begin{enumerate} + + \begin{figure} +\centering +\includegraphics[width=0.6\linewidth]{./pic9} +\caption{First} +\label{fig:pic9} +\end{figure} + + + + \begin{figure} +\centering +\includegraphics[width=0.6\linewidth]{./pic10GNU} +\caption{Second} +\label{fig:pic10} +\end{figure} + +\item let amount = 1;\\ +getAmount(n)\{\\ +amount = 0;\\ +for i = 1 to n \{\\ +for j = i to n\{\\ +amount = amount +j;\\ +end;\\ +end;\\ +return amount; + +\item let amount = 1;\\ +getAmount(n)\{\\ +if (n==0)\{\\ +return(1) \}\\ +else\{\\ +return(2*getAmount(n-1)+1);\\ +\}\\ + + + + + + + +\end{enumerate} +\newpage +\item Comprehending figures\\ + +Explain why the figure matches the equation $\frac{a+b}{2} \geq \sqrt{ab}$ with equality if and only if $a=b$ + +\begin{figure} +\centering +\includegraphics[width=0.7\linewidth]{./pic5} +\caption{} +\label{fig:pic5} +\end{figure} + +\newpage +\item Comprehending symbolic representation\\ + +What is the meaning of\\ +\[ +\sum_{ k \in \mathbb{N}}^{\infty} (2k+1) +\] +\newpage +\item Comprehending pseudocode + +What is the meaning of + +done = false;\\ +let a = 0;\\ +let b = 0;\\ +let n = 2;\\ +while(!done)\{\\ + while($a>0$)\{\\ + a=a+1;\\ + while ($b>0$)\{\\ + b=b+1;\\ + while($n>0$)\{\\ + n=n+1;\\ + if ($a^n +b^n = c^n$)\{\\ + done = true;\\ + \}\\ + \}\\ + \} \\ + \} \\ +\}\\ + + +\newpage +\item Applying symbolic representation to figure + +Describe the significance of either or both of these figures in mathematical symbols: + +\begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./pic1} +\caption{} +\label{fig:pic1} +\end{figure} + + +\newpage +\item Applying figure to symbolic representation + +Draw a figure that expresses through any three points that are not collinear, two can be used to identify a line, and the third can be used, combined with that line, to identify a line parallel to the first line. + +\newpage +\item Applying pseudocode to figure + +Write pseudocode (e.g., as has been seen earlier in these questions) to correspond with this figure: %(p. 93) +\begin{figure}[ht] +\centering +\includegraphics[width=0.7\linewidth]{./p93} + +\label{fig:p93} +\end{figure} + + +\newpage +\item Applying pseudocode to symbolic representation + +Write pseudocode for this calculation: + +${ n \choose k} = {n-1 \choose k-1}+ {n-1 \choose k}$ +\newpage +\item Synthesis: word problems to figures + +Draw a figure for this word problem:\\ +Pick an angle between 0 and $\pi/2$ radians, call it $\theta$.\\ +A right triangle can be drawn, the height of which is 1 plus the tangent of $\theta$, the base of which is 1 plus the cotangent of $\theta$. The angle $\theta$ is adjacent to the base. It will be the case that the hypotenuse of this triangle is the cosecant of $\theta$ plus the secant of $\theta$. +\newpage +\item Synthesis: word problems to symbolic representation\\ + +Express in symbols this word problem:\\ +The number of moves in a game of size n is given by twice the number of moves in a game of size (n-1), plus one more move. +\newpage +\item Synthesis: word problems to pseudocode + +Write pseudocode for this word problem:\\ +Two trains, initially 40 miles apart on the same track, going opposite directions, are getting closer to each other at the rate of 40 miles per hour. An insect flies from one train to the other and back, repeatedly. How far does the insect fly, before the trains collide? + +\end{enumerate} + +operation procedure +implication +vacuous true +law of excluded middle +modus ponens +negation +multiple quantifiers +formative use it to tailor the course +McGowan Tall 2013 Jour Math Behav Formative works \ No newline at end of file diff --git a/incomingOO.tex b/incomingOO.tex new file mode 100644 index 0000000..eafeb39 --- /dev/null +++ b/incomingOO.tex @@ -0,0 +1,11 @@ +Systematizing to show relationships, +analogies that exemplify the shared relationship, +offer the opportunity to perform generalization, abstraction. + +Mathematization, symbolization, makes the relationships clear, facilitating generalization. + +Abstraction, specialization and generalization are key ideas for object-orientation. + +It makes sense to see what students already know (even when it is not so) about symbolization and relationships, going into the course on object orientation. + +Even when the single relationship is "is a kind of", and the principle, Liskov's Substitutability Principle, is provided, students sometimes experience difficulty creating and using inheritance hierarchies. diff --git a/incomingTheory.tex b/incomingTheory.tex new file mode 100644 index 0000000..afa412b --- /dev/null +++ b/incomingTheory.tex @@ -0,0 +1,67 @@ +Product: +an assessment instrument/list of questions for incoming to algorithms, +in which we expect to see proofs about resource utilization + +Recall proof by mathematic induction:\\ +There is a proposition, $p$, that we want to show to be true for some domain (i.e., set) $D$. +There is some correspondence between the elements of $D$ and the natural numbers. +When the corresponding natural number, k, is at some value, say $k_0$ for which we can readily show that p is true, we take advantage of that ease, and prove $p(k_0)$, that is to say, prove the proposition p is true for the case $k_0$.\\ +Next we need to have a link, from one case to another. Consider a sequence, i.e., the idea "next" makes sense. Then, the implication "$p$ is true of k implies that $p$ is true of next(k) provides a link. We have a successor function for the natural numbers; the next natural number is obtained by adding 1. Consider the implication "$p$ is true of k implies that $p$ is true of $k+1$. +We can combine a base case, $p(k_0)$ with a linking implication, $p(k) \implies p(k+1)$, where the context in which the linking implication is true includes $k_0$, to show that $p$ is true of all the elements of the domain that are greater than or equal to $k_0$. +The above considerations make useful the following two part procedure. +Find a base case and prove it. +Find a linking implication and prove it, for a domain including the base case. + + +\begin{enumerate} + +\item Proofs of Termination +\begin{enumerate} +\item for ($i=0;i<10;i++$)\{\\ + disp(i);\\ +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item for ($i=0;i>10;i--$)\{\\ + disp(i);\\ +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item for ($i=n;i>0;i--$)\{\\ + disp(i);\\ +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item +i=n; +while ($i>n$)\{\\ + disp(i);\\ + i--; +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item +i=n; +while ($$)\{\\ + disp(i);\\ + update(condition); +\}\\ +Assuming there is no problem with disp or update, how do we prove that this loop terminates? +\end{enumerate} + +\item Proofs by Loop Invariant \\ +Consider the following situation:\\ +There is a proposition, $p$, that we want to show to be true for some domain (i.e., set) $D$, \textbf{and we will process elements of that domain using a loop}. +There is some correspondence between the elements of $D$ and the natural numbers. +When the corresponding natural number, k, is at some value, say $k_0$ for which we can readily show that p is true, we take advantage of that ease, and prove $p(k_0)$, that is to say, prove the proposition p is true for the case $k_0$. \textbf{We will choose our loop variable's first value to be $k_0$.}\\ +Next we need to have a link, from one case to another. Consider a sequence, i.e., the idea "next" makes sense. Then, the implication "$p$ is true of k implies that $p$ is true of next(k) provides a link. We have a successor function for the natural numbers; the next natural number is obtained by adding 1. Consider the implication "$p$ is true of k implies that $p$ is true of \textbf{next($k$). The loop specification produces a sequence, defining "next".} +We can combine a base case, $p(k_0)$ with a linking implication, $p(k) \implies p($next($k)$, where the context in which the linking implication is true includes $k_0$, to show that $p$ is true of all the elements of the domain that are \textbf{next after} or equal to $k_0$. +The above considerations make useful the following two part procedure. +Find a base case and prove it. +Find a linking implication and prove it, for a domain including the base case. + +In the specific situation of proof by loop invariant, these procedure steps are called:\\ +Prove that the property is true before the loop starts. +Prove that what happens in the loop does not, at the end of any single loop iteration, change the property to false. + +\item + +\end{enumerate} + + \ No newline at end of file diff --git a/inferiorfrontalgyrus.png b/inferiorfrontalgyrus.png new file mode 100644 index 0000000..8defe2e Binary files /dev/null and b/inferiorfrontalgyrus.png differ diff --git a/l73f1.jpeg b/l73f1.jpeg new file mode 100644 index 0000000..c889fbe Binary files /dev/null and b/l73f1.jpeg differ diff --git a/lismanNeoHebbian.jpg b/lismanNeoHebbian.jpg new file mode 100644 index 0000000..daf140b Binary files /dev/null and b/lismanNeoHebbian.jpg differ diff --git a/litMathPhenom.bib b/litMathPhenom.bib new file mode 100644 index 0000000..673fbad --- /dev/null +++ b/litMathPhenom.bib @@ -0,0 +1,48 @@ +@phdthesis{halmaghi2011undergraduate, +title={Undergraduate students' conceptions of inequalities}, +author={Halmaghi, Elena Filfteia}, +year={2011}, +school={Education: Faculty of Education}, +organization={Simon Fraser University} +} +@inproceedings{sanders2006mental, +title={Mental models of recursion revisited}, +author={Sanders, Ian and Galpin, Vashti and G{\"o}tschi, Tina}, +booktitle={ACM SIGCSE Bulletin}, +volume=38, +number=3, +pages={138--142}, +year=2006, +organization={ACM} +} +@article{alcock2005proof, + title={Proof validation in real analysis: Inferring and checking warrants}, + author={Alcock, Lara and Weber, Keith}, + journal={The Journal of Mathematical Behavior}, + volume={24}, + number={2}, + pages={125--134}, + year={2005}, + publisher={Elsevier} +} +@article{weber2004traditional, + title={Traditional instruction in advanced mathematics courses: A case study of one professor's lectures and proofs in an introductory real analysis course}, + author={Weber, Keith}, + journal={The Journal of Mathematical Behavior}, + volume={23}, + number={2}, + pages={115--133}, + year={2004}, + publisher={Elsevier} +} + +@article{smith2006sense, + title={A sense-making approach to proof: Strategies of students in traditional and problem-based number theory courses}, + author={Smith, Jennifer Christian}, + journal={The Journal of Mathematical Behavior}, + volume={25}, + number={1}, + pages={73--90}, + year={2006}, + publisher={Elsevier} +} \ No newline at end of file diff --git a/litSEEval.bib b/litSEEval.bib new file mode 100644 index 0000000..bfea60d --- /dev/null +++ b/litSEEval.bib @@ -0,0 +1,176 @@ +@article{Hainey201121, +title = "Evaluation of a game to teach requirements collection and analysis in software engineering at tertiary education level", +journal = "Computers \& Education", +volume = "56", +number = "1", +pages = "21 - 35", +year = "2011", +note = "Serious Games", +issn = "0360-1315", +doi = "10.1016/j.compedu.2010.09.008", +url = "http://www.sciencedirect.com/science/article/pii/S0360131510002605", +author = "Thomas Hainey and Thomas M. Connolly and Mark Stansfield and Elizabeth A. Boyle", +keywords = "Games-based learning", +keywords = "Software engineering", +keywords = "Requirements collection and analysis", +keywords = "Evaluation", +keywords = "Pedagogy", +abstract = "A highly important part of software engineering education is requirements collection and analysis which is one of the initial stages of the Database Application Lifecycle and arguably the most important stage of the Software Development Lifecycle. No other conceptual work is as difficult to rectify at a later stage or as damaging to the overall system if performed incorrectly. As software engineering is a field with a reputation for producing graduates who are inappropriately prepared for applying their skills in real life software engineering scenarios, it suggests that traditional educational techniques such as role-play, live-through case studies and paper-based case studies are insufficient preparation and that other approaches are required. To attempt to combat this problem we have developed a games-based learning application to teach requirements collection and analysis at tertiary education level as games-based learning is seen as a highly motivating, engaging form of media and is a rapidly expanding field. This paper will describe the evaluation of the requirements collection and analysis game particularly from a pedagogical perspective. The game will be compared to traditional methods of software engineering education using a pre-test/post-test, control group/experimental group design to assess if the game can act as a suitable supplement to traditional techniques and assess if it can potentially overcome shortcomings. The game will be evaluated in five separate experiments at tertiary education level.", +annote={eval framework Connolly Stansfield Hainey 2009 +control: traditional teaching\\ +pretest/posttest\\ +results knowledge question / learning effectiveness\\ +ranked ordinal data\\ +aspects and perceptions\\ +non-parametric statistical tests\\ +Kruskal Wallis\\ +Descriptive Statistics\\ +Mann-Whitney U- difference levels knowledge} +} + +@article{Chen2011479, +title = "Software engineering education: A study on conducting collaborative senior project development", +journal = "Journal of Systems and Software", +volume = "84", +number = "3", +pages = "479 - 491", +year = "2011", +note = "", +issn = "0164-1212", +doi = "10.1016/j.jss.2010.10.042", +url = "http://www.sciencedirect.com/science/article/pii/S0164121210002931", +author = "Chung-Yang Chen and P. Pete Chong", +keywords = "Software engineering education", +keywords = "Senior project", +keywords = "Collaborative development", +keywords = "Meetings-flow", +abstract = "Project and teamwork training is recognized as an important aspect in software engineering (SE) education. Senior projects, which often feature industrial involvement, serve the function of a ‘capstone course’ in SE curricula, by offering comprehensive training in collaborative software development. Given the characteristics of student team projects and the social aspects of software development, instructional issues in such a course must include: how to encourage teamwork, how to formalize and streamline stakeholder participation, and how to monitor students’ work, as well as sustain their desired collaborative effort throughout the development. In this paper, we present an exploratory study which highlights a particular case and introduces the meetings-flow approach. In order to investigate how this approach could contribute to the project's results, we examined its quantitative benefits in relation to the development of the project. We also conducted focus group interviews to discuss the humanistic findings and educational effects pertaining to this approach.", +annote={Objective:\\ +teach students how to have effective meetings for software development teams\\ +``Project and teamwork training is recognized as an important aspect in software engineering (SE) education. Senior projects, which often feature industrial involvement, serve the function of a capstone course in SE curricula, by offering comprehensive training in collaborative software development.'' +Evaulation:\\ +students finished ahead of schedule\\ +``The PIMIS student team used the MF approach and completed its project with the successful implementation and delivery of the required system. Project requirements were completed 5 weeks ahead of schedule''\\ + the in-process benefits to be evaluated were taken from two perspectives: product quality effectiveness and project process efficiency.\\ + statistical analysis and hypothesis testing\\ + (note that the defects include both code defects and design defects in the documents): +Requirement planning and task assignment meeting (PP)\\ +Internal testing and validation meeting (VAL)\\ +Configuration control meeting (CM)\\ + +Si: development scale for cycle i;\\ + +Sit: accumulated development scale (including both code and documentation);\\ + +Di: number of total defects revealed and removed by the meeting series in cycle (i);\\ + +Dci: number of defects resulting from current cycle (i) is revealed and removed in cycle i;\\ + +SPIri: the value of the schedule performance index (SPI) for cycle i; it is observed in the REQR review meeting;\\ + +SPIppi, SPIvali, SPIcmi: the SPI values recorded in the PP, VAL and CM, respectively, meetings of cycle i.\\} +} + + + +@article{Baker20053, +title = "An experimental card game for teaching software engineering processes", +journal = "Journal of Systems and Software", +volume = "75", +number = "1-2", +pages = "3 - 16", +year = "2005", +note = "Software Engineering Education and Training", +issn = "0164-1212", +doi = "10.1016/j.jss.2004.02.033", +url = "http://www.sciencedirect.com/science/article/pii/S0164121204000378", +author = "Alex Baker and Emily Oh Navarro and André van der Hoek", +keywords = "Software engineering education", +keywords = "Educational games", +keywords = "Software engineering simulation", +keywords = "Simulation games", +abstract = "The typical software engineering course consists of lectures in which concepts and theories are conveyed, along with a small toy software engineering project which attempts to give students the opportunity to put this knowledge into practice. Although both of these components are essential, neither one provides students with adequate practical knowledge regarding the process of software engineering. Namely, lectures allow only passive learning and projects are so constrained by the time and scope requirements of the academic environment that they cannot be large enough to exhibit many of the phenomena occurring in real-world software engineering processes. To address this problem, we have developed Problems and Programmers, an educational card game that simulates the software engineering process and is designed to teach those process issues that are not sufficiently highlighted by lectures and projects. We describe how the game is designed, the mechanics of its game play, and the results of an experiment we conducted involving students playing the game.", +annote={Objective:\\ + ``teach those process issues that are not sufficiently highlighted by lectures and projects''\\ + ``exhibit many of the phenomena occurring in real-world softwareengineering processes''\\ + Evaluation:\\ + ``initial evaluation of the game, we designed a simple experiment in which students were taught to play the game and then asked to submit written feedback in the form of answers to structured questions. While more subjective than some other evaluation methods, we feel that this was well suited to an initial evaluation of the concept, and allowed us flexibility in the information that we gathered. In the future, we plan to utilize more formal approaches namely, performing comparative studies in actual softwareengineering courses between the aptitudes of students who played the game and those who did not.''\\ + `` they completed a questionnaire stating their thoughts and feelings about the game in general, their opinions about the pedagogical effectiveness of the game in teaching softwareengineering process issues, and their educational and professional background in softwareengineering. Some of these questions asked for a numerical answer on a one to five scale, while others allowed students to write out their responses in free form'' +} +} + +@article{Pfahl2004127, +title = "Evaluating the learning effectiveness of using simulations in software project management education: results from a twice replicated experiment", +journal = "Information and Software Technology", +volume = "46", +number = "2", +pages = "127 - 147", +year = "2004", +note = "", +issn = "0950-5849", +doi = "10.1016/S0950-5849(03)00115-0", +url = "http://www.sciencedirect.com/science/article/pii/S0950584903001150", +author = "Dietmar Pfahl and Oliver Laitenberger and Günther Ruhe and Jörg Dorsch and Tatyana Krivobokova", +keywords = "COCOMO", +keywords = "Learning effectiveness", +keywords = "Replicated experiment", +keywords = "Software project management education", +keywords = "System dynamics simulation", +abstract = "The increasing demand for software project managers in industry requires strategies for the development of management-related knowledge and skills of the current and future software workforce. Although several educational approaches help to develop the necessary skills in a university setting, few empirical studies are currently available to characterise and compare their effects. + +This paper presents the results of a twice replicated experiment that evaluates the learning effectiveness of using a process simulation model for educating computer science students in software project management. While the experimental group applied a System Dynamics simulation model, the control group used the well-known COCOMO model as a predictive tool for project planning. + +The results of each empirical study indicate that students using the simulation model gain a better understanding about typical behaviour patterns of software development projects. The combination of the results from the initial experiment and the two replications with meta-analysis techniques corroborates this finding. Additional analysis shows that the observed effect can mainly be attributed to the use of the simulation model in combination with a web-based role-play scenario. This finding is strongly supported by information gathered from the debriefing questionnaires of subjects in the experimental group. They consistently rated the simulation-based role-play scenario as a very useful approach for learning about issues in software project management.", +annote={Objective:\\ +``Evaluating the learning effectiveness of using simulations in software project management education''\\ +Evaluation:\\ +``For evaluating the effectiveness of a training session using SD model simulation, a pre-testpost-test control group design was applied [12]. This design involves random assignment of subjects to an experimental group (A) and a control group (B). The subjects of both groups completed a pre-test and a post-test. The pre-test measured the performance of the two groups before the treatment, and the post-test measured the performance of the two groups after the treatment. The students did neither know that the post-test questions were identical to the pre-test questions, nor were they allowed to keep the pre-test questionnaires. The correct answers were only provided to the students after the end of the experiments.''\\ +``The initial experiment was conducted with graduate computer science students at the University of Kaiserslautern (KL), Germany, who were enrolled in the advanced software engineering class.''\\ +``The first replication of the initial study was conducted during a summer school with 12 graduate and post-graduate students (one Master degree, one PhD) of the University of Oulu, Finland, having their major in computer science, information technology, information engineering, microelectronics or mathematics. The second replication was performed with 13 senior undergraduate students at the University of Calgary, Canada, major in computer science, electrical engineering and computer engineering.''\\ +} +} + + +@article{Lee2011527, +title = "Empowering teachers to create educational software: A constructivist approach utilizing Etoys, pair programming and cognitive apprenticeship", +journal = "Computers \& Education", +volume = "56", +number = "2", +pages = "527 - 538", +year = "2011", +note = "", +issn = "0360-1315", +doi = "10.1016/j.compedu.2010.09.018", +url = "http://www.sciencedirect.com/science/article/pii/S0360131510002812", +author = "Young-Jin Lee", +keywords = "Interactive learning environment", +keywords = "Media in education", +keywords = "Programming and programming languages", +keywords = "Teaching/learning strategies", +abstract = "This study investigates whether a visual programming environment called Etoys could enable teachers to create software applications meeting their own instructional needs. Twenty-four teachers who participated in the study successfully developed their own educational computer programs in the educational technology course employing cognitive apprenticeship and pair programming approaches as the primary instructional strategies. Two educational software programs created by the participating teachers were described in order to explain what they were trying to do using Etoys and how they accomplished their goals. The results of an anonymous survey evaluating the difficulty of and the attitude toward learning Etoys indicate that teachers enjoyed learning Etoys and would like to continue to use it in the future although they found it was slightly more difficult, compared to their self-evaluated computer skill. The strengths and weaknesses of Etoys, the difficult computer programming concepts, and the educational implications of Etoys programming were also discussed.", +annote={Objective: Empowering teachers to create educational software\\ +Evaluation: an anonymous survey evaluating the difficulty of and the attitude toward learning +Etoys} +} + +@inbook{2009Hainey, +author={Thomas M. Connolly and Mark Stansfield and Thomas Hainey}, +title={Towards the Development of a Games-Based Learning Evaluation Framework}, +chapter={XV}, +pages={251-273}, +year=2009, +booktitle={Games-Based Learning Advancements for Multi-Sensory Human Computer Interfaces}, +publisher={Information Science Reference Ideas Group Inc, Global}, +address={Hershey, PA} +} + +@article{lethbridge2005studying, + title={Studying software engineers: Data collection techniques for software field studies}, + author={Lethbridge, Timothy C and Sim, Susan Elliott and Singer, Janice}, + journal={Empirical software engineering}, + volume={10}, + number={3}, + pages={311--341}, + year={2005}, + publisher={Springer} +} diff --git a/litSEQual.bib b/litSEQual.bib new file mode 100644 index 0000000..fab29d6 --- /dev/null +++ b/litSEQual.bib @@ -0,0 +1,526 @@ +@article{allert2002, + location = {http://www.scientificcommons.org/43516951}, + title = {How are learning objects used in learning processes? instructional roles of learning objects in lom}, + author = {Heidrun Allert and Hadhami Dhraief and Wolfgang Nejdl}, + year = {2002}, + keywords = {Metadata, Instructional Design, E-Learning, Standard for Learning Objects Metadata LOM}, + abstract = {In order to reuse and exchange learning objects we need information about these learning objects. The LOM draft standard defines a set of more than 70 attributes, which specify learning object properties like author, title, subject, and many others, including the relationship of one learning object to other learning objects. However, even though the LOM draft includes a category educational, no information is included in the standard to specify, which instructional roles are played by a learning object within a course. In this paper, we show how to include this important didactic information using the concept of instructional roles and relations in a way, which is extensible and flexible enough to specify not only general didactic criteria, but rather specific criteria, as prescribed by different instructional theories.}, + url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.7334}, + institution = {CiteSeerX - Scientific Literature Digital Library and Search Engine [http://citeseerx.ist.psu.edu/oai2] (United States)}, +} +@INPROCEEDINGS{Allert02howare, + author = {Heidrun Allert and Hadhami Dhraief and Wolfgang Nejdl}, + title = {How are learning objects used in learning processes? instructional roles of learning objects in lom}, + booktitle = {In ED-MEDIA 2002, World Conference on Educational Multimedia, Hypermedia & Telecommunications}, + year = {2002}, + pages = {40--42} +} + +@article {springerlink:10.1007/s11023-008-9113-7, + author = {Floridi, Luciano}, + affiliation = {University of Hertfordshire Research Chair in Philosophy of Information and GPI Hertfordshire UK}, + title = {The Method of Levels of Abstraction}, + journal = {Minds and Machines}, + publisher = {Springer Netherlands}, + issn = {0924-6495}, + keyword = {Computer Science}, + pages = {303-329}, + volume = {18}, + issue = {3}, + url = {http://dx.doi.org/10.1007/s11023-008-9113-7}, + note = {10.1007/s11023-008-9113-7}, + abstract = {The use of ``levels of abstraction'' in philosophical analysis ( levelism ) has recently come under attack. In this paper, I argue that a refined version of epistemological levelism should be retained as a fundamental method, called the method of levels of abstraction . After a brief introduction, in section ``Some Definitions and Preliminary Examples'' the nature and applicability of the epistemological method of levels of abstraction is clarified. In section ``A Classic Application of the Method of Abstraction'', the philosophical fruitfulness of the new method is shown by using Kant's classic discussion of the ``antinomies of pure reason'' as an example. In section ``The Philosophy of the Method of Abstraction'', the method is further specified and supported by distinguishing it from three other forms of ``levelism'': (i) levels of organisation; (ii) levels of explanation and (iii) conceptual schemes. In that context, the problems of relativism and antirealism are also briefly addressed. The conclusion discusses some of the work that lies ahead, two potential limitations of the method and some results that have already been obtained by applying the method to some long-standing philosophical problems.}, + year = {2008}, + annote={ideas need some discussion (Marr 1982, pp. 1920). +In particular, in the case of an information-processing system, Marr and his +followers suggest the adoption of three levels of analysis (all the following +quotations are from Marr (1982)): +(1) the computational level. This is a description of the abstract computational +theory of the device, in which the performance of the device is characterised as +a mapping from one kind of information structures, the abstract properties of +this mapping are defined precisely, and its appropriateness and adequacy for +the task at hand are demonstrated (p. 24); +(2) the algorithmic level. This is a description of the choice of representation for +the input and output and the algorithm to be used to transform one into the +other (pp. 2425); +(3) the implementational level. This is a description of the details of how the +algorithm and representation are realized physicallythe detailed computer +architecture, so to speak (p. 25). +The three levels are supposed to be loosely connected and in a one-to-many +mapping relation: for any computational description of a particular informationprocessing problem there may be several algorithms for solving that problem, and +any algorithm may be implemented in several ways. +Along similar lines, Pylyshyn (1984) has spoken of the semantic, the syntactic, +and the physical levels of description of an information-processing system, with the +(level of) functional architecture of the system playing the role of a bridge between +Marrs algorithmic and implementational levels.} +} + +@book{Marr, +author={Marr, D.}, +year= 1982, +title={Vision: A computational investigation into the human representation and processing of +visual information}, +publisher={San Francisco: W.H. Freeman}} +% Homer QP475 .M27 1982 + + +@book{Pylyshyn, +author={Pylyshyn, Z. W.}, +year=1984, +title={Computation and cognition: Toward a foundation for cognitive science}, +publisher={Cambridge, MA: MIT Press}} %Homer BF311 .P93 1984, QP475 .c63 1988 , QA76 .P94 + +@inbook{2007Pylyshyn, +author={Pylyshyn, Z. W.}, +year=2007, +title={Things and Places: How the Mind Connects with the World}, +booktitle={Jean Nicod Lectures}, +publisher={Cambridge, MA: MIT Press}} + +@article{Goldfarb01052010, +author = {Goldfarb, Liat and Treisman, Anne}, +title = {Are Some Features Easier to Bind Than Others?}, +volume = {21}, +number = {5}, +pages = {676-681}, +year = {2010}, +doi = {10.1177/0956797610365130}, +abstract ={A common perceptual error consists of binding the features of objects in the wrong combinations. Another common finding is that incongruent thoughts or feelings tend to be rejected by the cognitive system. We combined these two notions and found that the incongruence-suppression rule constrains the binding process. We used a task in which participants were asked to bind either congruent or incongruent features together. Whether those features were digits and physical sizes (Experiment 1) or color words and colored fonts (Experiment 2), we observed a new effect that we refer to as the binding congruency effect: When participants were asked to bind incongruent features together, the error rate increased, and participants replaced the incongruent features with congruent features. Experiment 3 demonstrated that the effect depends on the migration of the relevant feature within the same level.}, +URL = {http://pss.sagepub.com/content/21/5/676.abstract}, +eprint = {http://pss.sagepub.com/content/21/5/676.full.pdf+html}, +journal = {Psychological Science} +} + +@article{Giunchiglia1992323, +title = "A theory of abstraction", +journal = "Artificial Intelligence", +volume = "57", +number = "2–3", +pages = "323 - 389", +year = "1992", +note = "", +issn = "0004-3702", +doi = "10.1016/0004-3702(92)90021-O", +url = "http://www.sciencedirect.com/science/article/pii/000437029290021O", +author = "Fausto Giunchiglia and Toby Walsh", +abstract = "Informally, abstraction can be described as the process of mapping a representation of a problem onto a new representation. The aim of this paper is to propose the beginnings of a theory of reasoning with abstraction which captures and generalizes most previous work in the area. The theory allows us to study the properties of abstraction mappings and provides the foundations for the mechanization of abstraction inside an abstract proof checker." +} + +@article{Denning:1989:CD:63238.63239, + author = {Denning, P. and Comer, D. E. and Gries, David and Mulder, Michael C. and Tucker, Allen and Turner, A. Joe and Young, Paul R.}, + editor = {Denning, Peter J.}, + title = {Computing as a discipline}, + journal = {Commun. ACM}, + issue_date = {Jan. 1989}, + volume = {32}, + number = {1}, + month = jan, + year = {1989}, + issn = {0001-0782}, + pages = {9--23}, + numpages = {15}, + url = {http://doi.acm.org/10.1145/63238.63239}, + doi = {10.1145/63238.63239}, + acmid = {63239}, + publisher = {ACM}, + address = {New York, NY, USA}, +} + +@incollection {springerlink:10.1007/11663430_32, + author = {Engels, Gregor and Hausmann, Jan and Lohmann, Marc and Sauer, Stefan}, + affiliation = {Universität Paderborn, Germany}, + title = {Teaching UML Is Teaching Software Engineering Is Teaching Abstraction}, + booktitle = {Satellite Events at the MoDELS 2005 Conference}, + series = {Lecture Notes in Computer Science}, + editor = {Bruel, Jean-Michel}, + publisher = {Springer Berlin / Heidelberg}, + isbn = {978-3-540-31780-7}, + keyword = {Computer Science}, + pages = {306-319}, + volume = {3844}, + url = {http://dx.doi.org/10.1007/11663430_32}, + note = {10.1007/11663430_32}, + abstract = {As the Unified Modeling Language (UML) has by now seen widespread and successful use in the software industry and academia alike, it has also found its way into many computer science curricula. An outstanding advantage of teaching UML is that it enables an illustration of many crucial concepts of software engineering, far beyond its concrete notation. Most important among these concepts is that of abstraction. We present a course design which demonstrates the use of UML as a vehicle for teaching such core concepts of software engineering. Multimedia elements and tools help to efficiently convey the course’s message to the students.}, + year = {2006} +} +@INPROCEEDINGS{1191345, +author={Kramer, J.}, +booktitle={Software Engineering Education and Training, 2003. (CSEE T 2003). Proceedings. 16th Conference on}, +title={Abstraction - is it teachable? "the devil is in the detail"}, +year={2003}, +month={march}, +volume={}, +number={}, +pages={ 32}, +abstract={Not available}, +keywords={}, +doi={10.1109/CSEE.2003.1191345}, +ISSN={1093-0175 },} + +@inproceedings{Koppelman:2010:TAI:1822090.1822140, + author = {Koppelman, Herman and van Dijk, Betsy}, + title = {Teaching abstraction in introductory courses}, + booktitle = {Proceedings of the fifteenth annual conference on Innovation and technology in computer science education}, + series = {ITiCSE '10}, + year = {2010}, + isbn = {978-1-60558-820-9}, + location = {Bilkent, Ankara, Turkey}, + pages = {174--178}, + numpages = {5}, + url = {http://doi.acm.org/10.1145/1822090.1822140}, + doi = {10.1145/1822090.1822140}, + acmid = {1822140}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {abstraction, abstraction level, computer science, pedagogy, recursion}, +} +%observing students learning abstraction +% Mostrm, J. E., Boustedt, J., Eckerdal, A., McCartney, R., +%Sanders, K., Thomas, L., and Zander, C. 2008. Concrete +%examples of abstraction as manifested in students' +%transformative experiences. In Proceeding of the Fourth +%international Workshop on Computing Education Research +%(Sydney, Australia, September 06 - 07, 2008). ICER '08. +%ACM, New York, NY, 125-136. DOI= +%http://doi.acm.org/10.1145/1404520.140453 +@inproceedings{Mostrom:2008:CEA:1404520.1404533, + author = {Mostr\"{o}m, Jan Erik and Boustedt, Jonas and Eckerdal, Anna and McCartney, Robert and Sanders, Kate and Thomas, Lynda and Zander, Carol}, + title = {Concrete examples of abstraction as manifested in students' transformative experiences}, + booktitle = {Proceedings of the Fourth international Workshop on Computing Education Research}, + series = {ICER '08}, + year = {2008}, + isbn = {978-1-60558-216-0}, + location = {Sydney, Australia}, + pages = {125--136}, + numpages = {12}, + url = {http://doi.acm.org/10.1145/1404520.1404533}, + doi = {10.1145/1404520.1404533}, + acmid = {1404533}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {abstraction, learning theory, threshold concepts, transformation}, +} +%T. Colburn and G. Shute. Abstraction in computer +%science. Minds and Machines, 17(2):169184, 2007. +%% +%9] F. Detienne. Assessing the cognitive consequences of +%the object-oriented approach: A survey of empirical +%research on object-oriented design by individuals and +%teams. Interacting with Computers, 9:4772, 1997. +%% +%[15] J. Mead, S. Gray, J. Hamer, R. James, J. Sorva, C. S. +%Clair, and L. Thomas. A cognitive approach to +%identifying measurable milestones for programming +%skill acquisition. SIGCSE Bulletin, 38(4):182194, +%2006. +%% +%[16] B. Meyer. Testable, reusable units of cognition. +%Computer, 39(4):2024, 2006. +%% + +%[18] J. H. Meyer and R. Land. Threshold concepts and +%troublesome knowledge (2): Epistemological +%considerations and a conceptual framework for +%teaching and learning. Higher Education, 49:373388, +%2005 +%% +%0] R. Or-Bach and I. Lavy. Cognitive activities of +%abstraction in object orientation: an empirical study. +%SIGCSE Bull., 36(2):8286, 2004 +% +%24] K. Sanders, J. Boustedt, A. Eckerdal, R. McCartney, +%J. E. Mostrm, L. Thomas, and C. Zander. Student +%understanding of object-oriented programming as +%expressed in concept maps. In SIGCSE 08: +%Proceedings of the 39th SIGCSE technical symposium +%on Computer science education, pages 332336, New +%York, NY, USA, 2008. ACM. +% +% +@article{JOT:issue_2010_11/article1, + author = {Lone Leth Thomsen and Bent Thomsen and Kurt N\/{o}rmark}, + title = {Computational Abstraction Steps}, + journal = {Journal of Object Technology}, + volume = {9}, + number = {6}, + issn = {1660-1769}, + year = {2010}, + month = nov, + pages = {1-23}, + doi = {10.5381/jot.2010.9.6.a1}, + url = {http://www.jot.fm/contents/issue_2010_11/article1.html} +} + +@INPROCEEDINGS{4720415, +author={Haberman, B. and Muller, O.}, +booktitle={Frontiers in Education Conference, 2008. FIE 2008. 38th Annual}, +title={Teaching abstraction to novices: Pattern-based and ADT-based problem-solving processes}, +year={2008}, +month={oct.}, +volume={}, +number={}, +pages={F1C-7 -F1C-12}, +abstract={Abstraction is taught to computer-science students as part of a comprehensive curriculum. The students encounter the concept of abstraction in various contexts while learning the different modules, each of which emphasizes some specific aspects of the concept. In this paper we present two instructional approaches, both related to utilizing abstraction in problem-solving processes: (1) pattern-oriented instruction (POI), and (2) abstract data type (ADT)-oriented instruction. We present these methods with respect to their employment in teaching problem solving to novices, and elaborate on abstraction processes.}, +keywords={abstract data type-oriented instruction;abstraction processes;computer-science students;pattern-oriented instruction;problem-solving processes;teaching problem;abstract data types;computer aided instruction;computer science education;teaching;}, +doi={10.1109/FIE.2008.4720415}, +ISSN={0190-5848},} + +@article{Hazzan:2008:RTA:1383602.1383631, + author = {Hazzan, Orit}, + title = {Reflections on teaching abstraction and other soft ideas}, + journal = {SIGCSE Bull.}, + issue_date = {June 2008}, + volume = {40}, + number = {2}, + month = jun, + year = {2008}, + issn = {0097-8418}, + pages = {40--43}, + numpages = {4}, + url = {http://doi.acm.org/10.1145/1383602.1383631}, + doi = {10.1145/1383602.1383631}, + acmid = {1383631}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {abstraction, computer science education, reflection, soft ideas}, +} + +@article{Kramer:2007:AKC:1232743.1232745, + author = {Kramer, Jeff}, + title = {Is abstraction the key to computing?}, + journal = {Commun. ACM}, + issue_date = {April 2007}, + volume = {50}, + number = {4}, + month = apr, + year = {2007}, + issn = {0001-0782}, + pages = {36--42}, + numpages = {7}, + url = {http://doi.acm.org/10.1145/1232743.1232745}, + doi = {10.1145/1232743.1232745}, + acmid = {1232745}, + publisher = {ACM}, + address = {New York, NY, USA}, +} + + + +@incollection {springerlink:10.1007/978-0-85729-443-2\_3, + author = {Hazzan, Orit and Lapidot, Tami and Ragonis, Noa and Hazzan, Orit and Lapidot, Tami and Ragonis, Noa}, + affiliation = {Dept. Education in Technology & Science, Technion - Israel Institute of Technology, Technion City, Haifa, Israel}, + title = {Overview of the Discipline of Computer Science}, + booktitle = {Guide to Teaching Computer Science}, + publisher = {Springer London}, + isbn = {978-0-85729-443-2}, + keyword = {Computer Science}, + pages = {21-46}, + url = {http://dx.doi.org/10.1007/978-0-85729-443-2_3}, + note = {10.1007/978-0-85729-443-2_3}, + abstract = {This chapter proposes how to address in the MTCS course topics associated with the nature of the discipline of computer science and with cross-curriculum topics. The importance of these topics is explained by the fact that even today no consensus has been reached with respect to one agreed-upon definition for computer science, and different scholars view it differently. Specifically, the following topics are discussed in this chapter: what is computer science, the history of computer science, computer scientists, social issues of computer science, programming paradigms, and computer science soft ideas. For each topic, its meaning and its importance and relevance in the context of computer science education are explained, and then, several activities which deal with the said topic are presented.}, + year = {2011} +} + +%Logic and Abstraction as Capabilities of the Mind: Reconceptualizations of Computational Approaches to the Mind +%David J. Saab (Penn State University, USA) and Uwe V. Riss (SAP AG, CEC Karlsruhe, Germany) +%Copyright 2010. 17 pages. + +@inproceedings{quteprints48138, + booktitle = {14th Australasian Computing Education Conference (ACE 2012)}, + editor = {Michael de Raadt and Angela Carbone}, + month = {January}, + title = {Some empirical results for neo-Piagetian reasoning in novice programmers and the relationship to code explanation questions}, + author = {Malcolm W. Corney and Donna M. Teague and Alireza Ahadi and Raymond Lister}, + address = {RMIT University, Melbourne, VIC}, + publisher = {Australian Computer Society Inc}, + year = {2012}, + keywords = {novice programmer, CS1, neo-Piagetian}, + url = {http://eprints.qut.edu.au/48138/}, + abstract = {Recent research on novice programmers has suggested that they pass through neo-Piagetian stages: sensorimotor, preoperational, and concrete operational stages, before eventually reaching programming competence at the formal operational stage. This paper presents empirical results in support of this neo-Piagetian perspective. The major novel contributions of this paper are empirical results for some exam questions aimed at testing novices for the concrete operational abilities to reason with quantities that are conserved, processes that are reversible, and properties that hold under transitive inference. While the questions we used had been proposed earlier by Lister, he did not present any data for how students performed on these questions. Our empirical results demonstrate that many students struggle to answer these problems, despite the apparent simplicity of these problems. We then compare student performance on these questions with their performance on six explain in plain English questions.} +} + +@inproceedings{Lister2011, +author={Lister, R.}, +year=2011, +title={Concrete and Other Neo-Piagetian Forms of Reasoning in the Novice Programmer}, +booktitle={Thirteenth Australasian Computing Education +Conference (ACE 2011)}, +publisher = {Australian Computer Society Inc}, +month={January}, +pages={pp. 918}, +} + +%%OSS Pedroni SIGCSE2007 + + +%Meneelly ITiCSE 2008 + +%Costa-Soria EAEEIE 2009 +@article{Costa-Soria:2009:TSA:1595496.1563027, + author = {Costa-Soria, Crist\'{o}bal and P{\'e}rez, Jennifer}, + title = {Teaching software architectures and aspect-oriented software development using open-source projects}, + journal = {SIGCSE Bull.}, + issue_date = {September 2009}, + volume = {41}, + number = {3}, + month = jul, + year = {2009}, + issn = {0097-8418}, + pages = {385--385}, + numpages = {1}, + url = {http://doi.acm.org/10.1145/1595496.1563027}, + doi = {10.1145/1595496.1563027}, + acmid = {1563027}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {AOSD, reverse engineering, software architecture}, + annote={very nice, students learn from large open source, only 1 page, only OSS reference is Pedroni} +} + +@inproceedings{Costa-Soria:2009:TSA:1562877.1563027, + author = {Costa-Soria, Crist\'{o}bal and P{\'e}rez, Jennifer}, + title = {Teaching software architectures and aspect-oriented software development using open-source projects}, + booktitle = {Proceedings of the 14th annual ACM SIGCSE conference on Innovation and technology in computer science education}, + series = {ITiCSE '09}, + year = {2009}, + isbn = {978-1-60558-381-5}, + location = {Paris, France}, + pages = {385--385}, + numpages = {1}, + url = {http://doi.acm.org/10.1145/1562877.1563027}, + doi = {10.1145/1562877.1563027}, + acmid = {1563027}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {AOSD, reverse engineering, software architecture}, +} + + + + +@INPROCEEDINGS{4720643, +author={Nandigam, J. and Gudivada, V.N. and Hamou-Lhadj, A.}, +booktitle={Frontiers in Education Conference, 2008. FIE 2008. 38th Annual}, +title={Learning software engineering principles using open source software}, +year={2008}, +month={oct.}, +volume={}, +number={}, +pages={S3H-18 -S3H-23}, +abstract={Traditional lectures espousing software engineering principles hardly engage students attention due to the fact that students often view software engineering principles as mere academic concepts without a clear understanding of how they can be used in practice. Some of the issues that contribute to this perception include lack of experience in writing and understanding large programs, and lack of opportunities for inspecting and maintaining code written by others. To address these issues, we have worked on a project whose overarching goal is to teach students a subset of basic software engineering principles using source code exploration as the primary mechanism. We attempted to espouse the following software engineering principles and concepts: role of coding conventions and coding style, programming by intention to develop readable and maintainable code, assessing code quality using software metrics, refactoring, and reverse engineering to recover design elements. Student teams have examined the following open source Java code bases: ImageJ, Apache Derby, Apache Lucene, Hibernate, and JUnit. We have used Eclipse IDE and relevant plug-ins in this project.}, +keywords={open source software;software engineering education;source code exploration;students;computer science education;}, +doi={10.1109/FIE.2008.4720643}, +ISSN={0190-5848}, +annote={they have good references about metrics, they have a list of useful eclipse plugins, +they used Omondo and they generated sequence diagrams}} + + +%Raj, R, K, and Kazemian, F, "Using Open Source Software in Computer Science Courses," 36 + +@INPROCEEDINGS{4116849, +author={Raj, R.K. and Kazemian, F.}, +booktitle={Frontiers in Education Conference, 36th Annual}, +title={Using Open Source Software in Computer Science Courses}, +year={2006}, +month={oct.}, +volume={}, +number={}, +pages={21 -26}, +abstract={Open source software (OSS) has become mainstream in recent years, making a wide variety of software tools available to instructors and students. In particular, a large collection of OSS source code is now available for use in college courses in disciplines that involve software development. Concomitantly, computer science (CS) educators have been exploring different ways to reinvigorate the CS curriculum to make it more attractive, amenable, and applicable to college students. We regard appropriate OSS use to represent a major prong of a multi-pronged approach to a revamped CS curriculum. Due to our use of OSS in advanced CS courses, our students have gained useful insights into software design and development. They have also felt empowered as they worked on real-world team projects that do not necessarily end with the academic term. This paper uses a database system implementation course to illustrate our approach to OSS and provides an initial assessment}, +keywords={computer science courses;database system implementation course;open source software;software design;software development;software tools;computer aided instruction;computer science education;public domain software;software engineering;}, +doi={10.1109/FIE.2006.322357}, +ISSN={0190-5848}, +annote={OSS database engine, Scheme, and compilers, students stated their marketability had been increased, Some students suggested the use of an industrial strength +OSS database system Wheeler [33] also provides a general 4-step process +for evaluating OSS programs: (a) identifying OSS candidates, +(b) reading reviews, (c) compare leading programs, and (d) +analyzing the top candidates in greater depth. + +}} + +%Pedroni, M, Bay, T, Oriol, M, and Pedroni, A, "Open Source Projects in Programming Courses," SIGCSE, March 2007. + + + + +@article{Pedroni:2007:OSP:1227504.1227465, + author = {Pedroni, Michela and Bay, Till and Oriol, Manuel and Pedroni, Andreas}, + title = {Open source projects in programming courses}, + journal = {SIGCSE Bull.}, + issue_date = {March 2007}, + volume = {39}, + number = {1}, + month = mar, + year = {2007}, + issn = {0097-8418}, + pages = {454--458}, + numpages = {5}, + url = {http://doi.acm.org/10.1145/1227504.1227465}, + doi = {10.1145/1227504.1227465}, + acmid = {1227465}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {assessment, communities, motivation, open source, project}, +} + + + + + +%Nelson, D, and Ng, Y, M, "Teaching Computer Networking using Open Source Software," ITiCSE, 2000, pp. 13-16. + +%O'Hara, K, J, and Kay, J, S, "Open Source Software and Computer Science Education," The Journal of Computing Sciences in Colleges, Vol. 18, No. 3, February 2003. + +%Jaccheri, L, and Osterlie, T, "Open Source Software: A Source of Possibilities for Software Engineering Education and Empirical Software Engineering," First International Workshop on Emerging Trends in FLOSS Research and Development (FLOSS'07), 2007. + +%[24] Claypool, M., D. Finkel, and C.E. Wills An Open Source Laboratory +%for Operating Systems Projects, ACM/SIGCSE ITiCSE (Innovation and +%Technology in Computer Science Education), June 2001, pp. 145-148. +%[25] German, D.M., Experiences teaching a graduate course in Open Source +%Software Engineering, First International Conference on Open Source +%Systems (OSS2005), Genova, Italy, July 2005. + +%[30] Bezroukov, N., Open Source Software Development as a Special Type +%of Academic Research (Critique of Vulgar Raymondism), First +%Monday, 4(10), Oct. 1999. Accessed May 27, 2006. +%http://firstmonday.org/issues/issue4_10/bezroukov/index.html. + +%] Wheeler, D.A., How to Evaluate Open Source Software/Free Software +%(OSS/FS) Programs, 2006. Accessed May 27, 2006. +%http://www.dwheeler.com/oss_fs_eval.html + +%Here's a Java for project, OptFlux +%Rocha et al. BMC Systems Biology 2010, 4:45 +%http://www.biomedcentral.com/1752-0509/4/45 +%P. Roberts. Abstract thinking: a predictor of modelling ability? In Educators Symposium Models 2009. + +@INPROCEEDINGS{5673370, +author={Bell, T. and Pasternak, A. and Stephenson, C. and Tucker, A. and Vahrenhold, J.}, +booktitle={Frontiers in Education Conference (FIE), 2010 IEEE}, +title={Panel 2014; Implementing CS curricula in secondary education: An international perspective}, +year={2010}, +month={oct.}, +volume={}, +number={}, +pages={T2B-1 -T2B-3}, +abstract={Despite several well-received designs for Computer Science curricula in secondary education being published both on national and international level, the implementation of these curricula is still being impeded by a variety of factors. This panel is intended to present issues, and approaches to solving them, from an international perspective. The presenters bring together experience in curriculum design, implementation, and teacher training and certification, and have had some successes that will help to inform those who are struggling with barriers to successful implementation and sustained improvement to Computer Science education. Given the current efforts to standardize courses in secondary education both in North America and Europe, it is expected that the results of the discussion following the presentations will help inform and influence these implementation efforts.}, +keywords={Europe;North America;computer science education;course standardization;curriculum design;curriculum implementation;secondary education;teacher certification;teacher training;certification;computer science education;educational courses;teacher training;}, +doi={10.1109/FIE.2010.5673370}, +ISSN={0190-5848},} +% E. Allen, R. Cartwright, and C. Reis. Production +%programming in the classroom. In SIGCSE 03: +%Proceedings of the 34th SIGCSE technical symposium +%on Computer science education, pages 8993, New +%York, NY, USA, 2003. ACM Press. +%[2] D. Carrington and S.-K. Kim. Teaching software design +%with open source software. Frontiers in Education, +%3(33):S1C 914, November 2003. +%[3] C. P. Fuhrman. Appreciation of software design +%concerns via open-source tools and projects. In 10th +%Workshop on Pedagogies and Tools for the Teaching +%and Learning of Object Oriented Concepts, at 20th +%European Conference on Object Oriented Programming +%(ECOOP), Nantes, FR, July 2006. +%[4] K. J. OHara and J. S. Kay. Open source software and +%computer science education. J. Comput. Small Coll., +%18(3):17, 2003. diff --git a/litVertical2.bib b/litVertical2.bib new file mode 100644 index 0000000..9a2f043 --- /dev/null +++ b/litVertical2.bib @@ -0,0 +1,2848 @@ +% +%2015 +% +@article{aliyari2015effects, + title={The Effects of Fifa 2015 Computer Games on Changes in Cognitive, Hormonal and Brain Waves Functions of Young Men Volunteers}, + author={Aliyari, Hamed and Kazemi, Masoomeh and Tekieh, Elaheh and Salehi, Maryam and Sahraei, Hedayat and Daliri, Mohammad Reza and Agaei, Hassan and Minaei, Behroz and Lashgari, Reza and Srahian, Nahid and others}, + journal={Basic and Clinical Neuroscience}, + volume={6}, + number={3}, + pages={193--201}, + year={2015}, + publisher={Basic and Clinical Neuroscience} +} +@article{altenmuller2015apollo, + title={Apollo's gift: new aspects of neurologic music therapy}, + author={Altenm{\"u}ller, Eckart and Schlaug, Gottfried}, + journal={Progress in brain research}, + volume={217}, + pages={237--252}, + year={2015}, + publisher={Elsevier} +} +@article{atherton2015memory, + title={Memory trace replay: the shaping of memory consolidation by neuromodulation}, + author={Atherton, Laura A and Dupret, David and Mellor, Jack R}, + journal={Trends in Neurosciences}, + year={2015}, + publisher={Elsevier} +} +@article{bachmann2015brain, + title={On the brain-imaging markers of neural correlates of consciousness}, + author={Bachmann, Talis}, + journal={Frontiers in psychology}, + volume={6}, + year={2015}, + publisher={Frontiers Media SA} +} +@article{Bezdek2015338, + +title = "Neural evidence that suspense narrows attentional focus ", + +journal = "Neuroscience ", + +volume = "303", + +number = "", + +pages = "338 - 345", + +year = "2015", + +note = "", + +issn = "0306-4522", + +doi = "http://dx.doi.org/10.1016/j.neuroscience.2015.06.055", + +url = "http://www.sciencedirect.com/science/article/pii/S0306452215005965", + +author = "M.A. Bezdek and R.J. Gerrig and W.G. Wenzel and J. Shin and K. Pirog Revill and E.H. Schumacher", + +keywords = "attention", + +keywords = "emotions", + +keywords = "cognitive neuroscience", + +keywords = "narrative transportation", + +keywords = "suspense ", + +abstract = "Abstract The scope of visual attention changes dynamically over time. Although previous research has reported conditions that suppress peripheral visual processing, no prior work has investigated how attention changes in response to the variable emotional content of audiovisual narratives. We used fMRI to test for the suppression of spatially peripheral stimuli and enhancement of narrative-relevant central stimuli at moments when suspense increased in narrative film excerpts. Participants viewed films presented at fixation, while flashing checkerboards appeared in the periphery. Analyses revealed that increasing narrative suspense caused reduced activity in peripheral visual processing regions in the anterior calcarine sulcus and in default mode network nodes. Concurrently, activity increased in central visual processing regions and in frontal and parietal regions recruited for attention and dynamic visual processing. These results provide evidence, using naturalistic stimuli, of dynamic spatial tuning of attention in early visual processing areas due to narrative context. " + +} +@article{Bridge01082015, +author = {Bridge, Donna J. and Voss, Joel L.}, +title = {Binding among select episodic elements is altered via active short-term retrieval}, +volume = {22}, +number = {8}, +pages = {360-363}, +year = {2015}, +doi = {10.1101/lm.038703.115}, +abstract ={Of the many elements that comprise an episode, are any disproportionately bound to the others? We tested whether active short-term retrieval selectively increases binding. Individual objects from multiobject displays were retrieved after brief delays. Memory was later tested for the other objects. Cueing with actively retrieved objects facilitated memory of associated objects, which was associated with unique patterns of viewing behavior during study and enhanced ERP correlates of retrieval during test, relative to other reminder cues that were not actively retrieved. Active short-term retrieval therefore enhanced binding of retrieved elements with others, thus creating powerful memory cues for entire episodes.}, +URL = {http://learnmem.cshlp.org/content/22/8/360.abstract}, +eprint = {http://learnmem.cshlp.org/content/22/8/360.full.pdf+html}, +journal = {Learning \& Memory} +} +@article{cameron2015adult, + title={Adult Neurogenesis: Beyond Learning and Memory*}, + author={Cameron, Heather A and Glover, Lucas R}, + journal={Annual review of psychology}, + volume={66}, + pages={53--81}, + year={2015}, + publisher={Annual Reviews} +} +@article{cao2015neural, + title={Neural correlates underlying insight problem solving: Evidence from EEG alpha oscillations}, + author={Cao, Zhipeng and Li, Yadan and Hitchman, Glenn and Qiu, Jiang and Zhang, Qinglin}, + journal={Experimental brain research}, + pages={1--10}, + year={2015}, + publisher={Springer} +} +@article{cohen2015peri, + title={Peri-encoding predictors of memory encoding and consolidation}, + author={Cohen, Noga and Pell, Liat and Edelson, Micah G and Ben-Yakov, Aya and Pine, Alex and Dudai, Yadin}, + journal={Neuroscience \& Biobehavioral Reviews}, + volume={50}, + pages={128--142}, + year={2015}, + publisher={Elsevier} +} +@article{ding2015short, + title={Short-term meditation modulates brain activity of insight evoked with solution cue}, + author={Ding, Xiaoqian and Tang, Yi-Yuan and Cao, Chen and Deng, Yuqin and Wang, Yan and Xin, Xiu and Posner, Michael I}, + journal={Social cognitive and affective neuroscience}, + volume={10}, + number={1}, + pages={43--49}, + year={2015}, + publisher={Oxford University Press} +} +@article{eickhoff2015excessive, + title={Excessive Video Game Use, Sleep Deprivation, and Poor Work Performance Among US Marines Treated in a Military Mental Health Clinic: A Case Series}, + author={Eickhoff, Erin and Yung, Kathryn and Davis, Diane L and Bishop, Frank and Klam, Warren P and Doan, Andrew P}, + journal={Military medicine}, + volume={180}, + number={7}, + pages={e839--e843}, + year={2015}, + publisher={Association of Military Surgeons of the US}, + annote={Excessive use of video games may be associated with sleep deprivation, resulting in poor job performance and atypical mood disorders. Three active duty service members in the U.S. Marine Corps were offered mental health evaluation for sleep disturbance and symptoms of blunted affect, low mood, poor concentration, inability to focus, irritability, and drowsiness. All three patients reported insomnia as their primary complaint. When asked about online video games and sleep hygiene practices, all three patients reported playing video games from 30 hours to more than 60 hours per week in addition to maintaining a 40-hour or more workweek. Our patients endorsed sacrificing sleep to maintain their video gaming schedules without insight into the subsequent sleep deprivation. During the initial interviews, they exhibited blunted affects and depressed moods, but appeared to be activated with enthusiasm and joy when discussing their video gaming with the clinical provider. Our article illustrates the importance of asking about online video gaming in patients presenting with sleep disturbances, poor work performance, and depressive symptoms. Because excessive video gaming is becoming more prevalent worldwide, military mental health providers should ask about video gaming when patients report problems with sleep.} +} +@article{huang2015highest, + title={The highest form of intelligence: Sarcasm increases creativity for both expressers and recipients}, + author={Huang, Li and Gino, Francesca and Galinsky, Adam D}, + journal={Organizational Behavior and Human Decision Processes}, + year={2015}, + publisher={Elsevier} +} +@article{ingalhalikar2014sex, + title={Sex differences in the structural connectome of the human brain}, + author={Ingalhalikar, Madhura and Smith, Alex and Parker, Drew and Satterthwaite, Theodore D and Elliott, Mark A and Ruparel, Kosha and Hakonarson, Hakon and Gur, Raquel E and Gur, Ruben C and Verma, Ragini}, + journal={Proceedings of the National Academy of Sciences}, + volume={111}, + number={2}, + pages={823--828}, + year={2014}, + publisher={National Acad Sciences} +} +@article{ji2015origin, + title={The origin of glutamatergic synaptic inputs controls synaptic plasticity and its modulation by alcohol in mice nucleus accumbens}, + author={Ji, Xincai and Saha, Sucharita and Martin, Gilles E}, + journal={Frontiers in Synaptic Neuroscience}, + volume={7}, + year={2015}, + publisher={Frontiers Media SA} +} +@article{kafkas2015striatal, + title={Striatal and midbrain connectivity with the hippocampus selectively boosts memory for contextual novelty}, + author={Kafkas, Alexandros and Montaldi, Daniela}, + journal={Hippocampus}, + year={2015}, + publisher={Wiley Online Library} +} +@article{kalbfleisch2015editorial, + title={Editorial Note for the Research Topic Special Issue on Educational Neuroscience, Constructivism, Learning, and the Mediation of Learning and Creativity in the 21st Century}, + author={Kalbfleisch, Layne}, + journal={Frontiers in Psychology}, + volume={6}, + pages={133}, + year={2015}, + publisher={Frontiers} +} +@book{kemmerer, +author={David Kemmerer}, +title={Cognitive Neurscience of Language}, +publisher={Psychology Press}, +year={2015} +} +@article{kesner2015computational, + title={A computational theory of hippocampal function, and tests of the theory: new developments}, + author={Kesner, Raymond P and Rolls, Edmund T}, + journal={Neuroscience \& Biobehavioral Reviews}, + volume={48}, + pages={92--147}, + year={2015}, + publisher={Elsevier} +} +@book{kounios2015eureka, + title={The Eureka Factor: Aha Moments, Creative Insight, and the Brain}, + author={Kounios, John and Beeman, Mark}, + year={2015}, + publisher={Random House}, + annote={google book, general audience, nice} +} +@article{lavenex2015commentary, + title={Commentary: The ontogeny of human memory Where are we going?}, + author={Lavenex, Pamela Banta and Lavenex, Pierre}, + journal={International Journal of Behavioral Development}, + pages={0165025415573645}, + year={2015}, + publisher={SAGE Publications} +} +@article{lin2015neural, + title={Neural Correlates of Mathematical Problem Solving}, + author={Lin, Chun-Ling and Jung, Melody and Wu, Ying Choon and She, Hsiao-Ching and Jung, Tzyy-Ping}, + journal={International journal of neural systems}, + volume={25}, + number={02}, + pages={1550004}, + year={2015}, + publisher={World Scientific} +} +@article{llewellyn2015not, + title={Not only… but also: REM sleep creates and NREM Stage 2 instantiates landmark junctions in cortical memory networks}, + author={Llewellyn, Sue and Hobson, J Allan}, + journal={Neurobiology of learning and memory}, + year={2015}, + publisher={Elsevier} +} +@article{logothetis2015neural, + title={Neural-Event-Triggered fMRI of large-scale neural networks}, + author={Logothetis, Nikos K}, + journal={Current opinion in neurobiology}, + volume={31}, + pages={214--222}, + year={2015}, + publisher={Elsevier} +} +@article{luo2015neuronal, + title={Neuronal Modulations in Visual Cortex Are Associated with Only One of Multiple Components of Attention}, + author={Luo, Thomas Zhihao and Maunsell, John HR}, + journal={Neuron}, + volume={86}, + number={5}, + pages={1182--1188}, + year={2015}, + publisher={Elsevier} +} +@article{maass2015does, + title={Does Media Use Have a Short-Term Impact on Cognitive Performance?}, + author={Maass, Asja and Kl{\"o}pper, Klara Maria and Michel, Friederike and Lohaus, Arnold}, + journal={Journal of Media Psychology}, + year={2015}, + publisher={Hogrefe Publishing} +} +@article{Mains01072015, +author = {Mains, Tyler E and Cofrancesco, Joseph and Milner, Stephen M and Shah, Nina G and Goldberg, Harry}, +title = {Do questions help? The impact of audience response systems on medical student learning: a randomised controlled trial}, +volume = {91}, +number = {1077}, +pages = {361-367}, +year = {2015}, +doi = {10.1136/postgradmedj-2014-132987}, +abstract ={Background Audience response systems (ARSs) are electronic devices that allow educators to pose questions during lectures and receive immediate feedback on student knowledge. The current literature on the effectiveness of ARSs is contradictory, and their impact on student learning remains unclear.Objectives This randomised controlled trial was designed to isolate the impact of ARSs on student learning and students’ perception of ARSs during a lecture.Methods First-year medical student volunteers at Johns Hopkins were randomly assigned to either (i) watch a recorded lecture on an unfamiliar topic in which three ARS questions were embedded or (ii) watch the same lecture without the ARS questions. Immediately after the lecture on 5 June 2012, and again 2 weeks later, both groups were asked to complete a questionnaire to assess their knowledge of the lecture content and satisfaction with the learning experience.Results 92 students participated. The mean (95% CI) initial knowledge assessment score was 7.63 (7.17 to 8.09) for the ARS group (N=45) and 6.39 (5.81 to 6.97) for the control group (N=47), p=0.001. Similarly, the second knowledge assessment mean score was 6.95 (6.38 to 7.52) for the ARS group and 5.88 (5.29 to 6.47) for the control group, p=0.001. The ARS group also reported higher levels of engagement and enjoyment.Conclusions Embedding three ARS questions within a 30 min lecture increased students’ knowledge immediately after the lecture and 2 weeks later. We hypothesise that this increase was due to forced information retrieval by students during the learning process, a form of the testing effect.}, +URL = {http://pmj.bmj.com/content/91/1077/361.abstract}, +eprint = {http://pmj.bmj.com/content/91/1077/361.full.pdf+html}, +journal = {Postgraduate Medical Journal} +} +@article{martin2015grapes, + title={GRAPES—Grounding representations in action, perception, and emotion systems: How object properties and categories are represented in the human brain}, + author={Martin, Alex}, + journal={Psychonomic bulletin \& review}, + pages={1--12}, + year={2015}, + publisher={Springer} +} +@article{mercer2015stress, + title={Stress Relieving Video Games: Creating a Game for the Purpose of Stress Relief and Analyzing Its Effectiveness}, + author={Mercer, Nicole}, + year={2015} +} +@article{merlo2015amygdala, + title={Amygdala Dopamine Receptors Are Required for the Destabilization of a Reconsolidating Appetitive Memory}, + author={Merlo, Emiliano and Ratano, Patrizia and Ilioi, Elena C and Robbins, Miranda ALS and Everitt, Barry J and Milton, Amy L}, + journal={eneuro}, + volume={2}, + number={2}, + pages={ENEURO--0024}, + year={2015}, + publisher={eneuro}, + annote={hard to get?} +} +@incollection{quiroga2015concept, + title={Concept Cells in the Human Brain}, + author={Quiroga, Rodrigo Quian}, + booktitle={Advances in Cognitive Neurodynamics (IV)}, + pages={143--146}, + year={2015}, + publisher={Springer} +} +@article{rocchetti2015presynaptic, + title={Presynaptic D 2 Dopamine Receptors Control Long-Term Depression Expression and Memory Processes in the Temporal Hippocampus}, + author={Rocchetti, Jill and Isingrini, Elsa and Dal Bo, Gregory and Sagheby, Sara and Menegaux, Aurore and Tronche, Fran{\c{c}}ois and Levesque, Daniel and Moquin, Luc and Gratton, Alain and Wong, Tak Pan and others}, + journal={Biological psychiatry}, + volume={77}, + number={6}, + pages={513--525}, + year={2015}, + publisher={Elsevier} +} +@article{salimpoor2015predictions, + title={Predictions and the brain: How musical sounds become rewarding}, + author={Salimpoor, Valorie N and Zald, David H and Zatorre, Robert J and Dagher, Alain and McIntosh, Anthony Randal}, + journal={Trends in cognitive sciences}, + volume={19}, + number={2}, + pages={86--91}, + year={2015}, + publisher={Elsevier} +} +@article{sandrini2015modulating, + title={Modulating reconsolidation: a link to causal systems-level dynamics of human memories}, + author={Sandrini, Marco and Cohen, Leonardo G and Censor, Nitzan}, + journal={Trends in cognitive sciences}, + volume={19}, + number={8}, + pages={475--482}, + year={2015}, + publisher={Elsevier} +} +@article{schlegel2015artist, + title={The artist emerges: Visual art learning alters neural structure and function}, + author={Schlegel, Alexander and Alexander, Prescott and Fogelson, Sergey V and Li, Xueting and Lu, Zhengang and Kohler, Peter J and Riley, Enrico and Peter, U Tse and Meng, Ming}, + journal={NeuroImage}, + volume={105}, + pages={440--451}, + year={2015}, + publisher={Elsevier} +} +@article{schmalz2015getting, + title={Getting to the bottom of orthographic depth}, + author={Schmalz, Xenia and Marinus, Eva and Coltheart, Max and Castles, Anne}, + journal={Psychonomic bulletin \& review}, + pages={1--16}, + year={2015}, + publisher={Springer} +} +@article{scholl2015good, + title={The Good, the Bad, and the Irrelevant: Neural Mechanisms of Learning Real and Hypothetical Rewards and Effort}, + author={Scholl, Jacqueline and Kolling, Nils and Nelissen, Natalie and Wittmann, Marco K and Harmer, Catherine J and Rushworth, Matthew FS}, + journal={The Journal of Neuroscience}, + volume={35}, + number={32}, + pages={11233--11251}, + year={2015}, + publisher={Soc Neuroscience} +} +@incollection{schultheiss2015models, + title={Models and Theoretical Frameworks for Hippocampal and Entorhinal Cortex Function in Memory and Navigation}, + author={Schultheiss, Nathan W and Hinman, James R and Hasselmo, Michael E}, + booktitle={Analysis and Modeling of Coordinated Multi-neuronal Activity}, + pages={247--268}, + year={2015}, + publisher={Springer} +} +@article{spunt2015neural, + title={The neural basis of conceptualizing the same action at different levels of abstraction}, + author={Spunt, Robert P and Kemmerer, David and Adolphs, Ralph}, + journal={Social cognitive and affective neuroscience}, + pages={nsv084}, + year={2015}, + publisher={Oxford University Press} +} +@article{squire2015conscious, + title={Conscious and Unconscious Memory Systems}, + author={Squire, Larry R and Dede, Adam JO}, + journal={Cold Spring Harbor perspectives in biology}, + volume={7}, + number={3}, + pages={a021667}, + year={2015}, + publisher={Cold Spring Harbor Lab} +} +@article{watson2015sleep, + title={Sleep, memory \& brain rhythms}, + author={Watson, Brendon O and Buzs{\'a}ki, Gy{\"o}rgy}, + journal={Daedalus}, + volume={144}, + number={1}, + pages={67--82}, + year={2015}, + publisher={MIT Press} +} +@article{xie2015c957t, + title={The C957T polymorphism in the dopamine receptor D2 gene modulates domain-general category learning}, + author={Xie, Zilong and Maddox, W Todd and M@article{lin2015neural, + title={Neural Correlates of Mathematical Problem Solving}, + author={Lin, Chun-Ling and Jung, Melody and Wu, Ying Choon and She, Hsiao-Ching and Jung, Tzyy-Ping}, + journal={International journal of neural systems}, + volume={25}, + number={02}, + pages={1550004}, + year={2015}, + publisher={World Scientific} + }cGeary, John E and Chandrasekaran, Bharath}, + journal={Journal of neurophysiology}, + volume={113}, + number={9}, + pages={3281--3290}, + year={2015}, + publisher={Am Physiological Soc} +} +@article{wirebring2015learning, + title={Learning mathematics without a suggested solution method: Durable effects on performance and brain activity}, + author={Wirebring, Linnea Karlsson and Lithner, Johan and Jonsson, Bert and Liljekvist, Yvonne and Norqvist, Mathias and Nyberg, Lars}, + journal={Trends in Neuroscience and Education}, + volume={4}, + number={1}, + pages={6--14}, + year={2015}, + publisher={Elsevier} +} +@article{wirebring2015better, + title={Lesser Neural Pattern Similarity across Repeated Tests is Associated with Better Long-Term Memory Retention}, + author={Wirebring, Linnea Karlsson and Wiklund-H\:ornqvist and Eriksson Johan and Andersson Micael and Jonsson, Bert and Nyberg, Lars}, + journal={Journal of Neuroscience}, + volume={}, + number={}, + pages={9595--9602}, + year={2015} +} +% +%2014 +% +@article{aimone2014regulation, + title={Regulation and function of adult neurogenesis: from genes to cognition}, + author={Aimone, James B and Li, Yan and Lee, Star W and Clemenson, Gregory D and Deng, Wei and Gage, Fred H}, + journal={Physiological reviews}, + volume={94}, + number={4}, + pages={991--1026}, + year={2014}, + publisher={Am Physiological Soc} +} +@article{alger2014role, + title={The Role of Sleep in Human Declarative Memory Consolidation}, + author={Alger, Sara E and Chambers, Alexis M and Cunningham, Tony and Payne, Jessica D}, + year={2014}, + publisher={Springer}, + ammote={not free} +} +@article{cerf2014studying, + title={Studying Thoughts and Deliberations Using Single Neuron Recordings in Humans}, + author={Cerf, Moran and Gelbard-Sagiv, Hagar and Fried, Itzhak}, + journal={Single Neuron Studies of the Human Brain: Probing Cognition}, + pages={189}, + year={2014}, + publisher={MIT Press} +} +@article{chambers2014developmental, + title={Developmental neurocircuitry of motivation in adolescence: a critical period of addiction vulnerability}, + author={Chambers, R Andrew and Taylor, Jane R and Potenza, Marc N}, + journal={American Journal of Psychiatry}, + year={2014}, + publisher={Am Psychiatric Assoc} +} +@article{chang2014reorganization, + title={Reorganization and plastic changes of the human brain associated with skill learning and expertise}, + author={Chang, Yongmin}, + journal={Frontiers in human neuroscience}, + volume={8}, + year={2014}, + publisher={Frontiers Media SA} +} +@article{chib2014effects, + title={The effects of incentive framing on performance decrements for large monetary outcomes: behavioral and neural mechanisms}, + author={Chib, Vikram S and Shimojo, Shinsuke and O'Doherty, John P}, + journal={The Journal of Neuroscience}, + volume={34}, + number={45}, + pages={14833--14844}, + year={2014}, + publisher={Soc Neuroscience} +} +@article{cowansage2014direct, + title={Direct reactivation of a coherent neocortical memory of context}, + author={Cowansage, Kiriana K and Shuman, Tristan and Dillingham, Blythe C and Chang, Allene and Golshani, Peyman and Mayford, Mark}, + journal={Neuron}, + volume={84}, + number={2}, + pages={432--441}, + year={2014}, + publisher={Elsevier} +} +@article{deliens2014sleep, + title={Sleep and the processing of emotions}, + author={Deliens, Ga{\'e}tane and Gilson, M{\'e}dhi and Peigneux, Philippe}, + journal={Experimental brain research}, + volume={232}, + number={5}, + pages={1403--1414}, + year={2014}, + publisher={Springer} +} +@incollection{diekelmann2014your, + title={Your Interest in Sleep and Memory Posits a Semantic Learning Function to NREM Sleep. What Are Your Views of Associative Memory Enhancement by REM?}, + author={Diekelmann, Susanne and Born, Jan}, + booktitle={Dream Consciousness}, + pages={119--122}, + year={2014}, + publisher={Springer}, + annote={costs money} +} +@book{fried2014single, + title={Single Neuron Studies of the Human Brain: Probing Cognition}, + author={Fried, Itzhak and Rutishauser, Ueli and Cerf, Moran and Kreiman, Gabriel}, + year={2014}, + publisher={MIT Press} +} +@article{gregory2014resting, + title={Resting state connectivity immediately following learning correlates with subsequent sleep-dependent enhancement of motor task performance}, + author={Gregory, Michael D and Agam, Yigal and Selvadurai, Chindhuri and Nagy, Amanda and Vangel, Mark and Tucker, Matthew and Robertson, Edwin M and Stickgold, Robert and Manoach, Dara S}, + journal={NeuroImage}, + volume={102}, + pages={666--673}, + year={2014}, + publisher={Elsevier} +} +@article{hanslmayr2014brain, + title={How brain oscillations form memories—a processing based perspective on oscillatory subsequent memory effects}, + author={Hanslmayr, Simon and Staudigl, Tobias}, + journal={Neuroimage}, + volume={85}, + pages={648--655}, + year={2014}, + publisher={Elsevier} +} +@article{jung2014subcortical, + title={Subcortical Correlates of Individual Differences in Aptitude}, + author={Jung, Rex E and Ryman, Sephira G and Vakhtin, Andrei A and Carrasco, Jessica and Wertz, Chris and Flores, Ranee A}, + journal={PloS one}, + volume={9}, + number={2}, + pages={e89425}, + year={2014}, + publisher={Public Library of Science} +} +@article{karlsson2014learning, + title={Learning mathematics without a given solution method have beneficial effects on subsequent performance and modulates brain activity}, + author={Karlsson, Linnea and Lithner, Johan and Jonsson, Bert and Liljekvist, Yvonne and Norqvist, Mathias and Lars, Nyberg}, + year={2014}, + annote={how to get?} +} +@article{kelemen2014hippocampal, + title={Hippocampal corticosterone impairs memory consolidation during sleep but improves consolidation in the wake state}, + author={Kelemen, Eduard and Bahrendt, Marie and Born, Jan and Inostroza, Marion}, + journal={Hippocampus}, + volume={24}, + number={5}, + pages={510--515}, + year={2014}, + publisher={Wiley Online Library} +} +@article{kounios2014cognitive, + title={The cognitive neuroscience of insight}, + author={Kounios, John and Beeman, Mark}, + journal={Annual review of psychology}, + volume={65}, + pages={71--93}, + year={2014}, + publisher={Annual Reviews} +} +@article{luck2014potentiation, + title={The Potentiation of Associative Memory by Emotions: An Event-Related FMRI Study}, + author={Luck, David and Leclerc, Marie-Eve and Lepage, Martin}, + journal={Advances in Neuroscience}, + volume={2014}, + year={2014}, + publisher={Hindawi Publishing Corporation} +} +@article{maddox2014directing, + title={Directing eye gaze enhances auditory spatial cue discrimination}, + author={Maddox, Ross K and Pospisil, Dean A and Stecker, G Christopher and Lee, Adrian KC}, + journal={Current Biology}, + volume={24}, + number={7}, + pages={748--752}, + year={2014}, + publisher={Elsevier} +} +@article{mormann2014visual, + title={Visual Cognitive Adventures of Single Neurons in the Human Medial Temporal Lobe}, + author={Mormann, Florian and Ison, Matias J and Quiroga, Rodrigo Quian and Koch, Christof and Fried, Itzhak and Kreiman, Gabriel}, + journal={Single Neuron Studies of the Human Brain: Probing Cognition}, + pages={121}, + year={2014}, + publisher={MIT Press} +} +@article{murayama2014consolidation, + title={Consolidation power of extrinsic rewards: Reward cues enhance long-term memory for irrelevant past events.}, + author={Murayama, Kou and Kitagami, Shinji}, + journal={Journal of Experimental Psychology: General}, + volume={143}, + number={1}, + pages={15}, + year={2014}, + publisher={American Psychological Association}, + annote={not free Recent research suggests that extrinsic rewards promote memory consolidation through dopaminergic modulation processes. However, no conclusive behavioral evidence exists given that the influence of extrinsic reward on attention and motivation during encoding and consolidation processes are inherently confounded. The present study provides behavioral evidence that extrinsic rewards (i.e., monetary incentives) enhance human memory consolidation independently of attention and motivation. Participants saw neutral pictures, followed by a reward or control cue in an unrelated context. Our results (and a direct replication study) demonstrated that the reward cue predicted a retrograde enhancement of memory for the preceding neutral pictures. This retrograde effect was observed only after a delay, not immediately upon testing. An additional experiment showed that emotional arousal or unconscious resource mobilization cannot explain the retrograde enhancement effect. These results provide support for the notion that the dopaminergic memory consolidation effect can result from extrinsic reward. (PsycINFO Database Record (c) 2014 APA, all rights reserved)} +} +@article{ojemann2014human, + title={Human Lateral Temporal Cortical Single Neuron Activity during Language, Recent Memory, and Learning}, + author={Ojemann, George}, + journal={Single Neuron Studies of the Human Brain: Probing Cognition}, + pages={247}, + year={2014}, + publisher={MIT Press} +} +@article{patel2014human, + title={Human single neuron reward processing in the basal ganglia and anterior cingulate}, + author={Patel, Shaun R and Sierra-Mercado, Demetrio and Martinez-Rubio, Clarissa and Eskandar, Emad N}, + journal={Single Neuron Studies of the Human Brain: Probing Cognition}, + pages={205}, + year={2014}, + publisher={MIT Press} +} +@inproceedings{reilly2014examination, + title={An examination of mathematics preparation for and progress through three introductory computer science courses}, + author={Reilly, Christine F and Tomai, Emmett}, + booktitle={Frontiers in Education Conference (FIE), 2014 IEEE}, + pages={1--9}, + year={2014}, + organization={IEEE} +} +@article{rossi2014quantum, + title={Quantum Perspectives of Consciousness, Cognition and Creativity: The Dirac Equation in a New Contour Integral Model of Brain Plasticity}, + author={Rossi, EL and Rossi, KL}, + journal={J Appl Computat Math}, + volume={3}, + number={183}, + pages={2}, + year={2014} +} +@article{roux2014working, + title={Working memory and neural oscillations: alpha--gamma versus theta--gamma codes for distinct WM information?}, + author={Roux, Fr{\'e}d{\'e}ric and Uhlhaas, Peter J}, + journal={Trends in cognitive sciences}, + volume={18}, + number={1}, + pages={16--25}, + year={2014}, + publisher={Elsevier} +} +@article{rutishauser2014single, + title={Single Neuron Correlates of Declarative Memory Formation and Retrieval in the Human Medial Temporal Lobe}, + author={Rutishauser, Ueli and Schuman, Erin M and Mamelak, Adam N}, + journal={Single Neuron Studies of the Human Brain: Probing Cognition}, + pages={101}, + year={2014}, + publisher={MIT Press} +} +@article{rutishauser2014next, + title={The Next Ten Years and Beyond}, + author={Rutishauser, Ueli and Fried, Itzhak and Cerf, Moran and Kreiman, Gabriel}, + journal={Single Neuron Studies of the Human Brain: Probing Cognition}, + pages={347}, + year={2014}, + publisher={MIT Press} +} +@article{sali2014role, + title={The role of reward prediction in the control of attention.}, + author={Sali, Anthony W and Anderson, Brian A and Yantis, Steven}, + journal={Journal of experimental psychology: human perception and performance}, + volume={40}, + number={4}, + pages={1654}, + year={2014}, + publisher={American Psychological Association}, + annote={Previously rewarded stimuli involuntarily capture attention. The learning mechanisms underlying this value-driven attentional capture remain less understood. We tested whether theories of prediction-based associative reward learning explain the conditions under which reward feedback leads to value-based modulations of attentional priority. Across 4 experiments, we manipulated whether stimulus features served as unique predictors of reward outcomes. Participants received monetary rewards for correctly identifying a color-defined target in an initial search task (training phase) and then immediately completed a second, unrewarded visual search task in which color was irrelevant (test phase). In Experiments 1–3, monetary reward followed correct target selection during training, but critically, no target-defining features carried uniquely predictive information about reward outcomes. Under these conditions, we found no evidence of attentional capture by the previous target colors in the subsequent test phase. Conversely, when target colors in the training phase of Experiment 4 carried uniquely predictive information about reward magnitude, we observed significant attentional capture by the previously rewarded color. Our findings show that value-based attentional priority only develops for stimulus features that carry uniquely predictive information about reward, ruling out a purely motivational account and suggesting that mechanisms of reward prediction play an important role in shaping attentional priorities. (PsycINFO Database Record (c) 2014 APA, all rights reserved)} +} +@article{schonauer2014strengthening, + title={Strengthening procedural memories by reactivation in sleep}, + author={Sch{\"o}nauer, Monika and Geisler, Teresa and Gais, Steffen}, + journal={Journal of cognitive neuroscience}, + volume={26}, + number={1}, + pages={143--153}, + year={2014}, + publisher={MIT Press} +} +@article{schwabe2014reconsolidation, + title={Reconsolidation of human memory: brain mechanisms and clinical relevance}, + author={Schwabe, Lars and Nader, Karim and Pruessner, Jens C}, + journal={Biological psychiatry}, + volume={76}, + number={4}, + pages={274--280}, + year={2014}, + publisher={Elsevier} +} +@inproceedings{smith2014computer, + title={Computer science students' concepts of proof by induction}, + author={Smith, Th{\'e}r{\`e}se and McCartney, Robert}, + booktitle={Proceedings of the 14th Koli Calling International Conference on Computing Education Research}, + pages={51--60}, + year={2014}, + organization={ACM} +} +@article{susac2014case, + title={A case for neuroscience in mathematics education}, + author={Susac, Ana and Braeutigam, Sven}, + journal={Frontiers in human neuroscience}, + volume={8}, + year={2014}, + publisher={Frontiers Media SA} +} +@article{tononi2014sleep, + title={Sleep and the price of plasticity: from synaptic and cellular homeostasis to memory consolidation and integration}, + author={Tononi, Giulio and Cirelli, Chiara}, + journal={Neuron}, + volume={81}, + number={1}, + pages={12--34}, + year={2014}, + publisher={Elsevier} +} +@article{vuilleumier2014musical, + title={Musical Emotions in the Brain}, + author={Vuilleumier, Patrik}, + journal={Emotion Researcher}, + volume={11}, + year={2014} +} +@article{waisman2014brain, + title={Brain activity associated with translation between graphical and symbolic representations of functions in generally gifted and excelling in mathematics adolescents}, + author={Waisman, Ilana and Leikin, Mark and Shaul, Shelley and Leikin, Roza}, + journal={International Journal of Science and Mathematics Education}, + volume={12}, + number={3}, + pages={669--696}, + year={2014}, + publisher={Springer} +} +@article{walker2014sleep, + title={Sleep, memory and plasticity}, + author={Walker, Matthew P and Stickgold, Robert}, + journal={Neuroscience and Psychoanalysis}, + volume={1}, + pages={93}, + year={2014}, + publisher={Frenis Zero}, + annote={is a google book} +} +@article{zandieh2014conceptual, + title={Conceptual blending: Student reasoning when proving “conditional implies conditional” statements}, + author={Zandieh, Michelle and Roh, Kyeong Hah and Knapp, Jessica}, + journal={The Journal of Mathematical Behavior}, + volume={33}, + pages={209--229}, + year={2014}, + publisher={Elsevier} +} +@article{zhang2014neural, + title={Neural representations for the generation of inventive conceptions inspired by adaptive feature optimization of biological species}, + author={Zhang, Hao and Liu, Jia and Zhang, Qinglin}, + journal={cortex}, + volume={50}, + pages={162--173}, + year={2014}, + publisher={Elsevier} +} + +% +%2013 +% +@article{brosch2013impact, + title={The impact of emotion on perception, attention, memory, and decision-making}, + author={Brosch, Tobias and Scherer, Klaus R and Grandjean, Didier and Sander, David}, + journal={Swiss Med. Wkly}, + volume={143}, + pages={w13786}, + year={2013} +} +@article{dede2013hippocampal, + title={Hippocampal damage impairs recognition memory broadly, affecting both parameters in two prominent models of memory}, + author={Dede, Adam JO and Wixted, John T and Hopkins, Ramona O and Squire, Larry R}, + journal={Proceedings of the National Academy of Sciences}, + volume={110}, + number={16}, + pages={6577--6582}, + year={2013}, + publisher={National Acad Sciences} +} +@article{forcato2013role, + title={The role and dynamic of strengthening in the reconsolidation process in a human declarative memory: what decides the fate of recent and older memories?}, + author={Forcato, Cecilia and Fernandez, Rodrigo S and Pedreira, Mar{\'\i}a E}, + year={2013} +} +@book{hiebert2013conceptual, + title={Conceptual and procedural knowledge: The case of mathematics}, + author={Hiebert, James}, + year={2013}, + publisher={Routledge} +} +@article{islam2013dream, + title={Dream: from Phenomenology to Neurophysiology}, + author={Islam, Md Nazrul and Shah, Dev Kumar and Sapkota, Niraj Khatri}, + journal={Journal of Biomedical and Pharmaceutical Research}, + volume={2}, + number={2}, + pages={50--57}, + year={2013} +} +@article{kandel2013new, + title={The new science of mind and the future of knowledge}, + author={Kandel, Eric}, + journal={Neuron}, + volume={80}, + number={3}, + pages={546--560}, + year={2013}, + publisher={Elsevier} +} +@article{kleibeuker2013neural, + title={The neural coding of creative idea generation across adolescence and early adulthood}, + author={Kleibeuker, Sietske W and Koolschijn, P C{\'e}dric MP and Jolles, Dietsje D and De Dreu, Carsten KW and Crone, Eveline A}, + journal={Frontiers in human neuroscience}, + volume={7}, + year={2013}, + publisher={Frontiers Media SA} +} +@article{lindquist2013mind, + title={Mind wandering during lectures: Observations of the prevalence and correlates of attentional lapses, and their relationships with task characteristics and memory}, + author={Lindquist, Sophie India}, + year={2013} +} +@article{lisman2013habit, + title={Habit and nonhabit systems for unconscious and conscious behavior: Implications for multitasking}, + author={Lisman, John and Sternberg, Eliezer J}, + journal={Journal of cognitive neuroscience}, + volume={25}, + number={2}, + pages={273--283}, + year={2013}, + publisher={MIT Press} +} +@article{melby2013working, + title={Is working memory training effective? A meta-analytic review.}, + author={Melby-Lerv{\aa}g, Monica and Hulme, Charles}, + journal={Developmental psychology}, + volume={49}, + number={2}, + pages={270}, + year={2013}, + publisher={American Psychological Association} +} +@article{ouchi2013reduced, + title={Reduced adult hippocampal neurogenesis and working memory deficits in the Dgcr8-deficient mouse model of 22q11. 2 deletion-associated schizophrenia can be rescued by IGF2}, + author={Ouchi, Yasuo and Banno, Yuya and Shimizu, Yuko and Ando, Shouta and Hasegawa, Hitoki and Adachi, Koichi and Iwamoto, Takashi}, + journal={The Journal of Neuroscience}, + volume={33}, + number={22}, + pages={9408--9419}, + year={2013}, + publisher={Soc Neuroscience} +} +@article{paz2013physiological, + title={Physiological basis for emotional modulation of memory circuits by the amygdala}, + author={Paz, Rony and Pare, Denis}, + journal={Current opinion in neurobiology}, + volume={23}, + number={3}, + pages={381--386}, + year={2013}, + publisher={Elsevier} +} +@article{pourtois2013brain, + title={Brain mechanisms for emotional influences on perception and attention: what is magic and what is not}, + author={Pourtois, Gilles and Schettino, Antonio and Vuilleumier, Patrik}, + journal={Biological psychology}, + volume={92}, + number={3}, + pages={492--512}, + year={2013}, + publisher={Elsevier} +} +@article{quiroga2013brain, + title={Brain cells for grandmother}, + author={Quiroga, Rodrigo Quian and Fried, Itzhak and Koch, Christof}, + journal={Scientific American}, + volume={308}, + number={2}, + pages={30--35}, + year={2013}, + publisher={Nature Publishing Group} +} +@article{smith2013categorizing, + title={Categorizing the school experience of entering computing students}, + author={Smith, Th{\'e}r{\`e}se and McCartney, Robert}, + journal={Journal of Computing Sciences in Colleges}, + volume={28}, + number={3}, + pages={78--85}, + year={2013}, + publisher={Consortium for Computing Sciences in Colleges} +} +@inproceedings{smith2013mathematization, + title={Mathematization in teaching pumping lemmas}, + author={Smith, Tim and McCartney, Robert}, + booktitle={Frontiers in Education Conference, 2013 IEEE}, + pages={1671--1677}, + year={2013}, + organization={IEEE} +} +@article{stickgold2013sleep, + title={Sleep-dependent memory triage: evolving generalization through selective processing}, + author={Stickgold, Robert and Walker, Matthew P}, + journal={Nature Neuroscience}, + volume={16}, + number={2}, + pages={139--145}, + year={2013}, + publisher={Nature Publishing Group} +} +@article{tayler2013reactivation, + title={Reactivation of neural ensembles during the retrieval of recent and remote memory}, + author={Tayler, Kaycie K and Tanaka, Kazumasa Z and Reijmers, Leon G and Wiltgen, Brian J}, + journal={Current Biology}, + volume={23}, + number={2}, + pages={99--106}, + year={2013}, + publisher={Elsevier} +} +@article{vecchiato2013high, + title={High-resolution EEG analysis of power spectral density maps and coherence networks in a proportional reasoning task}, + author={Vecchiato, Giovanni and Susac, Ana and Margeti, Stavroula and Fallani, Fabrizio De Vico and Maglione, Anton Giulio and Supek, Selma and Planinic, Maja and Babiloni, Fabio}, + journal={Brain topography}, + volume={26}, + number={2}, + pages={303--314}, + year={2013}, + publisher={Springer} +} +% +%2012 +% +@article{abraham2012creativity, + title={Creativity and the brain: uncovering the neural signature of conceptual expansion}, + author={Abraham, Anna and Pieritz, Karoline and Thybusch, Kristin and Rutter, Barbara and Kr{\"o}ger, S{\"o}ren and Schweckendiek, Jan and Stark, Rudolf and Windmann, Sabine and Hermann, Christiane}, + journal={Neuropsychologia}, + volume={50}, + number={8}, + pages={1906--1917}, + year={2012}, + publisher={Elsevier} +} +@article{born2012system, + title={System consolidation of memory during sleep}, + author={Born, Jan and Wilhelm, Ines}, + journal={Psychological research}, + volume={76}, + number={2}, + pages={192--203}, + year={2012}, + publisher={Springer} +} +@book{cobb2012symbolizing, + title={Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design}, + author={Cobb, Paul and Yackel, Erna and McClain, Kay}, + year={2012}, + publisher={Routledge} +} +@book{devlin2012mathematical, + title={Introduction to Mathematical Thinking}, + author={Devlin, Keith}, + year={2012}, + publisher={Keith Devlin} +} +@article{diekelmann2012offline, + title={Offline consolidation of memory varies with time in slow wave sleep and can be accelerated by cuing memory reactivations}, + author={Diekelmann, Susanne and Biggel, Simon and Rasch, Bj{\"o}rn and Born, Jan}, + journal={Neurobiology of learning and memory}, + volume={98}, + number={2}, + pages={103--111}, + year={2012}, + publisher={Elsevier} +} +@article{dudai2012restless, + title={The restless engram: consolidations never end}, + author={Dudai, Yadin}, + journal={Annual review of neuroscience}, + volume={35}, + pages={227--247}, + year={2012}, + publisher={Annual Reviews} +} +@article{gentner2012analogical, + title={Analogical reasoning}, + author={Gentner, Dedre and Smith, Linsey}, + journal={Encyclopedia of human behavior}, + pages={130--136}, + year={2012}, + publisher={Elsevier Oxford, UK} +} +@article{green2012neural, + title={Neural correlates of creativity in analogical reasoning.}, + author={Green, Adam E and Kraemer, David JM and Fugelsang, Jonathan A and Gray, Jeremy R and Dunbar, Kevin N}, + journal={Journal of Experimental Psychology: Learning, Memory, and Cognition}, + volume={38}, + number={2}, + pages={264}, + year={2012}, + publisher={American Psychological Association}, + annote={Brain-based evidence has implicated the frontal pole of the brain as important for analogical mapping. Separately, cognitive research has identified semantic distance as a key determinant of the creativity of analogical mapping (i.e., more distant analogies are generally more creative). Here, we used functional magnetic resonance imaging to assess brain activity during an analogy generation task in which we varied the semantic distance of analogical mapping (as derived quantitatively from a latent semantic analysis). Data indicated that activity within an a priori region of interest in left frontopolar cortex covaried parametrically with increasing semantic distance, even after removing effects of task difficulty. Results implicate increased recruitment of frontopolar cortex as a mechanism for integrating semantically distant information to generate solutions in creative analogical reasoning. (PsycINFO Database Record (c) 2012 APA, all rights reserved)} +} +@book{gries2012science, + title={The science of programming}, + author={Gries, David}, + year={2012}, + publisher={Springer Science \& Business Media} +} +@article{huth2012continuous, + title={A continuous semantic space describes the representation of thousands of object and action categories across the human brain}, + author={Huth, Alexander G and Nishimoto, Shinji and Vu, An T and Gallant, Jack L}, + journal={Neuron}, + volume={76}, + number={6}, + pages={1210--1224}, + year={2012}, + publisher={Elsevier} +} +@article{imamoglu2012changes, + title={Changes in functional connectivity support conscious object recognition}, + author={Imamoglu, Fatma and Kahnt, Thorsten and Koch, Christof and Haynes, John-Dylan}, + journal={Neuroimage}, + volume={63}, + number={4}, + pages={1909--1917}, + year={2012}, + publisher={Elsevier} +} +@article{jeneson2012working, + title={Working memory, long-term memory, and medial temporal lobe function}, + author={Jeneson, Annette and Squire, Larry R}, + journal={Learning \& Memory}, + volume={19}, + number={1}, + pages={15--25}, + year={2012}, + publisher={Cold Spring Harbor Lab} +} +@article{lustenberger2012triangular, + title={Triangular relationship between sleep spindle activity, general cognitive ability and the efficiency of declarative learning}, + author={Lustenberger, Caroline and Maric, Angelina and D{\"u}rr, Roland and Achermann, Peter and Huber, Reto}, + year={2012} +} +@article{quiroga2012concept, + title={Concept cells: the building blocks of declarative memory functions}, + author={Quiroga, Rodrigo Quian}, + journal={Nature Reviews Neuroscience}, + volume={13}, + number={8}, + pages={587--597}, + year={2012}, + publisher={Nature Publishing Group} +} +@article{rottschy2012modelling, + title={Modelling neural correlates of working memory: a coordinate-based meta-analysis}, + author={Rottschy, Claudia and Langner, Robert and Dogan, Imis and Reetz, Kathrin and Laird, Angela R and Schulz, J{\"o}rg B and Fox, Peter T and Eickhoff, Simon B}, + journal={Neuroimage}, + volume={60}, + number={1}, + pages={830--846}, + year={2012}, + publisher={Elsevier} +} +@book{sipser2012introduction, + title={Introduction to the Theory of Computation}, + author={Sipser, Michael}, + year={2012}, + publisher={Cengage Learning} +} +@article{suthana2012memory, + title={Memory enhancement and deep-brain stimulation of the entorhinal area}, + author={Suthana, Nanthia and Haneef, Zulfi and Stern, John and Mukamel, Roy and Behnke, Eric and Knowlton, Barbara and Fried, Itzhak}, + journal={New England Journal of Medicine}, + volume={366}, + number={6}, + pages={502--510}, + year={2012}, + publisher={Mass Medical Soc}, + annote={}, +} +% +%2011 +% +@article{ahveninen2011attention, + title={Attention-driven auditory cortex short-term plasticity helps segregate relevant sounds from noise}, + author={Ahveninen, Jyrki and H{\"a}m{\"a}l{\"a}inen, Matti and J{\"a}{\"a}skel{\"a}inen, Iiro P and Ahlfors, Seppo P and Huang, Samantha and Lin, Fa-Hsuan and Raij, Tommi and Sams, Mikko and Vasios, Christos E and Belliveau, John W}, + journal={Proceedings of the National Academy of Sciences}, + volume={108}, + number={10}, + pages={4182--4187}, + year={2011}, + publisher={National Acad Sciences} +} + +@article{anderson2011cognitive, + title={Cognitive and metacognitive activity in mathematical problem solving: prefrontal and parietal patterns}, + author={Anderson, John R and Betts, Shawn and Ferris, Jennifer L and Fincham, Jon M}, + journal={Cognitive, Affective, \& Behavioral Neuroscience}, + volume={11}, + number={1}, + pages={52--67}, + year={2011}, + publisher={Springer} +} +@article{ballard2011dorsolateral, + title={Dorsolateral prefrontal cortex drives mesolimbic dopaminergic regions to initiate motivated behavior}, + author={Ballard, Ian C and Murty, Vishnu P and Carter, R McKell and MacInnes, Jeffrey J and Huettel, Scott A and Adcock, R Alison}, + journal={The Journal of Neuroscience}, + volume={31}, + number={28}, + pages={10340--10346}, + year={2011}, + publisher={Soc Neuroscience} +} +@article{chou2011sex, + title={Sex-linked white matter microstructure of the social and analytic brain}, + author={Chou, Kun-Hsien and Cheng, Yawei and Chen, I-Yun and Lin, Ching-Po and Chu, Woei-Chyn}, + journal={Neuroimage}, + volume={54}, + number={1}, + pages={725--733}, + year={2011}, + publisher={Elsevier} +} +@misc{Franklin, +author={Franklin, J. and A. Daoud}, +year={2011}, +title={Proof in mathematics: An introduction}, +howpublished={\url{web.maths.unsw.edu.au/∼jim/proofsch2.pdf}} +} +@article{lisman2011neohebbian, + title={A neoHebbian framework for episodic memory; role of dopamine-dependent late LTP}, + author={Lisman, John and Grace, Anthony A and Duzel, Emrah}, + journal={Trends in neurosciences}, + volume={34}, + number={10}, + pages={536--547}, + year={2011}, + publisher={Elsevier} +} +@article{wittmann2011behavioral, + title={Behavioral specifications of reward-associated long-term memory enhancement in humans}, + author={Wittmann, Bianca C and Dolan, Raymond J and D{\"u}zel, Emrah}, + journal={Learning \& Memory}, + volume={18}, + number={5}, + pages={296--300}, + year={2011}, + publisher={Cold Spring Harbor Lab} +} +% +%2010 +% +@article{deng2010new, + title={New neurons and new memories: how does adult hippocampal neurogenesis affect learning and memory?}, + author={Deng, Wei and Aimone, James B and Gage, Fred H}, + journal={Nature Reviews Neuroscience}, + volume={11}, + number={5}, + pages={339--350}, + year={2010}, + publisher={Nature Publishing Group} +} +@article{diekelmann2010memory, + title={The memory function of sleep}, + author={Diekelmann, Susanne and Born, Jan}, + journal={Nature Reviews Neuroscience}, + volume={11}, + number={2}, + pages={114--126}, + year={2010}, + publisher={Nature Publishing Group} +} + +@book{epp2010discrete, + title={Discrete mathematics with applications}, + author={Epp, Susanna}, + year={2010}, + publisher={Cengage Learning} +} +@article{geake2010functional, + title={Functional neural correlates of fluid and crystallized analogizing}, + author={Geake, John G and Hansen, Peter C}, + journal={Neuroimage}, + volume={49}, + number={4}, + pages={3489--3497}, + year={2010}, + publisher={Elsevier} +} +@ARTICLE{Miron-Spektor20111065, +author={Miron-Spektor, E. and Efrat-Treister, D. and Rafaeli, A. and Schwarz-Cohen, O.}, +title={Others' Anger Makes People Work Harder Not Smarter: The Effect of Observing Anger and Sarcasm on Creative and Analytic Thinking}, +journal={Journal of Applied Psychology}, +year={2011}, +volume={96}, +number={5}, +pages={1065-1075}, +doi={10.1037/a0023593}, +note={cited By 9}, +url={http://www.scopus.com/inward/record.url?eid=2-s2.0-80052845122&partnerID=40&md5=fa771b028a0b5fb543294b13c8081324}, +document_type={Article}, +source={Scopus}, +annote={not free, The authors examine whether and how observing anger influences thinking processes and problem-solving ability. In 3 studies, the authors show that participants who listened to an angry customer were more successful in solving analytic problems, but less successful in solving creative problems compared with participants who listened to an emotionally neutral customer. In Studies 2 and 3, the authors further show that observing anger communicated through sarcasm enhances complex thinking and solving of creative problems. Prevention orientation is argued to be the latent variable that mediated the effect of observing anger on complex thinking. The present findings help reconcile inconsistent findings in previous research, promote theory about the effects of observing anger and sarcasm, and contribute to understanding the effects of anger in the workplace. © 2011 American Psychological Association.} +} +@article{takeuchi2010training, + title={Training of working memory impacts structural connectivity}, + author={Takeuchi, Hikaru and Sekiguchi, Atsushi and Taki, Yasuyuki and Yokoyama, Satoru and Yomogida, Yukihito and Komuro, Nozomi and Yamanouchi, Tohru and Suzuki, Shozo and Kawashima, Ryuta}, + journal={The Journal of neuroscience}, + volume={30}, + number={9}, + pages={3297--3303}, + year={2010}, + publisher={Soc Neuroscience} +} +@article{thagard2011aha, + title={The AHA! experience: Creativity through emergent binding in neural networks}, + author={Thagard, Paul and Stewart, Terrence C}, + journal={Cognitive science}, + volume={35}, + number={1}, + pages={1--33}, + year={2011}, + publisher={Wiley Online Library} +} +@book{van2011slow, + title={Slow brain oscillations of sleep, resting state and vigilance}, + author={Van Someren, EJ}, + volume={193}, + year={2011}, + publisher={Elsevier} +} +% +%2010 +% + +@article{de2010cognitive, + title={Cognitive neuroscience meets mathematics education}, + author={De Smedt, Bert and Ansari, Daniel and Grabner, Roland H and Hannula, Minna M and Schneider, Michael and Verschaffel, Lieven}, + journal={Educational Research Review}, + volume={5}, + number={1}, + pages={97--105}, + year={2010}, + publisher={Elsevier} +} +@article{de2010traveling, + title={Traveling down the road: from cognitive neuroscience to mathematics education… and back}, + author={De Smedt, Bert and Verschaffel, Lieven}, + journal={ZDM}, + volume={42}, + number={6}, + pages={649--654}, + year={2010}, + publisher={Springer} +} +@ARTICLE{Mihov2010442, +author={Mihov, K.M. and Denzler, M. and Förster, J.}, +title={Hemispheric specialization and creative thinking: A meta-analytic review of lateralization of creativity}, +journal={Brain and Cognition}, +year={2010}, +volume={72}, +number={3}, +pages={442-448}, +doi={10.1016/j.bandc.2009.12.007}, +note={cited By 37}, +url={http://www.scopus.com/inward/record.url?eid=2-s2.0-77249168155&partnerID=40&md5=220f8fef0b7bbe4019b5b192ba05f36c}, +document_type={Article}, +source={Scopus}, +} +@article{pedreira2010responses, + title={Responses of human medial temporal lobe neurons are modulated by stimulus repetition}, + author={Pedreira, Carlos and Mormann, Florian and Kraskov, Alexander and Cerf, Moran and Fried, Itzhak and Koch, Christof and Quiroga, Rodrigo Quian}, + journal={Journal of neurophysiology}, + volume={103}, + number={1}, + pages={97--107}, + year={2010}, + publisher={Am Physiological Soc} +} +@article{shohamy2010dopamine, + title={Dopamine and adaptive memory}, + author={Shohamy, Daphna and Adcock, R Alison}, + journal={Trends in cognitive sciences}, + volume={14}, + number={10}, + pages={464--472}, + year={2010}, + publisher={Elsevier} +} +@article{tang2010short, + title={Short-term meditation induces white matter changes in the anterior cingulate}, + author={Tang, Yi-Yuan and Lu, Qilin and Geng, Xiujuan and Stein, Elliot A and Yang, Yihong and Posner, Michael I}, + journal={Proceedings of the National Academy of Sciences}, + volume={107}, + number={35}, + pages={15649--15652}, + year={2010}, + publisher={National Acad Sciences} +} +% +%2009 +% +@article{bulloch2009makes, + title={What makes relational reasoning smart? Revisiting the perceptual-to-relational shift in the development of generalization}, + author={Bulloch, Megan J and Opfer, John E}, + journal={Developmental Science}, + volume={12}, + number={1}, + pages={114--122}, + year={2009}, + publisher={Wiley Online Library} +} +@ARTICLE{Christoff20098719, +author={Christoff, K. and Gordon, A.M. and Smallwood, J. and Smith, R. and Schooler, J.W.}, +title={Experience sampling during fMRI reveals default network and executive system contributions to mind wandering}, +journal={Proceedings of the National Academy of Sciences of the United States of America}, +year={2009}, +volume={106}, +number={21}, +pages={8719-8724}, +doi={10.1073/pnas.0900234106}, +note={cited By 400}, +url={http://www.scopus.com/inward/record.url?eid=2-s2.0-66749166573&partnerID=40&md5=43ecf89e3cd33b08abd07717308b18ec}, +document_type={Article}, +source={Scopus}, +} +@article{darling2009research, + title={Research review/teacher learning: What matters}, + author={Darling-Hammond, Linda and Richardson, Nikole}, + journal={Educational leadership}, + volume={66}, + number={5}, + pages={46--53}, + year={2009} +} +@article{keller2009gender, + title={Gender differences in the functional and structural neuroanatomy of mathematical cognition}, + author={Keller, Katherine and Menon, Vinod}, + journal={Neuroimage}, + volume={47}, + number={1}, + pages={342--352}, + year={2009}, + publisher={Elsevier} +} +@article{kitamura2009adult, + title={Adult neurogenesis modulates the hippocampus-dependent period of associative fear memory}, + author={Kitamura, Takashi and Saitoh, Yoshito and Takashima, Noriko and Murayama, Akiko and Niibori, Yosuke and Ageta, Hiroshi and Sekiguchi, Mariko and Sugiyama, Hiroyuki and Inokuchi, Kaoru}, + journal={Cell}, + volume={139}, + number={4}, + pages={814--827}, + year={2009}, + publisher={Elsevier} +} +@article{kowatari2009neural, + title={Neural networks involved in artistic creativity}, + author={Kowatari, Yasuyuki and Lee, Seung Hee and Yamamura, Hiromi and Nagamori, Yusuke and Levy, Pierre and Yamane, Shigeru and Yamamoto, Miyuki}, + journal={Human brain mapping}, + volume={30}, + number={5}, + pages={1678--1690}, + year={2009}, + publisher={Wiley Online Library} +} +@article{krebs2009personality, + title={Personality traits are differentially associated with patterns of reward and novelty processing in the human substantia nigra/ventral tegmental area}, + author={Krebs, Ruth M and Schott, Bj{\"o}rn H and D{\"u}zel, Emrah}, + journal={Biological psychiatry}, + volume={65}, + number={2}, + pages={103--110}, + year={2009}, + publisher={Elsevier} +} +@article{molle2009hippocampus, + title={Hippocampus whispering in deep sleep to prefrontal cortex—for good memories?}, + author={M{\"o}lle, Matthias and Born, Jan}, + journal={Neuron}, + volume={61}, + number={4}, + pages={496--498}, + year={2009}, + publisher={Elsevier} +} +@article{nishida2009rem, + title={REM sleep, prefrontal theta, and the consolidation of human emotional memory}, + author={Nishida, Masaki and Pearsall, Jori and Buckner, Randy L and Walker, Matthew P}, + journal={Cerebral Cortex}, + volume={19}, + number={5}, + pages={1158--1166}, + year={2009}, + publisher={Oxford Univ Press} +} +@article{russoniello2009effectiveness, + title={The effectiveness of casual video games in improving mood and decreasing stress}, + author={Russoniello, Carmen V and O’Brien, Kevin and Parks, Jennifer M}, + journal={Journal of Cyber Therapy and Rehabilitation}, + volume={2}, + number={1}, + pages={53--66}, + year={2009} +} +@article{trouche2009recruitment, + title={Recruitment of adult-generated neurons into functional hippocampal networks contributes to updating and strengthening of spatial memory}, + author={Trouche, St{\'e}phanie and Bontempi, Bruno and Roullet, Pascal and Rampon, Claire}, + journal={Proceedings of the National Academy of Sciences}, + volume={106}, + number={14}, + pages={5919--5924}, + year={2009}, + publisher={National Acad Sciences} +} +@article{zamarian2009neuroscience, + title={Neuroscience of learning arithmetic—evidence from brain imaging studies}, + author={Zamarian, L and Ischebeck, A and Delazer, M}, + journal={Neuroscience \& Biobehavioral Reviews}, + volume={33}, + number={6}, + pages={909--925}, + year={2009}, + publisher={Elsevier} +} +% +%2008 +% +@article{abraham2008thinking, + title={Thinking about the future versus the past in personal and non-personal contexts}, + author={Abraham, Anna and Schubotz, Ricarda I and von Cramon, D Yves}, + journal={Brain research}, + volume={1233}, + pages={106--119}, + year={2008}, + publisher={Elsevier} +} +@article{fereday2008demonstrating, + title={Demonstrating rigor using thematic analysis: A hybrid approach of inductive and deductive coding and theme development}, + author={Fereday, Jennifer and Muir-Cochrane, Eimear}, + journal={International journal of qualitative methods}, + volume={5}, + number={1}, + pages={80--92}, + year={2008} +} +@article{fenker2008novel, + title={Novel scenes improve recollection and recall of words}, + author={Fenker, Daniela B and Frey, Julietta U and Schuetze, Hartmut and Heipertz, Dorothee and Heinze, Hans-Jochen and Duzel, Emrah}, + journal={Journal of cognitive neuroscience}, + volume={20}, + number={7}, + pages={1250--1265}, + year={2008}, + publisher={MIT Press} +} +@article{frey2008synaptic, + title={‘Synaptic tagging’and ‘cross-tagging’and related associative reinforcement processes of functional plasticity as the cellular basis for memory formation}, + author={Frey, Sabine and Frey, Julietta U}, + journal={Progress in brain research}, + volume={169}, + pages={117--143}, + year={2008}, + publisher={Elsevier} +} +@article{glaser2008conceptualization, + title={Conceptualization: On theory and theorizing using grounded theory}, + author={Glaser, Barney G}, + journal={International Journal of Qualitative Methods}, + volume={1}, + number={2}, + pages={23--38}, + year={2008} +} +@article{jacobs2008developing, + title={On developing a rich conception of variable}, + author={Jacobs, Sally and Trigueros, Maria}, + journal={Making the connection: Research and teaching in undergraduate mathematics education}, + number={73}, + pages={1}, + year={2008}, + publisher={MAA} +} +@article{karpicke2008critical, + title={The critical importance of retrieval for learning}, + author={Karpicke, Jeffrey D and Roediger, Henry L}, + journal={science}, + volume={319}, + number={5865}, + pages={966--968}, + year={2008}, + publisher={American Association for the Advancement of Science} +} +@article{polyn2008memory, + title={Memory search and the neural representation of context}, + author={Polyn, Sean M and Kahana, Michael J}, + journal={Trends in cognitive sciences}, + volume={12}, + number={1}, + pages={24--30}, + year={2008}, + publisher={Elsevier} +} +@article{talamini2008sleep, + title={Sleep directly following learning benefits consolidation of spatial associative memory}, + author={Talamini, Lucia M and Nieuwenhuis, Ingrid LC and Takashima, Atsuko and Jensen, Ole}, + journal={Learning \& Memory}, + volume={15}, + number={4}, + pages={233--237}, + year={2008}, + publisher={Cold Spring Harbor Lab} +} +@article{tall2008transition, + title={The transition to formal thinking in mathematics}, + author={Tall, David}, + journal={Mathematics Education Research Journal}, + volume={20}, + number={2}, + pages={5--24}, + year={2008}, + publisher={Springer} +} +@article{toni2008neurons, + title={Neurons born in the adult dentate gyrus form functional synapses with target cells}, + author={Toni, Nicolas and Laplagne, Diego A and Zhao, Chunmei and Lombardi, Gabriela and Ribak, Charles E and Gage, Fred H and Schinder, Alejandro F}, + journal={Nature neuroscience}, + volume={11}, + number={8}, + pages={901--907}, + year={2008}, + publisher={Nature Publishing Group} +} +@article{varma2008should, + title={How should educational neuroscience conceptualise the relation between cognition and brain function? Mathematical reasoning as a network process}, + author={Varma, Sashank and Schwartz, Daniel L}, + journal={Educational Research}, + volume={50}, + number={2}, + pages={149--161}, + year={2008}, + publisher={Taylor \& Francis} +} +@article{wagner2008memory, + title={Memory consolidation during sleep: Interactive effects of sleep stages and HPA regulation: Review}, + author={Wagner, Ullrich and Born, Jan}, + journal={Stress}, + volume={11}, + number={1}, + pages={28--41}, + year={2008}, + publisher={Taylor \& Francis} +} +@article{zacks2008neuroimaging, + title={Neuroimaging studies of mental rotation: a meta-analysis and review}, + author={Zacks, Jeffrey M}, + journal={Cognitive Neuroscience, Journal of}, + volume={20}, + number={1}, + pages={1--19}, + year={2008}, + publisher={MIT Press} +} +% +%2007 +% +@article{bridges2007did, + title={Did Brouwer really believe that?}, + author={Bridges, Douglas S}, + howpublished={\url{http://www.math.canterbury.ac.nz/\$ d.bridges/les/Brouwer.pdf}}, + year={2007} +} +@article{day2007nonintentional, + title={Nonintentional analogical inference in text comprehension}, + author={Day, Samuel B and Gentner, Dedre}, + journal={Memory \& cognition}, + volume={35}, + number={1}, + pages={39--49}, + year={2007}, + publisher={Springer} +} +@article{decety2007role, + title={The role of the right temporoparietal junction in social interaction: how low-level computational processes contribute to meta-cognition}, + author={Decety, Jean and Lamm, Claus}, + journal={The Neuroscientist}, + year={2007}, + publisher={Sage Publications} +} +@article{ellenbogen2007human, + title={Human relational memory requires time and sleep}, + author={Ellenbogen, Jeffrey M and Hu, Peter T and Payne, Jessica D and Titone, Debra and Walker, Matthew P}, + journal={Proceedings of the National Academy of Sciences}, + volume={104}, + number={18}, + pages={7723--7728}, + year={2007}, + publisher={National Acad Sciences} +} +@article{ji2007coordinated, + title={Coordinated memory replay in the visual cortex and hippocampus during sleep}, + author={Ji, Daoyun and Wilson, Matthew A}, + journal={Nature neuroscience}, + volume={10}, + number={1}, + pages={100--107}, + year={2007}, + publisher={Nature Publishing Group} +} +@article{kee2007preferential, + title={Preferential incorporation of adult-generated granule cells into spatial memory networks in the dentate gyrus}, + author={Kee, Nohjin and Teixeira, C{\'a}tia M and Wang, Afra H and Frankland, Paul W}, + journal={Nature neuroscience}, + volume={10}, + number={3}, + pages={355--362}, + year={2007}, + publisher={Nature Publishing Group} +} +@article{kesner2007behavioral, + title={A behavioral analysis of dentate gyrus function}, + author={Kesner, Raymond P}, + journal={Progress in brain research}, + volume={163}, + pages={567--576}, + year={2007}, + publisher={Elsevier} +} +@article{lee2007strategic, + title={Strategic differences in algebraic problem solving: Neuroanatomical correlates}, + author={Lee, Kerry and Lim, Zee Ying and Yeong, Stephanie HM and Ng, Swee Fong and Venkatraman, Vinod and Chee, Michael WL}, + journal={Brain research}, + volume={1155}, + pages={163--171}, + year={2007}, + publisher={Elsevier} +} +@article{marshall2007contribution, + title={The contribution of sleep to hippocampus-dependent memory consolidation}, + author={Marshall, Lisa and Born, Jan}, + journal={Trends in cognitive sciences}, + volume={11}, + number={10}, + pages={442--450}, + year={2007}, + publisher={Elsevier} +} +@article{ribeiro2007novel, + title={Novel experience induces persistent sleep-dependent plasticity in the cortex but not in the hippocampus}, + author={Ribeiro, Sidarta and Shi, Xinwu and Engelhard, Matthew and Zhou, Yi and Zhang, Hao and Gervasoni, Damien and Lin, Shi-Chieh and Wada, Kazuhiro and Lemos, Nelson AM and Nicolelis, Miguel AL}, + journal={Frontiers in Neuroscience}, + volume={1}, + number={1}, + pages={43}, + year={2007}, + publisher={Frontiers Research Foundation} +} +@article{rosken2007integrating, + title={Integrating intuition: The role of concept image and concept definition for students' learning of integral calculus}, + author={R{\"o}sken, Bettina and Rolka, Katrin}, + journal={The Montana Mathematics Enthusiast}, + volume={3}, + pages={181--204}, + year={2007} +} +@article{wittmann2007anticipation, + title={Anticipation of novelty recruits reward system and hippocampus while promoting recollection}, + author={Wittmann, Bianca C and Bunzeck, Nico and Dolan, Raymond J and D{\"u}zel, Emrah}, + journal={Neuroimage}, + volume={38}, + number={1}, + pages={194--202}, + year={2007}, + publisher={Elsevier} +} +% +%2006 +% +@article{adcock2006reward, + title={Reward-motivated learning: mesolimbic activation precedes memory formation}, + author={Adcock, R Alison and Thangavel, Arul and Whitfield-Gabrieli, Susan and Knutson, Brian and Gabrieli, John DE}, + journal={Neuron}, + volume={50}, + number={3}, + pages={507--517}, + year={2006}, + publisher={Elsevier} +} +@article{braun2006using, + title={Using thematic analysis in psychology}, + author={Braun, Virginia and Clarke, Victoria}, + journal={Qualitative research in psychology}, + volume={3}, + number={2}, + pages={77--101}, + year={2006}, + publisher={Taylor \& Francis} +} +@article{gais2006sleep, + title={Sleep after learning aids memory recall}, + author={Gais, Steffen and Lucas, Brian and Born, Jan}, + journal={Learning \& Memory}, + volume={13}, + number={3}, + pages={259--262}, + year={2006}, + publisher={Cold Spring Harbor Lab} +} +@article{hasselmo2006role, + title={The role of acetylcholine in learning and memory}, + author={Hasselmo, Michael E}, + journal={Current opinion in neurobiology}, + volume={16}, + number={6}, + pages={710--715}, + year={2006}, + publisher={Elsevier} +} +@book{viete2006analytic, + title={The analytic art}, + author={Vi{\`e}te, Fran{\c{c}}ois and Witmer, T Richard}, + year={2006}, + publisher={Courier Corporation} +} +@article{wagner2006brief, + title={Brief sleep after learning keeps emotional memories alive for years}, + author={Wagner, Ullrich and Hallschmid, Manfred and Rasch, Bj{\"o}rn and Born, Jan}, + journal={Biological psychiatry}, + volume={60}, + number={7}, + pages={788--790}, + year={2006}, + publisher={Elsevier} +} +% +%2005 +% +@article{frankland2005organization, + title={The organization of recent and remote memories}, + author={Frankland, Paul W and Bontempi, Bruno}, + journal={Nature Reviews Neuroscience}, + volume={6}, + number={2}, + pages={119--130}, + year={2005}, + publisher={Nature Publishing Group} +} +@article{kennedy2005association, + title={The association between students' use of an electronic voting system and their learning outcomes}, + author={Kennedy, Gregor E and Cutts, Quintin I}, + journal={Journal of Computer Assisted Learning}, + volume={21}, + number={4}, + pages={260--268}, + year={2005}, + publisher={Wiley Online Library} +} +@article{lisman2005hippocampal, + title={The hippocampal-VTA loop: controlling the entry of information into long-term memory}, + author={Lisman, John E and Grace, Anthony A}, + journal={Neuron}, + volume={46}, + number={5}, + pages={703--713}, + year={2005}, + publisher={Elsevier} +} + +@article{owen2005n, + title={N-back working memory paradigm: A meta-analysis of normative functional neuroimaging studies}, + author={Owen, Adrian M and McMillan, Kathryn M and Laird, Angela R and Bullmore, Ed}, + journal={Human brain mapping}, + volume={25}, + number={1}, + pages={46--59}, + year={2005}, + publisher={Wiley Online Library} +} +@article{quiroga2005invariant, + title={Invariant visual representation by single neurons in the human brain}, + author={Quiroga, R Quian and Reddy, Leila and Kreiman, Gabriel and Koch, Christof and Fried, Itzhak}, + journal={Nature}, + volume={435}, + number={7045}, + pages={1102--1107}, + year={2005}, + publisher={Nature Publishing Group} +} +@article{sarter2005unraveling, + title={Unraveling the attentional functions of cortical cholinergic inputs: interactions between signal-driven and cognitive modulation of signal detection}, + author={Sarter, Martin and Hasselmo, Michael E and Bruno, John P and Givens, Ben}, + journal={Brain Research Reviews}, + volume={48}, + number={1}, + pages={98--111}, + year={2005}, + publisher={Elsevier} +} +@article{wittmann2005reward, + title={Reward-related FMRI activation of dopaminergic midbrain is associated with enhanced hippocampus-dependent long-term memory formation}, + author={Wittmann, Bianca C and Schott, Bj{\"o}rn H and Guderian, Sebastian and Frey, Julietta U and Heinze, Hans-Jochen and D{\"u}zel, Emrah}, + journal={Neuron}, + volume={45}, + number={3}, + pages={459--467}, + year={2005}, + publisher={Elsevier} +} +% +%2004 +% +@article{hasselmo2004high, + title={High acetylcholine levels set circuit dynamics for attention and encoding and low acetylcholine levels set dynamics for consolidation}, + author={Hasselmo, Michael E and McGaughy, Jill}, + journal={Progress in brain research}, + volume={145}, + pages={207--231}, + year={2004}, + publisher={Elsevier} +} +@article{kishiyama2004restorff, + title={The von Restorff effect in amnesia: The contribution of the hippocampal system to novelty-related memory enhancements}, + author={Kishiyama, Mark M and Yonelinas, Andy P and Lazzara, MM}, + journal={Journal of cognitive neuroscience}, + volume={16}, + number={1}, + pages={15--23}, + year={2004}, + publisher={MIT Press} +} +@article{kuriyama2004sleep, + title={Sleep-dependent learning and motor-skill complexity}, + author={Kuriyama, Kenichi and Stickgold, Robert and Walker, Matthew P}, + journal={Learning \& Memory}, + volume={11}, + number={6}, + pages={705--713}, + year={2004}, + publisher={Cold Spring Harbor Lab} +} +@article{or2004cognitive, + title={Cognitive activities of abstraction in object orientation: an empirical study}, + author={Or-Bach, Rachel and Lavy, Ilana}, + journal={ACM SIGCSE Bulletin}, + volume={36}, + number={2}, + pages={82--86}, + year={2004}, + publisher={ACM} +} +@article{prince2004does, + title={Does active learning work? A review of the research}, + author={Prince, Michael}, + journal={JOURNAL OF ENGINEERING EDUCATION-WASHINGTON-}, + volume={93}, + pages={223--232}, + year={2004}, + publisher={AMERICAN SOCIETY FOR ENGINEERING EDUCATION} +} +@article{robertson2004awareness, + title={Awareness modifies the skill-learning benefits of sleep}, + author={Robertson, Edwin M and Pascual-Leone, Alvaro and Press, Daniel Z}, + journal={Current Biology}, + volume={14}, + number={3}, + pages={208--212}, + year={2004}, + publisher={Elsevier} +} +@article{sohn2004behavioral, + title={Behavioral equivalence, but not neural equivalence—neural evidence of alternative strategies in mathematical thinking}, + author={Sohn, Myeong-Ho and Goode, Adam and Koedinger, Kenneth R and Stenger, V Andrew and Fissell, Kate and Carter, Cameron S and Anderson, John R}, + journal={Nature neuroscience}, + volume={7}, + number={11}, + pages={1193--1194}, + year={2004}, + publisher={Nature Publishing Group} +} +@article{wagner2004sleep, + title={Sleep inspires insight}, + author={Wagner, Ullrich and Gais, Steffen and Haider, Hilde and Verleger, Rolf and Born, Jan}, + journal={Nature}, + volume={427}, + number={6972}, + pages={352--355}, + year={2004}, + publisher={Nature Publishing Group} +} + +% +%2003 +% +@article{anderson2003information, + title={An information-processing model of the BOLD response in symbol manipulation tasks}, + author={Anderson, John R and Qin, Yulin and Sohn, Myeong-Ho and Stenger, V Andrew and Carter, Cameron S}, + journal={Psychonomic Bulletin \& Review}, + volume={10}, + number={2}, + pages={241--261}, + year={2003}, + publisher={Springer} +} +@article{chambers2003developmental, + title={Developmental neurocircuitry of motivation in adolescence: a critical period of addiction vulnerability}, + author={Chambers, R Andrew and Taylor, Jane R and Potenza, Marc N}, + journal={American Journal of Psychiatry}, + year={2003}, + publisher={Am Psychiatric Assoc} +} + + +@article{knutson2003region, + title={A region of mesial prefrontal cortex tracks monetarily rewarding outcomes: characterization with rapid event-related fMRI}, + author={Knutson, Brian and Fong, Grace W and Bennett, Shannon M and Adams, Charles M and Hommer, Daniel}, + journal={Neuroimage}, + volume={18}, + number={2}, + pages={263--272}, + year={2003}, + publisher={Elsevier} +} +@book{loewenberg2003mathematical, + title={Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education}, + author={Loewenberg, Deborah and others}, + year={2003}, + publisher={Rand Corporation} +} +@book{rosen2003, + title={Discrete Mathematics and Its Applications, 5th ed.}, + author={Rosen, Kenneth H}, + year={2003}, + publisher={McGraw Hill} +} +@article{schendan2003fmri, + title={An FMRI study of the role of the medial temporal lobe in implicit and explicit sequence learning}, + author={Schendan, Haline E and Searl, Meghan M and Melrose, Rebecca J and Stern, Chantal E}, + journal={Neuron}, + volume={37}, + number={6}, + pages={1013--1025}, + year={2003}, + publisher={Elsevier} +} +@article{sederberg2003theta, + title={Theta and gamma oscillations during encoding predict subsequent recall}, + author={Sederberg, Per B and Kahana, Michael J and Howard, Marc W and Donner, Elizabeth J and Madsen, Joseph R}, + journal={The Journal of Neuroscience}, + volume={23}, + number={34}, + pages={10809--10814}, + year={2003}, + publisher={Soc Neuroscience} +} +@article{walker2003dissociable, + title={Dissociable stages of human memory consolidation and reconsolidation}, + author={Walker, Matthew P and Brakefield, Tiffany and Hobson, J Allan and Stickgold, Robert}, + journal={Nature}, + volume={425}, + number={6958}, + pages={616--620}, + year={2003}, + publisher={Nature Publishing Group} +} +@article{zysset2003functional, + title={Functional specialization within the anterior medial prefrontal cortex: a functional magnetic resonance imaging study with human subjects}, + author={Zysset, Stefan and Huber, Oswald and Samson, Andrea and Ferstl, Evelyn C and von Cramon, D Yves}, + journal={Neuroscience letters}, + volume={335}, + number={3}, + pages={183--186}, + year={2003}, + publisher={Elsevier} +} +% +%2002 +% +@incollection{dubinsky2002apos, + title={APOS: A constructivist theory of learning in undergraduate mathematics education research}, + author={Dubinsky, Ed and McDonald, Michael A}, + booktitle={The teaching and learning of mathematics at university level}, + pages={275--282}, + year={2002}, + publisher={Springer} +} +@article{ribeiro2002induction, + title={Induction of hippocampal long-term potentiation during waking leads to increased extrahippocampal zif-268 expression during ensuing rapid-eye-movement sleep}, + author={Ribeiro, Sidarta and Mello, Claudio V and Velho, Tarciso and Gardner, Timothy J and Jarvis, Erich D and Pavlides, Constantine}, + journal={The Journal of Neuroscience}, + volume={22}, + number={24}, + pages={10914--10923}, + year={2002}, + publisher={Soc Neuroscience} +} +% +%2001 +% +@article{paller2002observing, + title={Observing the transformation of experience into memory}, + author={Paller, Ken A and Wagner, Anthony D}, + journal={Trends in cognitive sciences}, + volume={6}, + number={2}, + pages={93--102}, + year={2002}, + publisher={Elsevier} +} +@inproceedings{rasslan2002definitions, + title={Definitions and images for the definite integral concept}, + author={Rasslan, Shaker and Tall, David}, + booktitle={PME CONFERENCE}, + volume={4}, + pages={4--089}, + year={2002} +} +@article{tall2001symbols, + title={Symbols and the bifurcation between procedural and conceptual thinking}, + author={Tall, David and Gray, Eddie and Ali, Maselan Bin and Crowley, Lillie and DeMarois, Phil and McGowen, Mercedes and Pitta, Demetra and Pinto, Marcia and Thomas, Michael and Yusof, Yudariah}, + journal={Canadian Journal of Math, Science \& Technology Education}, + volume={1}, + number={1}, + pages={81--104}, + year={2001}, + publisher={Taylor \& Francis} +} + +% +%2001 +% +@article{blood2001intensely, + title={Intensely pleasurable responses to music correlate with activity in brain regions implicated in reward and emotion}, + author={Blood, Anne J and Zatorre, Robert J}, + journal={Proceedings of the National Academy of Sciences}, + volume={98}, + number={20}, + pages={11818--11823}, + year={2001}, + publisher={National Acad Sciences} +} +@article{fletcher2001frontal, + title={Frontal lobes and human memory}, + author={Fletcher, PC and Henson, R Nx˙ A}, + journal={Brain}, + volume={124}, + number={5}, + pages={849--881}, + year={2001}, + publisher={Oxford Univ Press} +} +@article{hyman2001addiction, + title={Addiction and the brain: the neurobiology of compulsion and its persistence}, + author={Hyman, Steven E and Malenka, Robert C}, + journal={Nature reviews neuroscience}, + volume={2}, + number={10}, + pages={695--703}, + year={2001}, + publisher={Nature Publishing Group} +} +@article{knutson2001anticipation, + title={Anticipation of increasing monetary reward selectively recruits nucleus accumbens}, + author={Knutson, Brian and Adams, Charles M and Fong, Grace W and Hommer, Daniel}, + journal={J Neurosci}, + volume={21}, + number={16}, + pages={RC159}, + year={2001} +} +@article{lisman2001storage, + title={Storage, recall, and novelty detection of sequences by the hippocampus: elaborating on the SOCRATIC model to account for normal and aberrant effects of dopamine}, + author={Lisman, John E and Otmakhova, Nonna A}, + journal={Hippocampus}, + volume={11}, + number={5}, + pages={551--568}, + year={2001}, + publisher={Wiley Online Library} +} +@article{waelti2001dopamine, + title={Dopamine responses comply with basic assumptions of formal learning theory}, + author={Waelti, Pascale and Dickinson, Anthony and Schultz, Wolfram}, + journal={Nature}, + volume={412}, + number={6842}, + pages={43--48}, + year={2001}, + publisher={Nature Publishing Group} +} +% +%2000 +% +@article{bower2000postscript, + title={Postscript: integrating themes on discourse and design}, + author={Bower, J}, + journal={Symbolizing and Communicating in Mathematics Classrooms. Perspectives on Discourse, Tools, and Instructional Design, Erlbaum, Mahwah}, + pages={385--399}, + year={2000} +} +@article{bransford2000designs, + title={Designs for environments that invite and sustain mathematical thinking}, + author={Bransford, John and Zech, Linda and Schwarz, D and Barron, Bngid and Vye, Nancy}, + journal={Symbolizing and Communicating in Mathematics Classrooms}, + pages={275--324}, + year={2000} +} +@article{carlsson2000neurobiology, + title={On the neurobiology of creativity. Differences in frontal activity between high and low creative subjects}, + author={Carlsson, Ingegerd and Wendt, Peter E and Risberg, Jarl}, + journal={Neuropsychologia}, + volume={38}, + number={6}, + pages={873--885}, + year={2000}, + publisher={Elsevier} +} +@article{dorfler2000means, + title={Means for meaning}, + author={D{\"o}rfler, Willi}, + journal={Symbolizing and communicating in mathematics classrooms}, + pages={99--131}, + year={2000} +} +@article{dunbar2000scientists, + title={How scientists think in the real world: Implications for science education}, + author={Dunbar, Kevin}, + journal={Journal of Applied Developmental Psychology}, + volume={21}, + number={1}, + pages={49--58}, + year={2000}, + publisher={Elsevier} +} +@article{lehrer2000inter, + title={The inter-related development of inscriptions and conceptual understanding}, + author={Lehrer, Richard and Schauble, Leona and Carpenter, Susan and Penner, David}, + journal={Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design}, + pages={325--360}, + year={2000} +} +@article{lesh2000symbolizing, + title={Symbolizing, communicating, and mathematizing: Key components of models and modeling}, + author={Lesh, Richard and Doerr, Helen M}, + journal={Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design}, + pages={361--384}, + year={2000} +} +@article{maquet2000experience, + title={Experience-dependent changes in cerebral activation during human REM sleep}, + author={Maquet, Pierre and Laureys, Steven and Peigneux, Philippe and Fuchs, Sonia and Petiau, Christophe and Phillips, Christophe and Aerts, Joel and Del Fiore, Guy and Degueldre, Christian and Meulemans, Thierry and others}, + journal={Nature neuroscience}, + volume={3}, + number={8}, + pages={831--836}, + year={2000}, + publisher={Nature Publishing Group} +} +@article{martin2000synaptic, + title={Synaptic plasticity and memory: an evaluation of the hypothesis}, + author={Martin, SJ and Grimwood, PD and Morris, RGM}, + journal={Annual review of neuroscience}, + volume={23}, + number={1}, + pages={649--711}, + year={2000}, + publisher={Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA} +} +@article{nemirovskymonk, + title={Monk, S.(2000):—If you look at it the other way…“An exploration into the Nature of Symbolizing}, + author={Nemirovsky, R}, + journal={Symbolizing and Communicating in Mathematics Classrooms. Hillsdale NJ: Lawrence Erlbaum Associates} +} +@article{schultz2000neuronal, + title={Neuronal coding of prediction errors}, + author={Schultz, Wolfram and Dickinson, Anthony}, + journal={Annual review of neuroscience}, + volume={23}, + number={1}, + pages={473--500}, + year={2000}, + publisher={Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA} +} +@book{squire2000memory, + title={Memory: From mind to molecules}, + author={Squire, Larry R and Kandel, Eric R}, + year={2000}, + publisher={Macmillan} +} +@article{stickgold2000visual, + title={Visual discrimination learning requires sleep after training}, + author={Stickgold, Robert and James, LaTanya and Hobson, J Allan}, + journal={Nature neuroscience}, + volume={3}, + number={12}, + pages={1237--1238}, + year={2000}, + publisher={Nature Publishing Group} +} +@book{valiant2000circuits, + title={Circuits of the Mind}, + author={Valiant, Leslie G}, + year={2000}, + publisher={Oxford University Press} +} +@article{van2000appropriation, + title={The appropriation of mathematical symbols: A psychosemiotic approach to mathematics learning}, + author={van Oers, Bert}, + journal={Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design}, + pages={133--176}, + year={2000} +} +% +%1999 +% +@article{gurden1999integrity, + title={Integrity of the mesocortical dopaminergic system is necessary for complete expression of in vivo hippocampal--prefrontal cortex long-term potentiation}, + author={Gurden, H and Tassin, J-P and Jay, TM}, + journal={Neuroscience}, + volume={94}, + number={4}, + pages={1019--1027}, + year={1999}, + publisher={Elsevier} +} +@article{horger1999enhancement, + title={Enhancement of locomotor activity and conditioned reward to cocaine by brain-derived neurotrophic factor}, + author={Horger, Brian A and Iyasere, Christiana A and Berhow, Melissa T and Messer, Chad J and Nestler, Eric J and Taylor, Jane R}, + journal={The Journal of neuroscience}, + volume={19}, + number={10}, + pages={4110--4122}, + year={1999}, + publisher={Soc Neuroscience} +} +@article{kendall1999axial, + title={Axial coding and the grounded theory controversy}, + author={Kendall, Judy}, + journal={Western journal of nursing research}, + volume={21}, + number={6}, + pages={743--757}, + year={1999}, + publisher={Sage Publications} +} + +@article{robinson1999alterations, + title={Alterations in the morphology of dendrites and dendritic spines in the nucleus accumbens and prefrontal cortex following repeated treatment with amphetamine or cocaine}, + author={Robinson, Terry E and Kolb, Bryan}, + journal={European journal of neuroscience}, + volume={11}, + number={5}, + pages={1598--1604}, + year={1999}, + publisher={Wiley Online Library} +} +% +%1998 +% +@article{arcavi1998teaching, + title={Teaching mathematical problem solving: An analysis of an emergent classroom community}, + author={Arcavi, Abraham and Kessel, Cathy and Meira, Luciano and Smith, John P}, + journal={Research in collegiate mathematics education, III}, + volume={7}, + pages={1--70}, + year={1998} +} +@article{baranchik1998supplementary, + title={Supplementary methods for assessing student performance on a standardized test in elementary algebra}, + author={Baranchik, ALVIN and Cherkas, BARRY}, + journal={Research in Collegiate Mathematics Education}, + volume={3}, + pages={216--233}, + year={1998} +} +@book{black1998inside, + title={Inside the black box: Raising standards through classroom assessment}, + author={Black, Paul and Wiliam, Dylan}, + year={1998}, + publisher={Granada Learning} +} +@book{boyatzis1998transforming, + title={Transforming qualitative information: Thematic analysis and code development}, + author={Boyatzis, Richard E}, + year={1998}, + publisher={Sage} +} +@inproceedings{carlson1998cross, + title={A cross-sectional investigation of the development of the function concept}, + author={Carlson, Marilyn P}, + booktitle={Research in Collegiate Mathematics Education III, Conference Board of the Mathematical Sciences, Issues in Mathematics Education}, + volume={7}, + number={2}, + pages={114--162}, + year={1998} +} +@article{rattermann1998more, + title={More evidence for a relational shift in the development of analogy: Children's performance on a causal-mapping task}, + author={Rattermann, Mary Jo and Gentner, Dedre}, + journal={Cognitive Development}, + volume={13}, + number={4}, + pages={453--478}, + year={1998}, + publisher={Elsevier} +} +@article{gibson1998students, + title={Students’ use of diagrams to develop proofs in an introductory analysis course}, + author={Gibson, DAVID}, + journal={CBMS issues in mathematics education}, + volume={7}, + pages={284--307}, + year={1998} +} +@book{kaput1998research, + title={Research in Collegiate Mathematics Education III}, + author={Kaput, James J and Schoenfeld, Alan H and Dubinsky, Ed}, + volume={4}, + year={1998}, + publisher={American Mathematical Soc.} +} +@article{meel1998honors, + title={Honors students’ calculus understandings: Comparing Calculus\&Mathematica and traditional calculus students}, + author={Meel, DAVID E}, + journal={CBMS Issues in Mathematics Education}, + volume={7}, + pages={163--215}, + year={1998} +} +@article{parker1998restorff, + title={The von Restorff effect in visual object recognition memory in humans and monkeys: The role of frontal/perirhinal interaction}, + author={Parker, Amanda and Wilding, Edward and Akerman, Colin}, + journal={Journal of Cognitive Neuroscience}, + volume={10}, + number={6}, + pages={691--703}, + year={1998}, + publisher={MIT Press} +} +@article{santos1998instructional, + title={Instructional qualities of a successful mathematical problem-solving class∗}, + author={Santos-Trigo, Manuel}, + journal={International Journal of Mathematical Education in Science and Technology}, + volume={29}, + number={5}, + pages={631--646}, + year={1998}, + publisher={Taylor \& Francis} +} +@article{schacter1998cognitive, + title={The cognitive neuroscience of constructive memory}, + author={Schacter, Daniel L and Norman, Kenneth A and Koutstaal, Wilma}, + journal={Annual review of psychology}, + volume={49}, + number={1}, + pages={289--318}, + year={1998}, + publisher={Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA} +} +@article{schoenfeld1998reflections, + title={Reflections on a course in mathematical problem solving}, + author={Schoenfeld, Alan H}, + journal={Research in collegiate mathematics education III}, + pages={81--113}, + year={1998}, + publisher={American Mathematical Society Providence, RI} +} +% +%1997 +% +@article{aspinwall1997uncontrollable, + title={Uncontrollable mental imagery: Graphical connections between a function and its derivative}, + author={Aspinwall, Leslie and Shaw, Kenneth L and Presmeg, Norma C}, + journal={Educational Studies in Mathematics}, + volume={33}, + number={3}, + pages={301--317}, + year={1997}, + publisher={Springer} +} +@article{frey1997synaptic, + title={Synaptic tagging and long-term potentiation}, + author={Frey, Uwe and Morris, Richard GM}, + journal={Nature}, + volume={385}, + number={6616}, + pages={533--536}, + year={1997} +} +@article{masterman1997frontal, + title={Frontal-subcortical circuits: the anatomic basis of executive, social and motivated behaviors}, + author={Masterman, Donna L and Cummings, Jeffrey L}, + journal={Journal of Psychopharmacology}, + volume={11}, + number={2}, + pages={107--114}, + year={1997}, + publisher={Sage Publications} +} +@article{mulder1997short, + title={Short-and Long-term Plasticity of the Hippocampus to Nucleus Accumbens and Prefrontal Cortex Pathways in the Rat, In Vivo}, + author={Mulder, AB and Arts, MPM and Silva, FH}, + journal={European Journal of Neuroscience}, + volume={9}, + number={8}, + pages={1603--1611}, + year={1997}, + publisher={Wiley Online Library} +} +@article{rota1997phenomenology, + title={The phenomenology of mathematical beauty}, + author={Rota, Gian-Carlo}, + journal={Synthese}, + volume={111}, + number={2}, + pages={171--182}, + year={1997}, + publisher={Springer} +} + +% +%1996 +% +@article{almstrum1996investigating, + title={Investigating student difficulties with mathematical logic}, + author={Almstrum, Vicki L}, + journal={Teaching and Learning Formal Methods}, + pages={131--160}, + year={1996}, + publisher={Academic Press, Orlando, FL} +} +@book{berliner1996handbook, + title={Handbook of educational psychology}, + author={Berliner, David C and Calfee, Robert C}, + year={1996}, + publisher={Routledge}, + annote={recommended by Schoenfeld} +} +@article{fink1996brain, + title={Where in the brain does visual attention select the forest and the trees?}, + author={Fink, Gereon R and Halligan, Peter W and Marshall, John C and Frith, Chris D and Frackowiak, RSJ and Dolan, Raymond J}, + year={1996}, + publisher={Nature Publishing Group} +} +@article{klimesch1996theta, + title={Theta band power in the human scalp EEG and the encoding of new information.}, + author={Klimesch, W and Doppelmayr, M and Russegger, H and Pachinger, Th}, + journal={Neuroreport}, + volume={7}, + number={7}, + pages={1235--1240}, + year={1996}, + publisher={LWW} +} +% +%1995 +% +@misc{borko1995learning, + title={Learning to teach in DC Berliner \& RC Calfee (eds), Handbook of Education Psychology (Pp 673-708)}, + author={Borko, H and Putnam, A}, + year={1995}, + publisher={New York: Macmillan}, + annote={recommended by Schoenfeld} +} +@article{cipra1995bumpy, + title={The bumpy road to reform}, + author={Cipra, Barry}, + journal={UME Trends}, + volume={6}, + number={6}, + pages={16}, + year={1995} +} + @article{hunt1995subtlety, + title={The subtlety of distinctiveness: What von Restorff really did}, + author={Hunt, R Reed}, + journal={Psychonomic Bulletin \& Review}, + volume={2}, + number={1}, + pages={105--112}, + year={1995}, + publisher={Springer} + } +@article{leron1995abstract, + title={An abstract algebra story}, + author={Leron, Uri and Dubinsky, Ed}, + journal={American Mathematical Monthly}, + pages={227--242}, + year={1995}, + publisher={JSTOR} +} +% +%1994 +% +@book{darling1994review, + title={Review of research in education. 20 (1994)}, + author={Darling-Hammond, Linda}, + volume={20}, + year={1994}, + publisher={Amer Educational Research Assn}, + annote={recommended by Schoenfeld} +} +@article{gray1994duality, + title={Duality, ambiguity, and flexibility: A "proceptual" view of simple arithmetic}, + author={Gray, Eddie M and Tall, David O}, + journal={Journal for research in Mathematics Education}, + pages={116--140}, + year={1994}, + publisher={JSTOR} +} +@article{hart1994conceptual, + title={A conceptual analysis of the proof-writing performance of expert and novice students in elementary group theory}, + author={Hart, EW}, + journal={MAA NOTES}, + pages={49--62}, + year={1994}, + publisher={Mathematical Association of America} +} + +@article{ward1994structured, + title={Structured imagination: The role of category structure in exemplar generation}, + author={Ward, Thomas B}, + journal={Cognitive psychology}, + volume={27}, + number={1}, + pages={1--40}, + year={1994}, + publisher={Elsevier} +} +% +%1993 +% +@article{nelson1993proofs, + title={Proofs without words}, + author={Nelson, Roger B}, + journal={Mathematical Association of America}, + volume={84}, + pages={90}, + year={1993} +} +@article{schoenfeld1993learning, + title={Learning: The microgenetic analysis of one student’s evolving understanding of a complex subject matter domain}, + author={Schoenfeld, Alan H and Smith, John P and Arcavi, Abraham}, + journal={Advances in instructional psychology}, + volume={4}, + pages={55--175}, + year={1993}, + publisher={Erlbaum Hillsdale, NJ} +} +% +%1992 +% +@article{culotta1992calculus, + title={The calculus of education reform}, + author={Culotta, Elizabeth}, + journal={Science}, + volume={255}, + pages={1060--1062}, + year={1992} +} +@book{grouws1992handbook, + title={Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics.}, + author={Grouws, Douglas A}, + year={1992}, + publisher={Macmillan Publishing Co, Inc} +} +@book{kosslyn1992wet, + title={Wet mind: The new cognitive neuroscience}, + author={Kosslyn, Stephen Michael and Koenig, Olivier}, + year={1992}, + publisher={Simon and Schuster} +} +@article{mcleod1992research, + title={Research on affect in mathematics education: A reconceptualization}, + author={McLeod, Douglas B}, + journal={Handbook of research on mathematics teaching and learning}, + pages={575--596}, + year={1992} +} +@article{van1992jasper, + title={The Jasper series: An experiment with new ways to enhance mathematical thinking}, + author={Van Haneghan, JP and Barron, Linda and Young, MF and Williams, SM and Vye, NJ and Bransford, JD}, + journal={Enhancing thinking skills in the sciences and mathematics}, + pages={15--38}, + year={1992} +} +% +%1991 +% +@book{harel1991constructionism, + title={Constructionism.}, + author={Harel, Idit Ed and Papert, Seymour Ed}, + year={1991}, + publisher={Ablex Publishing} +} +@article{marty1991getting, + title={Getting to Eureka!: Higher Order Reasoning in Math}, + author={Marty, Roger H}, + journal={College teaching}, + volume={39}, + number={1}, + pages={3--6}, + year={1991}, + publisher={Taylor \& Francis} +} +% +%1990 +% + +@book{strauss1990basics, + title={Basics of qualitative research}, + author={Strauss, Anselm Leonard and Corbin, Juliet M and others}, + volume={15}, + year={1990}, + publisher={Sage Newbury Park, CA} +} +@article{yates1990theories, + title={Theories of cognitive development}, + author={Yates, Timothy}, + journal={Child and adolescent psychiatry. Baltimore (MD): Williams and Wilkins}, + pages={109--29}, + year={1990} +} +% +%1989 +% +@article{mason1989mathematical, + title={Mathematical abstraction as the result of a delicate shift of attention}, + author={Mason, John}, + journal={For the learning of mathematics}, + pages={2--8}, + year={1989}, + publisher={JSTOR} +} +% +%1988 +% +@article{fuys1988van, + title={The van Hiele model of thinking in geometry among adolescents}, + author={Fuys, David and Geddes, Dorothy and Tischler, Rosamond}, + journal={Journal for Research in Mathematics Education. Monograph}, + pages={i--196}, + year={1988}, + publisher={JSTOR} +} +@article{gentner1988metaphor, + title={Metaphor as structure mapping: The relational shift}, + author={Gentner, Dedre}, + journal={Child development}, + pages={47--59}, + year={1988}, + publisher={JSTOR} +} +@article{lutzer1988comprehension, + title={Comprehension of proverbs by average children and children with learning disorders}, + author={Lutzer, Victoria D}, + journal={Journal of learning disabilities}, + volume={21}, + number={2}, + pages={104--108}, + year={1988}, + publisher={Sage Publications} +} +% +%1987 +% +@book{fischbein1987intuition, + title={Intuition in science and mathematics: An educational approach}, + author={Fischbein, Efraim}, + volume={5}, + year={1987}, + publisher={Springer Science \& Business Media} +} +@article{squire1987memory, + title={Memory and brain}, + author={Squire, Larry R}, + journal={New York}, + year={1987} +} +@article{winn1987charts, + title={Charts, graphs, and diagrams in educational materials}, + author={Winn, Bill}, + journal={The psychology of illustration}, + volume={1}, + pages={152--198}, + year={1987} +} +% +%1986 +% +@article{gentner1986systematicity, + title={Systematicity and surface similarity in the development of analogy}, + author={Gentner, Dedre and Toupin, Cecile}, + journal={Cognitive science}, + volume={10}, + number={3}, + pages={277--300}, + year={1986}, + publisher={Wiley Online Library} +} +@article{wittrock1986handbook, + title={Handbook of research on teaching}, + author={Wittrock, Merlin C}, + year={1986}, + publisher={MacmillanWittrock, MC} +} +% +%1984 +% +@article{davis1984protein, + title={Protein synthesis and memory: a review.}, + author={Davis, Hasker P and Squire, Larry R}, + journal={Psychological bulletin}, + volume={96}, + number={3}, + pages={518}, + year={1984}, + publisher={American Psychological Association} +} +% +%1983 +% +@article{leron1983structuring, + title={Structuring mathematical proofs}, + author={Leron, Uri}, + journal={American Mathematical Monthly}, + pages={174--185}, + year={1983}, + publisher={JSTOR} +} +% +%1982 +% +@article{cohen1982modified, + title={A modified Moore method for teaching undergraduate mathematics}, + author={Cohen, David W}, + journal={American Mathematical Monthly}, + pages={473--490}, + year={1982}, + publisher={JSTOR} +} +% +%1981 +% + +% +%1980 +% +@article{gick1980analogical, + title={Analogical problem solving}, + author={Gick, Mary L and Holyoak, Keith J}, + journal={Cognitive psychology}, + volume={12}, + number={3}, + pages={306--355}, + year={1980}, + publisher={Elsevier} +} +% +%1978 +% +@article{milner1978theory, + title={A theory of type polymorphism in programming}, + author={Milner, Robin}, + journal={Journal of computer and system sciences}, + volume={17}, + number={3}, + pages={348--375}, + year={1978}, + publisher={Elsevier} +} +% +%1977 +% +@article{dormolen1977learning, + title={Learning to understand what giving a proof really means}, + author={Dormolen, J van}, + journal={Educational Studies in Mathematics}, + volume={8}, + number={1}, + pages={27--34}, + year={1977}, + publisher={Springer}, + annote={costs money} +} +% +%1976 +% +@book{wittgenstein1989wittgenstein, + title={Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939}, + author={Wittgenstein, Ludwig and Bosanquet, RG and Malcolm, N and Hrees, R and Symthies, Y and Diamond, Cora}, + year={1976}, + publisher={Cornell University Press} +} +% +%1974 +% +@article{kinsbourne1974mechanism, + title={The mechanism of the word-frequency effect on recognition memory}, + author={Kinsbourne, Marcel and George, James}, + journal={Journal of Verbal Learning and Verbal Behavior}, + volume={13}, + number={1}, + pages={63--69}, + year={1974}, + publisher={Elsevier} +} +% +%1973 +% +@book{freudenthal1973mathematics, + title={Mathematics as an educational task}, + author={Freudenthal, Hans}, + year={1973}, + publisher={Springer Science \& Business Media} +} +% +%1965 +% +@article{wallace1965review, + title={Review of the historical, empirical, and theoretical status of the Von Restorff phenomenon.}, + author={Wallace, William P}, + journal={Psychological bulletin}, + volume={63}, + number={6}, + pages={410}, + year={1965}, + publisher={American Psychological Association} +} +% +%1959 +% +@article{whitehead1959aims, + title={The aims of education}, + author={Whitehead, Alfred North}, + journal={Daedalus}, + volume={88}, + number={1}, + pages={192--205}, + year={1959}, + publisher={JSTOR} +} \ No newline at end of file diff --git a/literature.bib b/literature.bib new file mode 100644 index 0000000..f724036 --- /dev/null +++ b/literature.bib @@ -0,0 +1,1293 @@ +@book{marton2013classroom, + title={Classroom discourse and the space of learning}, + author={Marton, Ference and Tsui, Amy BM and Chik, Pakey PM and Ko, Po Yuk and Lo, Mun Ling}, + year={2013}, + publisher={Routledge} +} +@misc{criticalThinking, +howpublished={\url{www.criticalthinking.org/pages/defining-critical-thinking/410} viewed September 26, 2013} +} +@misc{piazza, +author={piazza}, +howpublished={\url{https://piazza.com/} viewed 2/14/2014} +} +@misc{bridges, +author={bridges}, +howpublished={\url{https://www.mathematik.uni-muenchen.de/~jberger/one.pdf} viewed 2/14/2104} +} +@misc{weber, +author={weber}, +howpublished={\url{http://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/teaching-and-learning/research-sampler-8-students-difficulties-with-proof#sthash.SMs7qEx9.dpuf}} +} +@misc{SimSE, +author={SimSE}, +howpublished={\url{http://www.ics.uci.edu/~emilyo/SimSE/}} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2014 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{bull2014supporting, +title={Supporting Reflective Practice in Software Engineering Education through a Studio-based Approach}, +author={Bull, Christopher and Whittle, Jon}, +journal={IEEE Software}, +pages={1}, +year={2014}, +publisher={IEEE} +} +@article{chen2011software, +title={Software engineering education: A study on conducting collaborative senior project development}, +author={Chen, Chung-Yang and Chong, P Pete}, +journal={Journal of Systems and Software}, +volume={84}, +number={3}, +pages={479--491}, +year={2011}, +publisher={Elsevier} +} +@article{chen2011design, +title={The design and development of a computerized tool for conducting senior projects in software engineering education}, +author={Chen, Chung-Yand and Teng, Kao-Chiuan}, +journal={Computers \& Education}, +volume={56}, +number={3}, +pages={802--817}, +year={2011}, +publisher={Elsevier} +} +@article{hainey2011evaluation, +title={Evaluation of a game to each requirements collection and analysis in software education at tertiary level}, +author={Hainey, Thomas and Connolly, Thomas M and Stansfield, Mark and Boyle, Elizabeth A}, +journal={Computers \& Education}, +volume={56}, +number={1}, +pages={21--35}, +year={2011}, +publisher={Elsevier} +} +@article{santos2011supporting, +title={Supporting Software Engineering Education through a Learning Objects and Experience Reports Repository}, +author={Santos, Rodrigo and Werner Cl{\'a}dis and Costa, Heitor and Vasconcelos, Simone}, +journal={23rd SEKE}, +pages={272--275}, +year={2011}, +publisher={} +} +@article{ardis2011advancing, +title={Advancing Software Engineering Professional Education}, +author={Ardis, Mark and Bourque, Pierre and Hilburn, Thomas and Lasfer, Kahina and Lucero, Scott and McDonald, James and Pyster, Art and Shaw, Mary}, +journal={IEEE Software}, +volume={28}, +number={4}, +pages={58-63}, +year={2011}, +publisher={IEEE} +} +@article{pyster2009graduate, +title={Graduate Software Engineering 2009 (GSwE2009) Curriculum Guidelines for Graduate Degree Programs in Software Engineering}, +author={Pyster, A}, +journal={Integrated Software and Systems Engineering Curriculum (iSSEc) series}, +volume={}, +number={}, +pages={}, +year={2009}, +publisher={} +} +@misc{GSwE, +author={GSwE}, +howpublished={\url{www.gswe2009.org}} +} +@article{bloom1956taxonomy, +title={Taxonomy of educational objectives. Vol. 1: Cognitive domain}, +author={Bloom, Benjamin S and others}, +journal={New York: McKay}, +year={1956} +} + +@article{hilburn2013software, +title={Software Assurance Competency Model}, +author={Hilburn, Thomas B and Ardis, Mark and Johnson, Glen and Kornecki, Andrew J and Mead, Nancy}, +journal={repository.cmu.edu}, +year=2013 +} +@article{moreno2012balancing, +title={Balancing software engineering education and industrial needs}, +author={Moreno, Ana M and Sanchez-Segura, Maria-Isabel and Medina-Dominguez, Fuensanta and Carvajal, Laura}, +journal={Journal of Systems and Software}, +volume={85}, +number={7}, +pages={1607--1620}, +year={2012}, +publisher={Elsevier} +} +@misc{sebokwiki, +title={Graduate Reference Curriculum for Systems Engineering (GRCSE) version 1.0}, +author={Art Pyster and David H. Olwell and Timothy L.J. Perris and Nichole Hutchinson and Stephanie Enck and James F. Anthony, Jr. and Devanandham Henry and Alice Squires}, +year={2012}, +publisher={Stevens Institute of Technology} +} +@article{halverson2014thematic, +author={Halverson, Lisa R and Graham, Charles R and String, Kristian J ad Drysdale, Jeffery S and Henrie, Curtis R}, +title={A thematic analysis of the most highly cited scholarship in the first decade of blended learning research}, +journal={The Internet and Higher Education}, +volume={20}, +pages={20--34}, +year={2014}, +publisher={Elsevier} +} +@article{petersen2008systematic, +author={Petersen, Kai and Feldt, Robert and Mujtaba, Shahid and Mattsson, Michael}, +title={Systematic mapping studies in software engineering}, +booktitle={12th International Conference on Evalutation and Assessment in Software Engineering}, +volume={17}, +pages={1}, +year={2008} +} +@article{sjoberg2005survey, +title={A survey of controlled experiments in software engineering}, +author={Sj{\o}berg, Dag IK and Hannay, Jo Erskine and Hansen, Over and Kampenes, Vigdis By and Karahasanovic, Amela and Liborg, N-K and Rekdal, Anette C}, +journal={Software Engineering, IEEE Transactions on}, +volume={31}, +number={9}, +pages={733--753}, +year={2005}, +pulisher={IEEE} +} +@article{cruzes2011recommend, +title={Recommended steps for thematic synthesis in software engineering}, +author={Cruzes, Daniela S and Dyba, Tore}, +booktitle={Empirical Software Engineering and Measurement (ESEM), 2011 International Symposium on}, +pages={275--284}, +year={2011}, +organization={IEEE} +} +@inproceedings{Weyuker2011empirical, +titie={Empirical soft are engineering research-the good, the bad, the ugly}, +author={Weyuker, Elaine J}, +booktitle={Empirical Software Engineering and Measurement (ESEM), 2011 International Syposium on}, +pages={1--9}, +year={2011}, +organization={IEEE} +} +@article{cruzes2011research, +title={Research synthesis in software engineering: A tertiary study}, +author={Cruzes, Daniela S and Dyb{\aa}, Tore}, +journal={Information and Software Technology}, +volume={53}, +number={5}, +pages={440--455}, +year={2011}, +publisher={Elsevier} +} + +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2013 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{baldwin2013roles, + title={The roles of mathematics in computer science}, + author={Baldwin, Douglas and Walker, Henry M and Henderson, Peter B}, + journal={ACM Inroads}, + volume={4}, + number={4}, + pages={74--80}, + year={2013}, + publisher={ACM} +} +@article{bussey2013variation, + title={Variation theory: A theory of learning and a useful theoretical framework for chemical education research}, + author={Bussey, Thomas J and Orgill, MaryKay and Crippen, Kent J}, + journal={Chemistry Education Research and Practice}, + volume={14}, + number={1}, + pages={9--22}, + year={2013}, + publisher={Royal Society of Chemistry} +} +@article{ginat2013proving, + title={Proving lower bound}, + author={Ginat, David}, + journal={ACM Inroads}, + volume={4}, + number={1}, + pages={24--25}, + year={2013}, + publisher={ACM} +} +@article{henderson2013marketing, + title={Marketing math thinking}, + author={Henderson, Peter B}, + journal={ACM Inroads}, + volume={4}, + number={1}, + pages={23--24}, + year={2013}, + publisher={ACM} +} +@article{marton2013meanings, + title={Meanings are acquired from experiencing differences against a background of sameness, rather than from experiencing sameness against a background of difference: Putting a conjecture to the test by embedding it in a pedagogical tool}, + author={Marton, Ference and Pang, Ming Fai}, + journal={Frontline Learning Research}, + volume={1}, + number={1}, + pages={24--41}, + year={2013} +} +@article{mcgowen2013flexible, + title={Flexible thinking and met-befores: Impact on learning mathematics}, + author={McGowen, Mercedes A and Tall, David O}, + journal={The Journal of Mathematical Behavior}, + volume={32}, + number={3}, + pages={527--537}, + year={2013}, + publisher={Elsevier} +} +@article{sun2013assessment, + title={Assessment of Prospective Teachers’ Multiple Proof Construction of a Trapezoid Area Formula}, + author={Sun, Xuhua}, + journal={New Waves-Educational Research \& Development}, + volume={16}, + number={1}, + year={2013} +} + +@article{malmi2013doctoral, + title={Doctoral studies in computing education research: part 1}, + author={Malmi, Lauri}, + journal={ACM Inroads}, + volume={4}, + number={4}, + pages={18--19}, + year={2013}, + publisher={ACM} +} +@article{hellqvist2013students, + title={Students’ experiences of participation in the disciplines Computer Science, Physics, and Earth Sciences as an aspect of novice students’ identity}, + author={Hellqvist, Magnus and Lindblad, Andreas and Peters, Anne-Kathrin}, + year={2013} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2012 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{aakerlind2012variation, + title={Variation and commonality in phenomenographic research methods}, + author={{\AA}kerlind, Gerlese S}, + journal={Higher Education Research \& Development}, + volume={31}, + number={1}, + pages={115--127}, + year={2012}, + publisher={Taylor \& Francis} +} +@article{boustedt2012students, + title={Students' different understandings of class diagrams}, + author={Boustedt, Jonas}, + journal={Computer Science Education}, + volume={22}, + number={1}, + pages={29--62}, + year={2012}, + publisher={Taylor \& Francis} +} +@incollection{jones2012proof, + title={Proof, proving, and teacher-student interaction: Theories and contexts}, + author={Jones, Keith and Herbst, Patricio}, + booktitle={Proof and proving in mathematics education}, + pages={261--277}, + year={2012}, + publisher={Springer} +} +@article{henderson2012mathematical, + title={Mathematical reasoning at the crossroads}, + author={Henderson, Peter B and Sitaraman, Murali}, + journal={ACM Inroads}, + volume={3}, + number={1}, + pages={30--31}, + year={2012}, + publisher={ACM} +} +@article{herman2012describing, + title={Describing the what and why of students’ difficulties in Boolean logic}, + author={Herman, Geoffrey L and Loui, Michael C and Kaczmarczyk, Lisa and Zilles, Craig}, + journal={ACM Transactions on Computing Education (TOCE)}, + volume={12}, + number={1}, + pages={3}, + year={2012}, + publisher={ACM} +} +@book{ling2012variation, + title={Variation theory and the improvement of teaching and learning}, + author={Ling Lo, Mun}, + year={2012}, + publisher={G{\"o}teborg: Acta Universitatis Gothoburgensis} +} + +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2011 +% % % % % % % % % % % % % % % % % % % % % % % % + +@article{bauldryappendix, + title={Appendix {C}: Projects in Real Analysis}, + author={Bauldry, William C}, + journal={Introduction to Real Analysis: An Educational Approach}, + pages={239--251}, + year=2011, + publisher={Wiley Online Library} +} +@book{epp2011discrete, + title={Discrete mathematics with applications}, + author={Epp, Susanna S}, + year={2011}, + publisher={Cengage Learning} +} +@book{rosen2011discrete, + title={Discrete Mathematics and Its Applications 7th edition}, + author={Rosen, Kenneth}, + year={2011}, + publisher={McGraw-Hill Science} +} +@article{weber2011and, + title={Why and how mathematicians read proofs: An exploratory study}, + author={Weber, Keith and Mejia-Ramos, Juan Pablo}, + journal={Educational Studies in Mathematics}, + volume={76}, + number={3}, + pages={329--344}, + year={2011}, + publisher={Springer} +} +@article{ling2011towards, + title={Towards a science of the art of teaching: Using variation theory as a guiding principle of pedagogical design}, + author={Ling, Lo Mun and Marton, Ference}, + journal={International Journal for Lesson and Learning Studies}, + volume={1}, + number={1}, + pages={7--22}, + year={2011}, + publisher={Emerald Group Publishing Limited} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2010 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{henderson2010matha, + title={MATH COUNTS Mathematical reasoning in computing education}, + author={Henderson, Peter B}, + journal={ACM Inroads}, + volume={1}, + number={3}, + pages={22--23}, + year={2010}, + publisher={ACM} +} +@article{henderson2010mathb, + title={MATH COUNTS Model checking}, + author={Henderson, Peter B}, + journal={ACM Inroads}, + volume={1}, + number={1}, + pages={33--33}, + year={2010}, + publisher={ACM} +} +@article{henderson2010mathc, + title={Math counts: Arguments, proofs, and...}, + author={Henderson, Peter B}, + journal={ACM SIGCSE Bulletin}, + volume={41}, + number={4}, + pages={21--22}, + year={2010}, + publisher={ACM} +} +@article{mcgowen2010metaphor, + title={Metaphor or Met-Before? The effects of previouos experience on practice and theory of learning mathematics}, + author={McGowen, Mercedes A and Tall, David O}, + journal={The Journal of Mathematical Behavior}, + volume={29}, + number={3}, + pages={169--179}, + year={2010}, + publisher={Elsevier} +} +@article{reid2010proof, + title={Proof in mathematics education}, + author={Reid, David A and Knipping, Christine}, + journal={Research, learning and teaching. Rotterdam: Sense Publisher}, + year={2010} +} +@article{rundgren2010critical, + title={CRITICAL FEATURES OF VISUALIZATIONS OF TRANSPORT THROUGH THE CELL MEMBRANE -- AN EMPIRICAL STUDY OF UPPER SECONDARY AND TERTIARY STUDENTS' MEANING-MAKING OF A STILL IMAGE AND AN ANIMATION}, + author={Rundgren, Carl-Johan and Tibell, Lena AE}, + journal={International Journal of Science and Mathematics Education}, + volume={8}, + number={2}, + pages={223--246}, + year={2010}, + publisher={Springer} +} +@techreport{thune2010students, + title={Students' Conceptions of Computer Programming}, + author={Thun{\'e}, Michael and Eckerdal, Anna}, + institution={Uppsala Universitet}, + year={2010} +} +% % % % % % % % % % % +% 2009 +% % % % % % % % % % % + +% % % % % % % % % % % +% 2008 +% % % % % % % % % % % + +@book{corbin2008basics, + title={Basics of qualitative research: Techniques and procedures for developing grounded theory}, + author={Corbin, Juliet and Strauss, Anselm}, + year={2008}, + publisher={Sage} +} +@article{hanna2008proofs, + title={Proofs as bearers of mathematical knowledge}, + author={Hanna, Gila and Barbeau, Ed}, + journal={ZDM}, + volume={40}, + number={3}, + pages={345--353}, + year={2008}, + publisher={Springer} +} +@inproceedings{Herman:2008:PIE:1404520.1404527, + author = {Herman, Geoffrey L. and Kaczmarczyk, Lisa and Loui, Michael C. and Zilles, Craig}, + title = {Proof by Incomplete Enumeration and Other Logical Misconceptions}, + booktitle = {Proceedings of the Fourth International Workshop on Computing Education Research}, + series = {ICER '08}, + year = {2008}, + isbn = {978-1-60558-216-0}, + location = {Sydney, Australia}, + pages = {59--70}, + numpages = {12}, + url = {http://doi.acm.org/10.1145/1404520.1404527}, + doi = {10.1145/1404520.1404527}, + acmid = {1404527}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {concept inventory, digital logic, discrete math, formal logic, misconceptions}, +} +@article{selden2008overcoming, + title={Overcoming students’ difficulties in learning to understand and construct proofs}, + author={Selden, Annie and Selden, John}, + journal={Making the Connection: Research and Practice in Undergraduate Mathematics}, + pages={95--110}, + year={2008} +} + @article{weber2008mathematicians, + title={How mathematicians determine if an argument is a valid proof}, + author={Weber, Keith}, + journal={Journal for Research in Mathematics Education}, + pages={431--459}, + year={2008}, + publisher={JSTOR} + } + +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2007 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{booth1997phenomenography, + title={On phenomenography, learning and teaching}, + author={Booth, Shirley}, + journal={Higher education research \& development}, + volume={16}, + number={2}, + pages={135--158}, + year={1997}, + publisher={Taylor \& Francis} +} +@article{dahlin2007enriching, + title={Enriching the theoretical horizons of phenomenography, variation theory and learning studies}, + author={Dahlin, Bo}, + journal={Scandinavian Journal of Educational Research}, + volume={51}, + number={4}, + pages={327--346}, + year={2007}, + publisher={Taylor \& Francis} +} + +@inproceedings{suhonen2007applications, + title={Applications of variation theory in computing education}, + author={Suhonen, Jarkko and Davies, Janet and Thompson, Errol and others}, + booktitle={Proc. of the Seventh Baltic Sea Conference on Computing Education Research-Volume 88}, + pages={217--220}, + year={2007}, + organization={Australian Computer Society, Inc.} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2006 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{marton2006some, + title={On some necessary conditions of learning}, + author={Marton, Ference and Pang, Ming Fai}, + journal={The Journal of the Learning sciences}, + volume={15}, + number={2}, + pages={193--220}, + year={2006}, + publisher={Taylor \& Francis} +} + +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2005 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{akerlind2005learninga, + title={Learning about phenomenography: Interviewing, data analysis and the qualitative research paradigm}, + author={Akerlind, Gerlese}, + journal={Doing developmental phenomenography}, + pages={63}, + year={2005}, + publisher={RMIT University Press} +} + +@article{akerlind2005phenomenographic, + title={Phenomenographic methods: A case illustration}, + author={Akerlind, Gerlese}, + journal={Doing developmental phenomenography}, + pages={103}, + year={2005}, + publisher={RMIT University Press} +} +@article{akerlind2005learningd, + title={Learning to do phenomenography: A reflective discussion}, + author={Akerlind, Gerlese and Bowden, John A and Green, Pam}, + journal={Doing developmental phenomenography}, + pages={74}, + year={2005}, + publisher={RMIT University Press} +} +@inproceedings{eckerdal2005novice, + title={Novice {J}ava programmers' conceptions of object and class, and variation theory}, + author={Eckerdal, Anna and Thun{\'e}, Michael}, + booktitle={ACM SIGCSE Bulletin}, + volume={37}, + number={3}, + pages={89--93}, + year={2005}, + organization={ACM} +} +@inproceedings{eckerdal2005does, + title={What does it take to learn 'programming thinking'?}, + author={Eckerdal, Anna and Thun{\'e}, Michael and Berglund, Anders}, + booktitle={Proc. of the first international workshop on Computing education research}, + pages={135--142}, + year={2005}, + organization={ACM} +} + +@article{runesson2005beyond, + title={Beyond discourse and interaction. Variation: a critical aspect for teaching and learning mathematics}, + author={Runesson, Ulla}, + journal={Cambridge journal of education}, + volume={35}, + number={1}, + pages={69--87}, + year={2005}, + publisher={Taylor \& Francis} +} +@article{weber2005problem, + title={Problem-solving, proving, and learning: The relationship between problem-solving processes and learning opportunities in the activity of proof construction}, + author={Weber, Keith}, + journal={The Journal of Mathematical Behavior}, + volume={24}, + number={3}, + pages={351--360}, + year={2005}, + publisher={Elsevier} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2004 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{weber2004semantic, + title={Semantic and syntactic proof productions}, + author={Weber, Keith and Alcock, Lara}, + journal={Educational Studies in Mathematics}, + volume={56}, + number={2-3}, + pages={209--234}, + year={2004}, + publisher={Springer} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2003 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{dixon200320, + title={20 Studies That Revolutionized Child Psychology.}, + author={Dixon, WE}, + journal={Journal of Abnormal and Social Psychology}, + volume={63}, + pages={375--382}, + year={2003} +} +@phdthesis{fagen2003assessing, + title={Assessing and enhancing the introductory science course in physics and biology: Peer instruction, classroom demonstrations, and genetics vocabulary}, + author={Fagen, Adam Paul}, + year={2003}, + school={Harvard University Cambridge, Massachusetts} +} + +@article{selden2003validations, + title={Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?}, + author={Selden, Annie and Selden, John}, + journal={Journal for research in mathematics education}, + pages={4--36}, + year={2003}, + publisher={JSTOR} +} +@article{weber2003students, + title={Students’ difficulties with proof}, + author={Weber, Keith}, + journal={Retrieved September}, + volume={14}, + pages={2005}, + year={2003} +} +@article{weber2003research, + title={Research Sampler 8: students’ difficulties with proof}, + author={Weber, Keith}, + journal={The Mathematical Association of America: Online. Mathematical Association of America. Retrieved on October}, + volume={1}, + pages={2009}, + year={2003}, + url={\url{http://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelines-recommendations/teaching-and-learning/research-sampler-8-students-difficulties-with-proof }} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2002 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{alcock2002definitions, + title={Definitions: dealing with categories mathematically.}, + author={Alcock, Lara and Simpson, AP}, + journal={For the learning of mathematics.}, + volume={22}, + number={2}, + pages={28--34}, + year={2002}, + publisher={FLM} +} +@inproceedings{knuth2002mapping, + title={Mapping the conceptual terrain of middle school students’ competencies in justifying and proving}, + author={Knuth, Eric J and Choppin, J and Slaughter, M and Sutherland, Jamie}, + booktitle={Proceedings of the 24th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education}, + volume={4}, + pages={1693--1670}, + year={2002}, + organization={Clearinghouse for Science, Mathematics, and Environmental Education Athens, GA} +} +@book{krantz2002handbook, + title={Handbook of logic and proof techniques for computer science}, + author={Krantz, Steven George}, + year={2002}, + publisher={Springer} +} +@article{raman2002coordinating, + title={Coordinating informal and formal aspects of mathematics: Student behavior and textbook messages}, + author={Raman, Manya}, + journal={The Journal of Mathematical Behavior}, + volume={21}, + number={2}, + pages={135--150}, + year={2002}, + publisher={Elsevier} +} +@article{reid2002students, + title={Students' conceptions of statistics: A phenomenographic study}, + author={Reid, Anna and Petocz, Peter}, + journal={Journal of Statistics Education}, + volume={10}, + number={2}, + pages={1--28}, + year={2002} +} +@article{weber2002beyond, + title={Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique}, + author={Weber, Keith}, + journal={For the Learning of Mathematics}, + pages={14--17}, + year={2002}, + publisher={JSTOR} +} +@inproceedings{weber2002role, + title={The role of instrumental and relational understanding in proofs about group isomorphisms}, + author={Weber, Keith}, + booktitle={Proceedings from the 2nd International Conference for the Teaching of Mathematics}, + year={2002} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2001 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{recio2001institutional, + title={Institutional and personal meanings of mathematical proof}, + author={Recio, Angel M and Godino, Juan D}, + journal={Educational Studies in Mathematics}, + volume={48}, + number={1}, + pages={83--99}, + year={2001}, + publisher={Springer} +} +@article{weber2001student, + title={Student difficulty in constructing proofs: The need for strategic knowledge}, + author={Weber, Keith}, + journal={Educational Studies in Mathematics}, + volume={48}, + number={1}, + pages={101--119}, + year={2001}, + publisher={Springer} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2000 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{bowden2000phenomenography, + title={Phenomenography}, + author={Bowden, John A and Walsh, Eleanor}, + journal={Phenomenography}, + pages={v}, + year={2000}, + publisher={RMIT University Press} +} +@article{bowden2000nature, + title={The nature of phenomenographic research}, + author={Bowden, John A}, + journal={Phenomenography}, + pages={1--18}, + year={2000} +} +@article{hanna2000proof, + title={Proof, explanation and exploration: An overview}, + author={Hanna, Gila}, + journal={Educational studies in mathematics}, + volume={44}, + number={1-2}, + pages={5--23}, + year={2000}, + publisher={Springer} +} +@book{national2000principles, + title={Principles and standards for school mathematics}, + author={National Council of Teachers of Mathematics}, + volume={1}, + year={2000}, + publisher={Natl Council of Teachers of} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1999 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{dreyfus1999johnny, + title={Why Johnny can't prove}, + author={Dreyfus, Tommy}, + journal={Educational studies in mathematics}, + volume={38}, + number={1-3}, + pages={85--109}, + year={1999}, + publisher={Springer} +} +@article{mahavier1999moore, + title={What is the Moore method?}, + author={Mahavier, William S}, + journal={Problems, Resources, and Issues in Mathematics Undergraduate Studies}, + volume={9}, + number={4}, + pages={339--354}, + year={1999}, + publisher={Taylor \& Francis} +} +@inproceedings{pinto1999student, + title={Student constructions of formal theory: giving and extracting meaning}, + author={Pinto, M{\'a}rcia Maria Fusaro and Tall, David and Zaslavsky, O}, + booktitle={Proceedings of the Conference of the International Group for}, + volume={100}, + pages={1230}, + year={1999}, + organization={ERIC} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1998 +% % % % % % % % % % % % % % % % % % % % % % % % +@book{davis1998mathematical, + title={The mathematical experience}, + author={Davis, Philip J and Hersh, Reuben}, + year={1998}, + publisher={Houghton Mifflin Harcourt} +} +@article{harel1998two, + title={Two dual assertions: The first on learning and the second on teaching (or vice versa)}, + author={Harel, Guershon}, + journal={American Mathematical Monthly}, + pages={497--507}, + year={1998}, + publisher={JSTOR} +} +@article{harel1998students, + title={Students’ proof schemes: Results from exploratory studies}, + author={Harel, Guershon and Sowder, Larry}, + journal={Research in collegiate mathematics education III}, + volume={7}, + pages={234--282}, + year={1998} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1997 +% % % % % % % % % % % % % % % % % % % % % % % % + +@article{martzloff1997note, + title={Note on the Recent Chinese and Mongolian Translations of Euclid's< i> Elements}, + author={Martzloff, Jean-Claude}, + journal={Historia Mathematica}, + volume={24}, + number={2}, + pages={200--202}, + year={1997}, + publisher={Elsevier} +} +@book{strauss1997grounded, + title={Grounded theory in practice}, + author={Strauss, Anselm and Corbin, Juliet M}, + year={1997}, + publisher={Sage} +} + +@article{wyndhamn1997word, + title={Word problems and mathematical reasoning—A study of children's mastery of reference and meaning in textual realities}, + author={Wyndhamn, Jan and S{\"a}lj{\"o}, Roger}, + journal={Learning and Instruction}, + volume={7}, + number={4}, + pages={361--382}, + year={1997}, + publisher={Elsevier} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1996 +% % % % % % % % % % % % % % % % % % % % % % % % +@incollection{hanna1996proof, + title={Proof and proving}, + author={Hanna, Gila and Jahnke, H Niels}, + booktitle={International handbook of mathematics education}, + pages={877--908}, + year={1996}, + publisher={Springer} +} +@article{yackel1996sociomathematical, + title={Sociomathematical norms, argumentation, and autonomy in mathematics}, + author={Yackel, Erna and Cobb, Paul}, + journal={Journal for research in mathematics education}, + pages={458--477}, + year={1996}, + publisher={JSTOR} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1995 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{selden1995unpacking, + title={Unpacking the logic of mathematical statements}, + author={Selden, John and Selden, Annie}, + journal={Educational Studies in Mathematics}, + volume={29}, + number={2}, + pages={123--151}, + year={1995}, + publisher={Springer} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1994 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{moore1994making, + title={Making the transition to formal proof}, + author={Moore, Robert C}, + journal={Educational Studies in Mathematics}, + volume={27}, + number={3}, + pages={249--266}, + year={1994}, + publisher={Springer} +} +@article{schoenfeld1994we, + title={What do we know about mathematics curricula?}, + author={Schoenfeld, Alan H}, + journal={The Journal of Mathematical Behavior}, + volume={13}, + number={1}, + pages={55--80}, + year={1994}, + publisher={JAI} +} +@article{thompson1994students, + title={Students, functions, and the undergraduate curriculum}, + author={Thompson, Patrick W}, + journal={Research in collegiate mathematics education}, + volume={1}, + pages={21--44}, + year={1994} +} +@article{thurston1994proof, + title={On proof and progress in mathematics}, + author={Thurston, William P}, + journal={arXiv preprint math/9404236}, + year={1994} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1993 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{hersh1993proving, + title={Proving is convincing and explaining}, + author={Hersh, Reuben}, + journal={Educational Studies in Mathematics}, + volume={24}, + number={4}, + pages={389--399}, + year={1993}, + publisher={Springer} +} +@article{ramsden1993theories, + title={Theories of learning and teaching and the practice of excellence in higher education}, + author={Ramsden, Paul}, + journal={Higher Education Research and Development}, + volume={12}, + number={1}, + pages={87--97}, + year={1993}, + publisher={Taylor \& Francis} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1992 +% % % % % % % % % % % % % % % % % % % % % % % % +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1991 +% % % % % % % % % % % % % % % % % % % % % % % % +@incollection{alibert1991research, + title={Research on mathematical proof}, + author={Alibert, Daniel and Thomas, Michael}, + booktitle={Advanced mathematical thinking}, + pages={215--230}, + year={1991}, + publisher={Springer} +} +@article{hanna1991mathematical, + title={Mathematical proof}, + author={Hanna, Gila}, + journal={Advanced mathematical thinking}, + pages={54--61}, + year={1991}, + publisher={Springer} +} +@article{marty1991getting, + title={Getting to Eureka!: Higher Order Reasoning in Math}, + author={Marty, Roger H}, + journal={College Teaching}, + volume={39}, + number={1}, + pages={3--6}, + year={1991}, + publisher={Taylor \& Francis} +} +@incollection{tall1991psychology, + title={The psychology of advanced mathematical thinking}, + author={Tall, David}, + booktitle={Advanced mathematical thinking}, + pages={3--21}, + year={1991}, + publisher={Springer} +} +@article{teppo1991van, + title={Van Hiele levels of geometric thought revisited}, + author={Teppo, Anne}, + journal={The Mathematics Teacher}, + pages={210--221}, + year={1991}, + publisher={JSTOR} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1990 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{hanna1990some, + title={Some pedagogical aspects of proof}, + author={Hanna, Gila}, + journal={Interchange}, + volume={21}, + number={1}, + pages={6--13}, + year={1990}, + publisher={Springer} +} +@article{senk1989van, + title={Van Hiele levels and achievement in writing geometry proofs}, + author={Senk, Sharon L}, + journal={Journal for Research in Mathematics Education}, + pages={309--321}, + year={1989}, + publisher={JSTOR} +} +@article{volmink1990nature, + title={The nature and role of proof in mathematics education}, + author={Volmink, JD}, + journal={Pythagoras}, + volume={23}, + pages={7--10}, + year={1990} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1989 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{tall1989nature, + title={The nature of mathematical proof}, + author={Tall, David}, + journal={Mathematics Teaching}, + volume={127}, + pages={28--32}, + year={1989} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1988 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{alibert1988towards, + title={Towards new customs in the classroom}, + author={Alibert, Daniel}, + journal={For the learning of mathematics}, + volume={8}, + number={2}, + pages={31--35}, + year={1988}, + publisher={ERIC} +} +@book{franklin1988introduction, + title={Introduction to proofs in mathematics}, + author={Franklin, James and Daoud, Albert and Daoud, Albert Tatar and Franklin, James}, + year={1988}, + publisher={Prentice Hall Sydney} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1987 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{balacheff1987processus, + title={Processus de preuve et situations de validation}, + author={Balacheff, Nicolas}, + journal={Educational studies in mathematics}, + volume={18}, + number={2}, + pages={147--176}, + year={1987}, + publisher={Springer} +} +@article{vygotsky1987zone, +title={Zone of Proximal Development}, +author={Vygotsky, L.}, +journal={Mind in society: The development of higher psychological processes}, +pages={52--91}, +year={1987} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1986 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{horner1986teaching, + title={Teaching Generalized Table Bussing The Importance of Negative Teaching Examples}, + author={Horner, Robert H and Eberhard, Janet M and Sheehan, Martin R}, + journal={Behavior modification}, + volume={10}, + number={4}, + pages={457--471}, + year={1986}, + publisher={Sage Publications} +} +@article{marton1986phenomenography, + title={Phenomenography: A research approach to investigating different understandings of reality}, + author={Marton, Ference}, + journal={Journal of thought}, + volume={21}, + number={3}, + pages={28--49}, + year={1986}, + publisher={San Fracisco} +} +@article{marty1986teaching, + title={Teaching proof techniques}, + author={Marty, Roger H}, + journal={Mathematics in College}, + pages={46--53}, + year={1986}, + publisher={Instructional Resource Center, City University of New York} +} + +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1985 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{senk1985well, + title={How well do students write geometry proofs?}, + author={Senk, Sharon L}, + journal={The mathematics teacher}, + pages={448--456}, + year={1985}, + publisher={JSTOR} +} +@inproceedings{svensson1985contextual, + title={Contextual analysis--the development of a research approach}, + author={Svensson, Lennart}, + booktitle={2nd conference on qualitative research in psychology, Leusden, The Netherlands}, + pages={12--15}, + year={1985} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1984 +% % % % % % % % % % % % % % % % % % % % % % % % +@book{marton1984experience, + title={The experience of learning}, + author={Marton, Ference and Hounsell, Dai and Entwistle, Noel James and others}, + year={1984}, + publisher={Scottish Academic Press Edinburgh} +} +@book{svensson1984three, + title={Three approaches to descriptive research}, + author={Svensson, Lennart}, + year={1984}, + publisher={ERIC Clearinghouse} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1982 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{mason1982thinking, + title={Thinking mathematically}, + author={Mason, John and Burton, Leone and Stacey, Kaye}, + journal={AMC}, + volume={10}, + pages={12}, + year={1982} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1981 +% % % % % % % % % % % % % % % % % % % % % % % % + +@article{marton1981phenomenography, + title={Phenomenography—describing conceptions of the world around us}, + author={Marton, Ference}, + journal={Instructional science}, + volume={10}, + number={2}, + pages={177--200}, + year={1981}, + publisher={Springer} +} +@article{renz1981mathematical, + title={Mathematical proof: What it is and what it ought to be}, + author={Renz, Peter}, + journal={Two-Year College Mathematics Journal}, + pages={83--103}, + year={1981}, + publisher={JSTOR} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1979 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{marton1979conceptions, + title={Conceptions of research in student learning}, + author={Marton, Ference and Svensson, Lennart}, + journal={Higher Education}, + volume={8}, + number={4}, + pages={471--486}, + year={1979}, + publisher={Springer} +} +@book{saljo1979learning, + title={Learning in the learner's perspective. {I}. Some common-sense conceptions}, + author={ S{\"a}lj{\"o}, Roger}, + year={1979}, + publisher={ERIC Clearinghouse} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1978 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{vygotsky1978mind, + title={Mind in society (M. Cole, V. John-Steiner, S. Scribner, \& E. Souberman, Eds.)}, + author={Vygotsky, Lev S}, + journal={Cambridge, MA: Harvard UniversityPress. VygotskyMind in society1978}, + year={1978} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1977 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{jones1977moore, + title={The Moore method}, + author={Jones, F Burton}, + journal={American Mathematical Monthly}, + pages={273--278}, + year={1977}, + publisher={JSTOR} +} +@article{manin2009course, + title={A course in mathematical logic for mathematicians}, + author={Manin, Yu I}, + journal={New York}, + year={2009} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1976 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{marton1976qualitative, + title={ON QUALITATIVE DIFFERENCES IN LEARNING -- {II} {O}UTCOME AS A FUNCTION OF THE LEARNER'S CONCEPTION OF THE TASK}, + author={Marton, Ference and S{\"a}lj{\"o}, R}, + journal={British Journal of Educational Psychology}, + volume={46}, + number={2}, + pages={115--127}, + year={1976}, + publisher={Wiley Online Library} +} +@book{svensson1976study, + title={Study skill and learning}, + author={Svensson, Lennart}, + year={1976} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1972 +% % % % % % % % % % % % % % % % % % % % % % % % +@book{newell1972human, + title={Human problem solving}, + author={Newell, Allen and Simon, Herbert Alexander and others}, + volume={104}, + number={9}, + year={1972}, + publisher={Prentice-Hall Englewood Cliffs, NJ} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1970 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{smedslund1970circular, + title={Circular relation between understanding and logic}, + author={Smedslund, Jan}, + journal={Scandinavian Journal of Psychology}, + volume={11}, + number={1}, + pages={217--219}, + year={1970}, + publisher={Wiley Online Library} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1967 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{glaser1968discovery, + title={The Discovery of Grounded Theory; Strategies for Qualitative Research.}, + author={Glaser, Barney G and Strauss, Anselm L and Strutzel, Elizabeth}, + journal={Nursing Research}, + volume={17}, + number={4}, + pages={364}, + year={1968}, + publisher={LWW} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1938 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{lewin1938will, + title={Will and needs.}, + author={Lewin, Kurt}, + year={1938}, + publisher={Kegan Paul, Trench, Trubner \& Company} +} \ No newline at end of file diff --git a/literatureClickersTheory.bib b/literatureClickersTheory.bib new file mode 100644 index 0000000..5692ae4 --- /dev/null +++ b/literatureClickersTheory.bib @@ -0,0 +1,114 @@ + + + + + + + + +@book{1999Krantz, +title={How to Teach Mathematics}, +author={Steven G. Krantz}, +publisher={American Mathematical Society}, +edition=2, +year=1999, +annote={R. L. Moore would hand out a single sheet with definitions, axioms and theorems, and challenge the students to prove the theorems on the board. Then,``Moore would rip the person apart. And that set the tone for the class.'' ``Moore did not allow his students to read books or papers.'' ``They were not allowed to read, and they were not allowed to collaborate outside of class. Moore was merciless in weeding out those students who did not cooperate or did not fit.'' }} + + + +@inproceedings{Sigman:2007:ESF:1227310.1227463, + author = {Sigman, Scott}, + title = {Engaging students in formal language theory and theory of computation}, + booktitle = {Proceedings of the 38th SIGCSE technical symposium on Computer science education}, + series = {SIGCSE '07}, + year = {2007}, + isbn = {1-59593-361-1}, + location = {Covington, Kentucky, USA}, + pages = {450--453}, + numpages = {4}, + url = {http://doi.acm.org/10.1145/1227310.1227463}, + doi = {10.1145/1227310.1227463}, + acmid = {1227463}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {Moore method, discovery learning, formal language theory, inquiry learning, problem based learning, theory of computation}, + annote={``Engaging and maintaining student engagement with the content of a +course in formal language theory and the theory of computation is +notoriously difficult. ``; +``students perception of the +relevance of the required mathematical material to computer science +as they have studied the discipline''; +``Students fail to appreciate the +relevance of the material due to its theoretical nature''; +`` the approach has been and remains +controversial, it nevertheless has proven effective in addressing the +problem of student engagement.''; + +8. REFERENCES +[1] Armoni, M., Rodgers, S., Vardi, M., and Verma, R. Automata +theory-its relevance to computer science students and course +content. ACM SIGCSE Bulletin, 38, 1 (March 2006), 197-198. +[2] Brookes, W. 2004. Computing theory with relevance. In +Proceedings of the Sixth Conference on Australasian +Computing Education - Volume 30 (Dunedin, New Zealand). +R. Lister and A. Young, Eds. ACM International Conference +Proceeding Series, vol. 57. Australian Computer Society, +Darlinghurst, Australia, 9-13. +[3] Chesevar, C., Cobo, M. and Yurcik, W. Using theoretical +computer simulators for formal languages and automata +theory. Inroads ACM SIGCSE Bulletin, 35, 2 (June 2003), +33-37. +[4] Cogliati, J., Goosey, F., Grinder, M., Pascoe, B., Ross, R., and +Willams, C. Realizing the promise of visualization in the +theory of computing. ACM Journal of Educational Resources +in Computing, 5, 2 (June 2005), Article No. 5. +[5] Gramond, E. and Rodgers, S. Using JFLAP to interact with +theorems in automata theory. ACM SIGCSE Bulletin, 31, 1 +(March 1999), 336-340. +[6] Grinder, M., Kim, S., Lutey, T., Ross, R., Walsh, K. Loving to +learn theory: active learning modules for the theory of +computing. ACM SIGCSE Bulletin, 34, 1, (Feb. 2002) , 371- +375. +[7] Hawkins, H. and Healy, C. Introducing practical applications +into a computational theory class. Journal of Computing +Sciences in Colleges, 20, 2 (Dec. 2004), 219 225. +[8] The Joint Taskforce on Computing Curricula. Computing +curricula 2001. IEEE Computer Society \& ACM., December +15, 2001. +[9] Jones, F. The Moore Method. American Mathematical +Monthly, 84 (Apr. 1977), 273-277. +[10] The Liberal Arts Computer Science Consortium. A 2004 model +for a liberal arts degree in computer science. February 2004. +[11] Parker, G. Getting more from Moore. Primus, 2 (Sept. 1992), +235-246. +[12] Verma, R. M. A visual and interactive automata theory course +emphasizing breadth of automata. In Proceedings of the 10th +Annual SIGCSE Conference on innovation and Technology in +Computer Science Education (Caparica, Portugal, June 27 - 29, +2005). ITiCSE '05. ACM Press, New York, NY, 325-329. +} +} + +@book{rogers1995becoming, + title={On becoming a person: A therapist's view of psychotherapy}, + author={Rogers, C.}, + year={1995}, + publisher={Mariner Books} +} + +@article{porter2013halving, + title={Halving Fail Rates using Peer Instruction: A Study of Four Computer Science Courses}, + author={Porter, L. and Bailey-Lee, C. and Simon, B.}, + year={2013} +} + +@inproceedings{koile2007supporting, + title={Supporting feedback and assessment of digital ink answers to in-class exercises}, + author={Koile, K. and Chevalier, K. and Rbeiz, M. and Rogal, A. and Singer, D. and Sorensen, J. and Smith, A. and Tay, K.S. and Wu, K.}, + booktitle={PROCEEDINGS OF THE NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE}, + volume={22}, + number={2}, + pages={1787}, + year={2007}, + organization={Menlo Park, CA; Cambridge, MA; London; AAAI Press; MIT Press; 1999} +} \ No newline at end of file diff --git a/literatureFIE.bib b/literatureFIE.bib new file mode 100644 index 0000000..7b99d91 --- /dev/null +++ b/literatureFIE.bib @@ -0,0 +1,646 @@ +@article{Simon:2012:PIT:2076450.2076459, + author = {Simon, Beth and Cutts, Quintin}, + title = {Peer instruction: a teaching method to foster deep understanding}, + journal = {Commun. ACM}, + issue_date = {February 2012}, + volume = {55}, + number = {2}, + month = feb, + year = {2012}, + issn = {0001-0782}, + pages = {27--29}, + numpages = {3}, + url = {http://doi.acm.org/10.1145/2076450.2076459}, + doi = {10.1145/2076450.2076459}, + acmid = {2076459}, + publisher = {ACM}, + address = {New York, NY, USA}, +} +@article{Simon:2012:IPI:2189835.2189858, + author = {Simon, Beth and Cutts, Quintin}, + title = {How to implement a peer instruction-designed CS principles course}, + journal = {ACM Inroads}, + issue_date = {June 2012}, + volume = {3}, + number = {2}, + month = jun, + year = {2012}, + issn = {2153-2184}, + pages = {72--74}, + numpages = {3}, + url = {http://doi.acm.org/10.1145/2189835.2189858}, + doi = {10.1145/2189835.2189858}, + acmid = {2189858}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {CS principles, computer science education, pedagogy, peer instruction}, +} +@article{wood2012role, + title={The Role of the Lecturer as Tutor: Doing What Effective Tutors Do in a Large Lecture Class}, + author={Wood, W.B. and Tanner, K.D.}, + journal={CBE-Life Sciences Education}, + volume={11}, + number={1}, + pages={3--9}, + year={2012}, + publisher={Am Soc Cell Biol} +} +@article{Smith01032011, +author = {Smith, M.K. and Wood, W.B. and Krauter, K. and Knight, J.K.}, +title = {Combining Peer Discussion with Instructor Explanation Increases Student Learning from In-Class Concept Questions}, +volume = {10}, +number = {1}, +pages = {55-63}, +year = {2011}, +doi = {10.1187/cbe.10-08-0101}, +abstract ={Use of in-class concept questions with clickers can transform an instructor-centered “transmissionist” environment to a more learner-centered constructivist classroom. To compare the effectiveness of three different approaches using clickers, pairs of similar questions were used to monitor student understanding in majors’ and nonmajors’ genetics courses. After answering the first question individually, students participated in peer discussion only, listened to an instructor explanation only, or engaged in peer discussion followed by instructor explanation, before answering a second question individually. Our results show that the combination of peer discussion followed by instructor explanation improved average student performance substantially when compared with either alone. When gains in learning were analyzed for three ability groups of students (weak, medium, and strong, based on overall clicker performance), all groups benefited most from the combination approach, suggesting that peer discussion and instructor explanation are synergistic in helping students. However, this analysis also revealed that, for the nonmajors, the gains of weak performers using the combination approach were only slightly better than their gains using instructor explanation alone. In contrast, the strong performers in both courses were not helped by the instructor-only approach, emphasizing the importance of peer discussion, even among top-performing students.}, +URL = {http://www.lifescied.org/content/10/1/55.abstract}, +eprint = {http://www.lifescied.org/content/10/1/55.full.pdf+html}, +journal = {CBE-Life Sciences Education} +} +@inproceedings{porter2011peer, + title={Peer instruction: do students really learn from peer discussion in computing}, + author={Porter, L. and Lee, C.B. and Simon, B. and Zingaro, D.}, + booktitle={Proceedings of the Seventh International Workshop on Computing Education Research. ACM}, + pages={45--52}, + year={2011} +} +@inproceedings{porter2011experience, + title={Experience report: a multi-classroom report on the value of peer instruction}, + author={Porter, L. and Bailey Lee, C. and Simon, B. and Cutts, Q. and Zingaro, D.}, + booktitle={Proceedings of the 16th annual joint conference on Innovation and technology in computer science education}, + pages={138--142}, + year={2011}, + organization={ACM} +} +@inproceedings{Zingaro2010x4, + author = { Daniel Zingaro }, + title = { Experience Report: Peer Instruction in Remedial Computer Science }, + booktitle = { Proceedings of World Conference on Educational Multimedia, Hypermedia and Telecommunications 2010 }, + year = { 2010 }, + month = { June }, + pages = { 5030--5035 }, + address = { Toronto, Canada }, + publisher = { AACE }, + url = { http://www.editlib.org/p/36184 } +} +@article{roediger2010benefits, + title={Benefits of testing memory: Best practices and boundary conditions.}, + author={Roediger III, H.L. and Agarwal, P.K. and Kang, S.H.K. and Marsh, E.J.}, + year={2010}, + publisher={Psychology Press} +} +@inproceedings{Simon:2010:ERP:1734263.1734381, + author = {Simon, Beth and Kohanfars, Michael and Lee, Jeff and Tamayo, Karen and Cutts, Quintin}, + title = {Experience report: peer instruction in introductory computing}, + booktitle = {Proceedings of the 41st ACM technical symposium on Computer science education}, + series = {SIGCSE '10}, + year = {2010}, + isbn = {978-1-4503-0006-3}, + location = {Milwaukee, Wisconsin, USA}, + pages = {341--345}, + numpages = {5}, + url = {http://doi.acm.org/10.1145/1734263.1734381}, + doi = {10.1145/1734263.1734381}, + acmid = {1734381}, + publisher = {ACM}, + address = {New York, NY, USA}, + keywords = {active learning, classroom response, clickers, cs1, peer instruction, prs}, +} +@misc{WiemanCRSGuide, +howpublished = {\url{http://www.cwsei.ubc.ca/resources/files/Clicker_guide_CWSEI_CU-SEI.pdf}}, +year=2010, +} +@misc{CMhw, +howpublished={\url{http://www.cs.cmu.edu/~flac/pdf/flac-intro-6up.pdf }}, +year=2011, +} +@article{Smith02012009, +author = {Smith, M. K. and Wood, W. B. and Adams, W. K. and Wieman, C. and Knight, J. K. and Guild, N. and Su, T. T.}, +title = {Why Peer Discussion Improves Student Performance on In-Class Concept Questions}, +volume = {323}, +number = {5910}, +pages = {122-124}, +year = {2009}, +doi = {10.1126/science.1165919}, +abstract ={When students answer an in-class conceptual question individually using clickers, discuss it with their neighbors, and then revote on the same question, the percentage of correct answers typically increases. This outcome could result from gains in understanding during discussion, or simply from peer influence of knowledgeable students on their neighbors. To distinguish between these alternatives in an undergraduate genetics course, we followed the above exercise with a second, similar (isomorphic) question on the same concept that students answered individually. Our results indicate that peer discussion enhances understanding, even when none of the students in a discussion group originally knows the correct answer.}, +URL = {http://www.sciencemag.org/content/323/5910/122.abstract}, +eprint = {http://www.sciencemag.org/content/323/5910/122.full.pdf}, +journal = {Science} +} +@article {BJET:BJET920, +author = {Draper, Stephen W.}, +title = {Catalytic assessment: understanding how MCQs and EVS can foster deep learning}, +journal = {British Journal of Educational Technology}, +volume = {40}, +number = {2}, +publisher = {Blackwell Publishing Ltd}, +issn = {1467-8535}, +url = {http://dx.doi.org/10.1111/j.1467-8535.2008.00920.x}, +doi = {10.1111/j.1467-8535.2008.00920.x}, +pages = {285--293}, +year = {2009}, +abstract = {One technology for education whose adoption is currently expanding rapidly in UK higher education is that of electronic voting systems (EVS). As with all educational technology, whether learning benefits are achieved depends not on the technology but on whether an improved teaching method is introduced with it. EVS inherently relies on the multiple-choice question (MCQ) format, which many feel is associated with the lowest kind of learning of disconnected facts. This paper, however, discusses several ways in which teaching with MCQs, and so with EVS, has transcended this apparent disadvantage, has based itself on deep learning in the sense of focusing on learning relationships between items rather than on recalling disconnected true–false items, and so has achieved substantial learning advantages. Six possible learning designs based on MCQs are discussed, and a new function for (e-)assessment is identified, namely catalytic assessment, where the purpose of test questions is to trigger subsequent deep learning without direct teaching input.}, +} +@article{bruff2008classroom, + title={Classroom Response Systems (Clickers)}, + author={Bruff, D.}, + journal={Center for Teaching}, + year={2008} +} +@misc{bruffURL, +author={Derek Bruff}, +howpublished ={\url{http://cft.vanderbilt.edu/teaching-guides/technology/clickers/}, +}} +@article {JCAL:JCAL133, +author = {Kennedy, G. E. and Cutts, Q. I.}, +title = {The association between students' use of an electronic voting system and their learning outcomes}, +journal = {Journal of Computer Assisted Learning}, +volume = {21}, +number = {4}, +publisher = {Blackwell Science Ltd}, +issn = {1365-2729}, +url = {http://dx.doi.org/10.1111/j.1365-2729.2005.00133.x}, +doi = {10.1111/j.1365-2729.2005.00133.x}, +pages = {260--268}, +keywords = {electronic voting system, engagement, interactivity, lectures}, +year = {2005}, +abstract = {Abstract + This paper reports on the use of an electronic voting system (EVS) in a first-year computing science subject. Previous investigations suggest that students' use of an EVS would be positively associated with their learning outcomes. However, no research has established this relationship empirically. This study sought to establish whether there was an association between students' use of an EVS over one semester and their performance in the subject's assessment tasks. The results from two stages of analysis are broadly consistent in showing a positive association between EVS usage and learning outcomes for students who are, relative to their class, more correct in their EVS responses. Potential explanations for this finding are discussed as well as modifications and future directions of this program of research.}, +} +@article{Purchase2004, +author={Helen C. Purchase and Christopher Mitchell and Iadh Ounis}, +title={Gauging Students Understanding Through Interactive Lectures}, +year={2004}, +journal={Lecture Notes in Computer Science, 3112} +} +@article{chi1996constructing, + title={Constructing self-explanations and scaffolded explanations in tutoring}, + author={Chi, M.T.H.}, + journal={Applied Cognitive Psychology}, + volume={10}, + number={7}, + pages={33--49}, + year={1996} +} +@book{Yin1994, +author={Robert K. Yin}, +title={Case Study Research, Design and Methods}, +edition=2, +publisher={Sage Publications}, +annote={ +This book is about case studies for research and publication, rather than for teaching in, e.g., law school. +The types of research question for which case study is the appropriate technique are those questions starting with ``How'', and ``Why'', so perhaps ``How did we figure out that the relevant items to students learning the pumping lemma include use of the contrapositive, and negation of statements using quantifiers?'', or ``Why didn't Makan learn the pumping lemma until now?'' +Case study adds direct observation and systematic interviewing to methods available with historical data (primary and secondary documents, cultural and physical artifacts). +Reviewing literature on a topic serves to develop sharper and more insightful questions on it. +from p.15: ``And, yes, case studies have a distinctive place in evaluation research (gives references). there are at least five different applications. The most important is to explain the causal links in real-life interventions that are too complex for the survey or experimental strategies. In evaluation language, the explanations would link program implementation with program effects. \\ +the case study strategy may be used to explore those siutation in which the intervention being evaluated has no clear, single set of outcomes.\\ +Case study research is remarkably hard.\\} +} + + + + + + + +@article {Denis, +author = {M Denis and E Mellet and S Kosslyn}, +title = {Neuroimaging of mental imagery: An introduction}, +journal = {Eur. J. Cognitive Psychol.}, +volume = {16}, +pages = {625}, +year = {2004} +} + +@article {Goldina, +author = {GA Goldin and C Janvier}, +title = {Representations and the psychology of mathematics education}, +journal = {J. Math. Behav.}, +volume = {17}, +pages = {1}, +year = {1998} +} + +@article {Goldinb, +author = {Goldin GA}, +title = {Representational systems, learning, and problem solving in mathematics}, +journal = {J. Math. Behav.}, +volume = {17}, +pages = {137}, +year = {1998} +} + +@article {corter, +author = {JE Corter and DC Zahner}, +title = {Use of external visual representations in probability problem solving}, +journal = {Stat. Educ. Res. J., International Association for Statistical Education (IASE/ISI)}, +volume = {6}, +pages = {22}, +year = {2007} +} + +@article {mesquita, +author = {Mesquita AL}, +title = {On conceptual obstacles linked with external representation in geometry}, +journal = {J. Math. Behav.}, +volume = {17}, +pages = {183}, +year = {1998} +} + + @article{BBloom1984, + jstor_articletype = {research-article}, + title = {The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring}, + author = {Bloom, Benjamin S.}, + journal = {Educational Researcher}, + jstor_issuetitle = {}, + volume = {13}, + number = {6}, + jstor_formatteddate = {Jun. - Jul., 1984}, + pages = {pp. 4-16}, + url = {http://www.jstor.org/stable/1175554}, + ISSN = {0013189X}, + abstract = {}, + language = {English}, + year = {1984}, + publisher = {American Educational Research Association}, + copyright = {Copyright 1984 American Educational Research Association}, + } + + @article{lasry:1066, +author = {Nathaniel Lasry and Eric Mazur and Jessica Watkins}, +collaboration = {}, +title = {Peer instruction: From Harvard to the two-year college}, +publisher = {AAPT}, +year = {2008}, +journal = {American Journal of Physics}, +volume = {76}, +number = {11}, +pages = {1066-1069}, +keywords = {educational courses; educational institutions; physics education; problem solving; teaching}, +url = {http://link.aip.org/link/?AJP/76/1066/1}, +doi = {10.1119/1.2978182} +} + +@article{hake:64, +author = {Richard R. Hake}, +collaboration = {}, +title = {Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses}, +publisher = {AAPT}, +year = {1998}, +journal = {American Journal of Physics}, +volume = {66}, +number = {1}, +pages = {64-74}, +keywords = {teaching; education; classical mechanics}, +url = {http://link.aip.org/link/?AJP/66/64/1}, +doi = {10.1119/1.18809} +} + +@book{HINTIKKA, +author={Jaakko Hintikka}, +title={Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning}, publisher={Cambridge University Press}, +year= 2007} + +@book{Mattuck, +author={Arthur Mattuck}, +title={Introduction to Analysis}, +publisher={Prentice Hall}, +year=1999} + +@book{Sipser, +author={Michael Sipser}, +title={Introduction to the Theory of Computation}, +publisher={Cengage}, +year=2013} +@misc{fpo, +author={Carlos Ivan Chesnevar and Ana Gabriela Maguitman and Maria Paula Gonzalez and +Maria Laura Cobo }, +title={Teaching fundamentals of computing theory: a constructivist approach.}, +publisher={Journal of Computer Science and Technology}, +howpublished={\url{http://www.freepatentsonline.com/article/Journal-Computer-Science-Technology/146892302.html}}} + +@article{crouch2001peer, + title={Peer instruction: Ten years of experience and results}, + author={Crouch, C.H. and Mazur, E.}, + journal={American Journal of Physics}, + volume={69}, + pages={970}, + year={2001} +} + +@book{meyers1993promoting, + title={Promoting Active Learning. Strategies for the College Classroom.}, + author={Meyers, C. and Jones, T.B.}, + year={1993}, + publisher={ERIC} +} + +@book{Velleman, + title={How to Prove It}, + author={Daniel J. Velleman}, + year={1998 }, + publisher={Cambridge University Press} +} + +@article{PETbrainmath, +author={Brian Butterworth}, +title={What makes a prodigy?}, +year=2001, +journal={Nature Neuroscience}, +volume=4, +number=1, +url={\url{http://www.mathematicalbrain.com/pdf/PRODIGY.PDF}} +} + +@article{ScienceDaily, +author={Denise C. Park}, +title={Math ability requires crosstalk in the brain.}, +year=2012, +journal={ScienceDaily}}%contains journal reference + +@article{SA2012, +journal={Scientific American}, + pages={26 - 33}, + year=2012, + title={Sex, Math and Scientific Achievement}, + author={Diane F. Halpern and Camilla P. Benbow and David C. Geary and Ruben C. Gur and Janet Shibley Hyde and Morton Ann Gernsbacher}} + + @article{Maloney2012380, +title = "Reducing the sex difference in math anxiety: The role of spatial processing ability", +journal = "Learning and Individual Differences", +volume = "22", +number = "3", +pages = "380 - 384", +year = "2012", +note = "", +issn = "1041-6080", +doi = "10.1016/j.lindif.2012.01.001", +url = "http://www.sciencedirect.com/science/article/pii/S1041608012000027", +author = "Erin A. Maloney and Stephanie Waechter and Evan F. Risko and Jonathan A. Fugelsang", +keywords = "Math anxiety", +keywords = "Sex effects", +keywords = "Spatial processing" +} + +@article{rivera2012neural, + title={Neural Correlates of Gender, Culture, and Race and Implications to Embodied Thinking in Mathematics}, + author={Rivera, F.}, + journal={Towards Equity in Mathematics Education}, + pages={515--543}, + year={2012}, + publisher={Springer} +} + +@article{tomasi2012gender, + title={Gender differences in brain functional connectivity density}, + author={Tomasi, D. and Volkow, N.D.}, + journal={Human brain mapping}, + volume={33}, + number={4}, + pages={849--860}, + year={2012}, + publisher={Wiley Online Library} +} +@article{horwitz2012introduction, + title={Introduction to Research Topic--Brain Connectivity Analysis: Investigating Brain Disorders. Part 1: The Review Articles}, + author={Horwitz, B. and Horovitz, S.G.}, + journal={Frontiers in systems neuroscience}, + volume={6}, + year={2012}, + publisher={Frontiers Media SA} +} + +@article{tall2012cognitive, + title={Cognitive Development of Proof}, + author={Tall, D. and Yevdokimov, O. and Koichu, B. and Whiteley, W. and Kondratieva, M. and Cheng, Y.H.}, + journal={Proof and Proving in Mathematics Education}, + pages={13--49}, + year={2012}, + publisher={Springer} +} + +@inbook{bloom40retro, +author={Lorin Anderson and Lauren Sosniak}, +title={Excerpts from the ``Taxonomy of Education Objectives, The Classification of Educational Goals, Handbook I: Cognitive domain''}, +booktitle={Bloom's Taxonomy A Forty-year Retrospective}, +publisher={University of Chicago Press}, +year=1994, +chapter={II}, +pages={9-27} +} + +@misc{diagramsReasoning, +howpublished={\url{http://web.archive.org/web/20110721195349/http://www.ed.uiuc.edu/eps/PES-Yearbook/1998/lomas.html}}, +title={Diagrams in Mathematical Education: A Philosophical Appraisal}, +author={Dennis Lomas} +} + + @article{arnoux2010using, + title={Using mental imagery processes for teaching and research in mathematics and computer science}, + author={Arnoux, P. and Finkel, A.}, + journal={International Journal of Mathematical Education in Science and Technology}, + volume={41}, + number={2}, + pages={229--242}, + year={2010}, + publisher={Taylor \& Francis}, + abstract={Abstract +The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We give two detailed examples.} +} + +%[12] P. Thompson, Imagery and the development of mathematical reasoning, in Theories of Learning Mathematics, Erlbaum, Hillsdale, NJ, 1996, pp. 267283., from arnoux +%Paivio + +@article{pillay2010learning, + title={Learning difficulties experienced by students in a course on formal languages and automata theory}, + author={Pillay, N.}, + journal={ACM SIGCSE Bulletin}, + volume={41}, + number={4}, + pages={48--52}, + year={2010}, + publisher={ACM} +} +@inproceedings{rodger2009increasing, + title={Increasing engagement in automata theory with JFLAP}, + author={Rodger, S.H. and Wiebe, E. and Lee, K.M. and Morgan, C. and Omar, K. and Su, J.}, + booktitle={ACM SIGCSE Bulletin}, + volume={41}, + pages={403--407}, + year={2009}, + organization={ACM} +}% number={1}, + +@inproceedings{rodger2007increasing, + title={Increasing interaction and support in the formal languages and automata theory course}, + author={Rodger, S.H. and Lim, J. and Reading, S.}, + booktitle={ACM SIGCSE Bulletin}, + volume={39}, + pages={58--62}, + year={2007}, + organization={ACM} +}% number={3}, +@book{linz2011introduction, + title={An introduction to formal languages and automata}, + author={Linz, P.}, + year={2011}, + publisher={Jones \& Bartlett Learning} +} +@misc{CBL, +author={Cynthia Bailey-Lee}, +howpublished={\url{http://www.peerinstruction4cs.org/}}} + +@inproceedings{huttel2012experiences, + title={Experiences with web-based peer assessment of coursework}, + author={H{\"u}ttel, H. and N{\o}rmark, K.}, + booktitle={Proceedings of the 4th International Conference on Computer Supported Education-CSEDU}, + year={2012} +} +@inproceedings{vijayalaskhmi2012activity, + title={Activity based teaching learning in formal languages and automata theory-An experience}, + author={Vijayalaskhmi, M. and Karibasappa, KG}, + booktitle={Engineering Education: Innovative Practices and Future Trends (AICERA), 2012 IEEE International Conference on}, + pages={1--5}, + year={2012}, + organization={IEEE} +} +@article{xing2010graphical, + title={A graphical framework for assisting proofs}, + author={Xing, C.C.}, + journal={Journal of Computing Sciences in Colleges}, + volume={25}, + number={5}, + pages={48--57}, + year={2010}, + publisher={Consortium for Computing Sciences in Colleges} +} + +@inproceedings{dharaneetharan2011alternative, + title={An alternative approach of Pumping Lemma to prove a language to be non regular}, + author={Dharaneetharan, GD and Raj, VB and Devi, RK}, + booktitle={Recent Trends in Information Technology (ICRTIT), 2011 International Conference on}, + pages={1078--1080}, + year={2011}, + organization={IEEE} +} + +@article{steffen2011introduction, + title={Introduction to active automata learning from a practical perspective}, + author={Steffen, B. and Howar, F. and Merten, M.}, + journal={Formal Methods for Eternal Networked Software Systems}, + pages={256--296}, + year={2011}, + publisher={Springer} +} +@inproceedings{zander2009student, + title={Student transformations: are they computer scientists yet?}, + author={Zander, C. and Boustedt, J. and McCartney, R. and Mostr{\"o}m, J.E. and Sanders, K. and Thomas, L.}, + booktitle={Proceedings of the fifth international workshop on Computing education research workshop}, + pages={129--140}, + year={2009}, + organization={ACM} +} + +@article{meyer2006threshold, + title={Threshold concepts and troublesome knowledge}, + author={Meyer, J.H.F. and Land, R.}, + journal={Overcoming Barriers to Student Learning: Threshold concepts and troublesome knowledge.}, + pages={19}, + year={2006}, + publisher={Routledge} +} + + +@inproceedings{simon2010experience, + title={Experience report: peer instruction in introductory computing}, + author={Simon, B. and Kohanfars, M. and Lee, J. and Tamayo, K. and Cutts, Q.}, + booktitle={Proceedings of the 41st ACM technical symposium on Computer science education}, + pages={341--345}, + year={2010}, + organization={ACM} +} + +@inproceedings{pargas2006things, + title={Things are clicking in computer science courses}, + author={Pargas, R.P. and Shah, D.M.}, + booktitle={ACM SIGCSE Bulletin}, + volume={38}, + number={1}, + pages={474--478}, + year={2006}, + organization={ACM} +} +@inproceedings{chase2000combining, + title={Combining cooperative learning and peer instruction in introductory computer science}, + author={Chase, JD and Okie, E.G.}, + booktitle={ACM SIGCSE Bulletin}, + volume={32}, + number={1}, + pages={372--376}, + year={2000}, + organization={ACM} +} + + +@article{bateman2007applying, + title={Applying collaborative tagging to e-learning}, + author={Bateman, S. and Brooks, C. and McCalla, G. and Brusilovsky, P.}, + journal={Proc. of ACM WWW}, + volume={3}, + number={4}, + year={2007} +} +@techreport{morgan1997technology, + title={Technology and Bloom's taxonomy: tools to facilitate higher-level learning in chemistry}, + author={Morgan, M.E.}, + year={1997}, + institution={DTIC Document} +} +@inproceedings{hamalainen2004problem, + title={Problem-based learning of theoretical computer science}, + author={H\"{a}m\"{a}l\"{a}inen, W.}, + booktitle={Frontiers in Education, 2004. FIE 2004. 34th Annual}, + pages={S1H--1}, + year={2004}, + organization={IEEE} +} + +@phdthesis{weidmann2003science, + title={Science Education Perceptions of Teaching and Learning Automata Theory in a College- Level Computer Science Course a thesis}, + author={Weidmann, P.K.}, + year={2003}, + school={The University of Texas at Austin} +} + +@book{Constructionism, +editor={Idit Harel and Seymour Papert}, +title={Constructionism}, +year=1991, +publisher={Ablex Publishing}} + +@inbook{PHfractions, +author={Seymour Papert and Idit Harel}, +title={Software Design as a Learning Environment}, +booktitle={Constructionism}, +chapter={4}, +year=1991, +publisher={Ablex Publishing}} + +@article{baeten2010models, + title={Models of computation: automata and processes}, + author={Baeten, JCM}, + journal={Technische Universiteit Eindhoven, Syllabus 2IT15}, + year={2010} +} +@book{devlinintro, +author={Keith Devlin}, +title={Introduction to Mathematical Thinking}, +publisher={Keith Devlin}, +year=2012} + +} + + + \ No newline at end of file diff --git a/literatureQualRes.bib b/literatureQualRes.bib new file mode 100644 index 0000000..f21222c --- /dev/null +++ b/literatureQualRes.bib @@ -0,0 +1,861 @@ +@article{kinnunen2012phenomenography, +title={Phenomenography and grounded theory as research methods in computing education research field}, +author={Kinnunen, P{}ivi and Simon, Beth}, +journal={Computer Science Education}, +volume={22}, +number={2}, +pages={199--218}, +year={2012}, +publisher={Taylor \& Francis} +} + +@book{2007Creswell, +author={Creswell}, +title={Qualitative Inquiry and Research Design, Choosing Among Five Approaches}, +edition=2, +year=2007, +publisher={Thousand Oaks, CA: Sage}} +@book{2009Creswell, +author={Cresswell}, +title={Research design: Qualitative, Quantitative, and Mixed Methods Approaches}, +edition=3, +year=2009, +publisher={Thousand Oaks, CA: Sage}, +annote={}} +@book{2003Creswell, +author={Creswell}, +title={Research design: Qualitative, Quantitative, and Mixed Methods Approaches}, +edition=2, +year=2003, +publisher={Thousand Oaks, CA: Sage}, +annote={useful checklist of questions for designing qualitative procedure, +includes\\ +basic characterestics of qual studies\\ +is specific type of qualitative strategy of inquiry to be used in the study mentioned?\\ +Is the history of, a definition of, and applications for the strategy mentioned?\\ +does the reader gain an understanding of the researcher's role in the study (past experiences, personal connections to sites and people, steps in gining entry and sensitive ethical issues)?\\ +Is the purposeful sampling strategy for sites and individuals identified?\\Are the specific forms of data collection mentioned and a rationale given for their use?\\ +Are the prodcuedres for recording infomration (such as protocols) during the data collection producere mentioned?\\ +are the data analysis setps identified?\\ +is there evidence that the researcher has organized the data for analysis?\\ +Has the researcher reviewed thedata generally to obtain a sense of the information?\\ +has coding been used with the data?\\ +have the codes been developed to forma description or to identiy themes?\\ +are the themes interrelated to show a higher level of analysis and abstraction?\\ +are the ways that the data will be represened--such as tables, graphs and figures--mentioned?\\ +have the bases for interpreting the analysis (personal experience, the literature, questions, action agenda) been specified?\\ +has the researcher mentioned the outcome of the study? (develop a theory? provide a complex picture of themes?)\\ +Have multiple strategies been cited for validating the findings?\\ +}} + +%[Tiefel 2005] Tiefel, Sandra: Kodierung nach der Grounded Theory lern- und bildungstheoretisch +%modifiziert: Kodierleitlinien fur die Analyse biographischen Lernens. +%In: Zeitschrift fur qualitative Bildungs-, Beratungs- und Sozialforschung 6 (2005), Nr. 1, +%S. 6584 +@article{Tiefel, +author={Sandra Tiefel}, +title={Kodierung nach der Grounded Theory lern- und bildungstheoretisch +modifiziert: Kodierleitlinien f\"ur die Analyse biographischen Lernens}, +journal={Zeitschrift f\"ur qualitative Bildungs-, Beratungs- und Sozialforschung}, +volume=6, +number=1, +pages={64-85}, +year=2005, +annote={}} + +@book{Vygotsky, +title={The Collected Works of L. S. Vygotsky}, +author={L. S. Vygotsky}, +year=1999, +publisher={Kluwer}, +annote={}} + +@article{YamagataLynch2003, +title={Using Activity Theory as an Analytic Lens for Examining Technology Professional Development in Schools}, +author={Lisa C. Yamagata-Lynch}, +year=2003, +journal={Mind, Culture and Activity}, +page={100-119}, +annote={ +this paper is beautifully written. + +Vygotsky was with Piaget one of the first to use constructivist epistemology\\ +semiotic process includes situations in which people learn as they interact with each other and a mediating artifact-tool, (Isay seems to match with computer) and people interact with the tool, mediated action + +She writes }} + + +@inbook{GubaLincoln1994, +author={E. G. Guba and Y. S. Lincoln}, +title={Competing paradigms in qualitative research}, +booktitle={Handbook of qualitative research}, +publisher={Thousand Oaks, CA: Sage}, +pages={105-117}, +year=1994} + +@article{Charmaz, +author={Charmaz}, +annote={}} + +%from Caelli +@inbook{1997Thorne, +author={Thorne}, +title={the art (and science) of critiquing qualitative research}, +booktitle={Completing a qualitative project: Details and dialogue}, +year=1997, +pages={117-132}, +publisher={Thousand Oaks, CA: Sage}, +annote={}} + +@article{2000Sandelowski, +author={Sandelowski}, +year=2000, +title={Focus on research methods: Whatever happened to qualitative description?}, +journal={Research in Nursing and Health}, +number=23, +pages={334-340}, +annote={}} + +@book{Kvale, +author={S. Kvale}, +title={InterViews: An introduction to qualitative research interviewing}, +publisher={Thousand Oaks, CA: Sage}, +year=1996, +annote={}} + +@book{LincolnGuba, +author={Lincoln and Guba}, +title={Naturalistic Inquiry}, +year=1985, +publisher={Newbury Park, CA: Sage}, +annote={}} + +@book{Silverman, +author={D. Silverman}, +title={Doing qualitative research: A practical handbook}, +year=2000, +publisher={Thousand Oaks, CA: Sage}, +annote={}} + +%from Caelli, about methodology +@book{vanManen1998, +author={M. van Manen}, +title={Researching Lived Experience: Human science for an action sensitive pedagogy}, +year=1998, +publisher={London, Canada: The Althouse Press}, +annote={}} + +@article{Rawnsley1998, +author={M. M. Rawnsley}, +title={Ontology, epistemology, and methodology: A clarification}, +journal={Nursing Science Quarterly}, +year=1998, +volume=11, +number=1, +pages={2-4}} + +@article{King1995, +author={K. E. King}, +title={Method and methodology in feminist research: What is the difference?}, +journal={Journal of Advanced Nursing}, +year=1995, +volume=20, +pages={19-22}} +@book{Creswell2012, +author={John W. Creswell}, +title={Educational Research Planning, Conducting and Evaluating Quantitative and Qualitative Research}, +year=2012, +edition=4, +publisher={Pearson}, +annote={}} + +@book{StraussCorbin, +author={Anselm Strauss and Juliet Corbin}, +title={Grounded Theory in Practice}, +year=1997, +publisher={Sage: Thousand Oaks}, +annote={}} + +@book{Crotty, +author={Michael Crotty}, +title={The Foundations of Social Research Meaning and Perspective in the Research Process}, +year=1998, +publisher={Sage: Thousand Oaks}, +annote={scaffold, framework for guidance, ``bewilderment at the array of methodologies and methods laid out before their gaze'', ``terminology is far from consistent in research literature and social science texts. One frequently finds the same term used in a number of different, sometimes even contradictory, ways.'' +What methodologies and methods will we employ, and how do we justify those?\\ +We need a process that can answer our questions.\\ +More: reaches to the assumptions about reality that we make. +What kind of knowledge do we believe will be attained. +Research outcomes: how should observers regard?, take seriously? These are epistemological questions. +What methods do we propose to use:\\ +What methodology governs our choice and use of methods?\\ +What theoretical perspective lies behind the methodology in question?\\ +What epistemology informs this theoretical perspective?\\ +Ethnography: a methodology\\ +Symbolic interactionism: a theoretical perspective\\ +constructionism: an epistemology (way of understanding how we know what we know)\\ +epistemology informs the theoretical perspective that informs the methodology that informst the methods\\ +Epistemologies:usually one of: objectivism, constructionism, subjectivism\\ +Research methods: concrete techniques, described in detail with examples +Methodology: our strategy or plan, our research design, describing choice and use of methods and the links to desired outcomes\\ +Theoretical perspective\\ +philosophical stance behind our chosen methodology\\ +how it provides a context for our process\\ +how it provides a basis for the logic and the criteria\\ +state the assumptions we bring, and incorporate into methodology\\ +our view of the world and the social life within it\\ +Ontology is the study of being\cite{Crotty}, with what entities exist.\\ +consistently constructivist, because we do not believe that all understandings, scientific and non-scientific alike are on the same footing as constructions. \\ +in our observing, interpreting, reporting and everything we do as researchers, we inject assumptions\\ +Has the very nice table 1, with a representative sampling of each category, not exhaustive\\ +Epistemologies\\ +Objectivism, Constructionism, Subjectivism, and their variants.\\ +Theoretical frameworks, theoretical perspectives\\ +Postivism and postpostivism, interpretivism, having these three subdivisions: symbolic interactionism, phenomenology and hermeneutics (which could be remembered as many people, one person, no people), then another theoretical perspective is critical inquiry, another is feminism, postmodernism and more.\\ +Methodologies:\\ +Experimental research\\ +Survey research\\ +Ethnography\\ +Phenomenological research\\ +Grounded theory\\ +Heuristic inquiry\\ +Action research\\ +Discourse Analysis\\ +Feminist standpoint research, etc.\\ +Now for methods:\\ +Sampling\\ +Measurement and scaling\\ +Questionnaire\\ +Observation, with participant and non-participant subdivisions\\ +Interview\\ +Focus group\\ +Case study\\ +Life history\\ +Narrative\\ +Visual ethnographic methods\\ +Statistical analysis\\ +Data reduction\\ +Theme identification\\ +Cooperative analysis\\ +Cognitive mapping\\ +Interpretive methods\\ +Document analysis\\ +Content analysis\\ +Conversational analysis, etc.\\ +}} + +@book{Grbich, +author={C. Grbich}, +title={Qualitative Data Analysis: An introduction}, +publisher={Thousand Oaks, Sage}, +year=2007, +annote={}} + +@book{Wolcott, +author={H. F. Wolcott}, +title={Writing up qualitative research}, +edition=3, +publisher={Thousand Oaks, Sage}, +year=2009, +annote={}} + +@book{Patton, +author={M. Q. Patton}, +title={Qualitative research and evaluation methods}, +edition=3, +publisher={Thousand Oaks, Sage}, +year=2002, +annote={}} + +@book{MilesH, +author={M. B. Miles and A. Huberman}, +title={Qualitative data analysis: A source book of new methods}, +edition=2, +publisher={London: Sage}, +year=1994, +annote={}} + +@book{Merriam2002, +author={Sharan B. Merriam}, +title={Qualitative Research in Practice}, +year=2002, +publisher={Jossey-Bass}, +annote={\begin{itemize} +\item Problem +\begin{itemize} +\item Is the problem appropriate for qualitative inquiry? +Is the question one of meaning, understanding, or process? +\item Is the problem clearly stated? +\item Is the problem situated in the literature? That is, is the literature used to put the problem in context? +\item Is the relationship of the problem to previous research made clear? +\item Is the researcher's perspective and relationship to the problem discussed? +Are assumptions and biases revealed? +\item Is a convincing argument explicitly or implicitly made for the importance or significance of this research? Do we know how it will contribute to the knowledge base and practice? +\end{itemize} +\item Methods +\begin{itemize} +\item Is the particular qualitative research design identified and described (basic interprestive, grounded theory, phenomenology, ethnography, and so on)? +\item Is sample selection described including rationale for criteria used in the selection? +\item Are data collection methods described and are they congruent with the problem being investigated and the type of qualitative design? +\item How were the data managed and analyzed'? +\item What stragegies were used to ensure for validity and reliability? +\item What ethical considerations are discussed? +\end{itemize} + +\item Findings +\begin{itemize} +\item Are the participants of the study descirbed? (This may be in Methods.) +\item Are the findings clearly organized and easy to follow? +\item Are the findings directly responsive to the problem of the study? that is, do they ``answer'' the question(s) raised by the study? +\item Do the data presented in support of the findings (quotatios from interviews, incidents from field notes, material from documents, and so on) provide adequate and convincing evidence for the findings? +\end{itemize} + +\item Discussion +\begin{itemize} +\item Are the findings ``positioned'' and discussed in terms of the literature and previous research? +\item Are the study's insights and contributions to the larger body of knowledge clearly stated and discussed: +\item Are implications for practice discussed? +\item Do the study's implications follow from the data? +\item Are there suggestions for future research? +\end{itemize} +\end{itemize}}} + +@article{Seale1999, +author={C. Seale}, +title={Quality in qualitative research}, +journal={Qualitative Inquiry}, +year=1999, +volume=5, +number=4, +pages={465-478}, +annote={Think of social research as a craft skill. +Learn it by reading from any of many sources, and by watching others perform. +Recognize quality (i.e., good work) when we see it. +Triangulation is helpful. +achieving validity and reliability are goals, want to see connection between social research, theory and philosophy (this last because underpinning of social research), +so philosophy can have value, but does not have to be governing. +Over time( 1980's-1990's) ``bewildering variety'' of new concepts about validity +for qual. research, ``conceptual proliferation'', Lincoln and guba 1985, trustworthiness from 4: truth value, applicability, consistency and neutrality.\\ +vs. mulitple constructed realities,\\ +The above being criticized, the following are suggested:\\ +concern with credibility, member checking, transferability rather than applicability, +dependability instead of consistency,\\ +auditing (self-criticism) instead of consistency\\ +auditng also for confirmability, which is instead of neutrality or objectivity\\ +Is there really a conflict between multiple constructed realities and single tangible reality.\\ +Add authenticity, by representing a range of different realities.\\ +``The issue of quality criteria in constructivism is \ldots not well resolved, and further critique is needed''. +Philosophy: inconclusive, but claimed as foundational.\\ +Partial solution: an approach to social research that takes the view that, although we always perceive the world from a particular viewpoint, the world acts back on us to constrain the points of view that are possible. The researcher treading this middle way is continually aware of the somewhat constructed nature of research but avoids the wholesale application of constructivism to his or her own practice, which would result in a descent into nihilism. \ldots some accounts are more plausible than others \ldots plausibility can be judged \ldots +How dhoulf we make contact with an external reality that affirms or disaffirms claims? Is not all observation funcamentally driven by preexisting theoretical assumptions? Subtle realism seems inadequate \ldots foundationalist habit of thought which I believe researchers should break.\\ +validity and reiability no longer seem adequate \ldots peer auditing \ldots expose to a critical readership the judgements and methodological decisions made in the course of the research study.\\ +craft skill: triangulation\\ +use of several methods at once so that biases of any one method might be cancelled out by those of others (Denzin, -70's and onwards\\ +``has no relevance for genuine interpretivists''(Blaikie)\\ +vs. not necessary to connect with ontological and epistemological positions\\ +``How can we reliably reason that the basis of past experience that the sun will rise tomorrow?''\\ +triangulation as constructivist: way of explaining how accounts or actions in one setting (I say: viewpoint) are influenced or constrained in the other\\ +soft constructivist version of triangulation: triangulation is less a strategy for validating than an alternative to validation, \ldots which increases scope, depth and consistency\\ +triangulation is good for enhancing quality \ldots craft skill\\ +possible to benefit from just about any of the key methodological discussions\\ + + +}} + +@book{Merriam2009, +author={Sharan B. Merriam}, +title={Qualitative Research A Guide to Design and Implementation}, +year=2009, +publisher={Jossey-Bass}, +annote={}} + +@book{Creswell2007, +author={J. W. Creswell}, +title={Qualitative Inquiry \& Research Design: Choosing among five approaches}, +edition=2, +pages={15-33}, +year=2007, +publisher={Sage, Inc., US}, +annote={begins with philosophical assumptions, also researcher's own world view, paradigms, sets of beliefs,\\ +Creswell wants to bridge philosophy and practice. +five philosophical assumptions lead to an individual's choice of qualitative research:\\ +ontology (nature of reality)\\ +epistemology (how we know what we know) get close to the participants\\ +axiology (the role of values in research)(values that shape the narrative, e.g., education is good), so, report your values and biases\\ +rhetorical assumptions (the language of research: use first person, literary, informal limited definitions)\\ +methodological assumptions (methods used in the process, inductive, emerging)\\ +Then there are paradigms for research (for making claims about knowledge), lots, change with time, but note these four:\\ +postpositivism--scientific approach, reductionist, logical, collect data, seek cause-effect, a priori use of theory\\ +constructivism--participants have subjective meanings of their experiences, inquirers do not start from theory, they inductively develop theory , e.g. Crotty, Charmaz, participants develop their subjective meanings in conversations, researcher trying to make sense of the meanings that the participants have constructed\\ +advocacy/participatory --where constructivism does not advocate action, and postpositivism fails to consider these people, power relationships, create a political debate/discussion so to effect change\\ +pragmatism--freedom to choose, mixed methods, choose what and how to research based upon where they want to do with their research\\ +There are theoretical frameworks (interpretive communities, inform procedures)\\ +postmodern theories\\ +feminist research\\ +critical theory, critical race theory\\ +queer theory\\ +disability inquiry\\ + + +} +} +@article{Kawulich, +author={B. B. Kawulich}, +year=2005, +month={May}, +title={Participant observation as a data collection method}, +journal={Forum: Qualitative Social Research}, +volume= 6, +number=2, +annote={} +} + +@article{Roulston2003, +author={K. Roulston and K. deMarrais and J. B. Lewis}, +year=2003, +title={Learning to interview in the social sciences}, +journal={Qualitative Inquiry}, +volume=9, +number=4, +pages={643-668}, +annote={} +} + +@article{Caelli, +author={Kate Caelli and Lynne Ray and J. Mill}, +year=2003, +title={'Clear as mud''' Toward greater clarity in generic qualitative research}, +journal={International Journal of Qualitative Methods}, +howpublished={\url={https://ejournals.library.ualberta.ca/index.php/IJQM/article/viewArticle/4521}}, +annote={concerned about how to do a (generic qualitative) study well, +especially if the work is not according to an established qualitative approach\\ +generic studies are common and will continue\\ +infeasible for researchers to engage in deeply theoretical and methodologically sophisticated study\\ +seek to discover and understand a phenomenon, a process of the perspectives and worldviews of the people involved(p.11), Merriam 1998, cited in Caeli\\ +many generic qual: a sparse understanding of the importance of an epistemological or theoreical position from which to begin research\\ +processes are of necessity rigorous, demanding and meticulous, must be scrupulously applied throughout\\ +Thorne: more interpretive, Sandelowski, less interpretivem more descriptive\\ +want quality criteria that apply specifically to generic qualitative approaches\\ +What needs to be there, for generic research to be credible (as qualitative)?\\ +cites Sandelowski and Barroso as proposing shift from epistemology to aesthetic and rhetorical concerns\\ +responsibility for laying out the merits of a particulary study lies with the author, enough detail so that the reader can judge\\ +research reports must address:\\ +the theoretical positioning of the researcher\\ +congruence between methodology and methods\\ +strategies to establish rigor\\ +analytic lens through which data are examined\\ +researchers should speak about the research and the approach and the methods chosen to explore the topic\\ +researchers should specify their disciplinary affiliation\\ +methodology reflects the beliefs about knowledge and existence that arise from the values in the philosophic framework that is to be employed (van Manen 1998)\\ +Methodology also reflects theoretical frameworks that guide how the research should proceed, +(according to Rawnsley 1998, King 1995, Guba and Lincoln 1994, Harding 1987) +clear recognition of the values and assumptions inherent in the theoretical framework\\ +BAD:lack of methodological clarity\\ +researchers need to articular a knowledgable, theoretically informed choice regarding their approach to rigor and slect an approach that is philosophically and methodologically congruent with their inquiry. Researchers approache to these two issues must reflect an understanding that rigor is deeply theoretical issue, not a technical one.\\ +We use the term ``analytic lens'' to refer to the methodologic and interpretive presuppositions that a researcher brings to bear on his or her data.\\ +the analytic lens is about how the researcher engages with his or her data\\ +closely examine the assumptios they bring to bear on the study, and explain them in any manuscript\\ +the study should be contiguous to the positions and assumptions that led to the research question\\ +it is only through understanding these elements that the quality of a study can be evaluated.\\ +The researcher's position is of utmost importance, must make assumptions clear, ensure methods are congruent +to assumptions, especially when borrowing methods from established approaches, because these methods can +have attached a deeply theoretical whole, and their use implies allegiance to a set of assumptions, +which the borrower might contravene, or ignore, making hard for reviewers, don't be claiming things, like ``saturation'', without inquiring into the real definition. Don't be claiming approach wihtout the methodological depth and interpretation that go with that method. \\ +Thematic analysis might add not at all to an understanding of the topic of interest, e.g., identifying themes without taking research to next step to show meaning beyond the themes, and it is the meanings that need to be embedded into the theoretical and historical context of the research. + +key issues 1 declaration of researcher's position\\ +2 congruence between methodology and method\\ +3 clear articulation of the researcher's approach to rigor\\ +4 explanation of his or her analytic lens +} +} + +@article{Cary1999, +author={L. J. Cary}, +title={Unexpected stories: Life history and the limits of representation}, +journal={Qualitative Inquiry}, +year=1999, +volume=5, +number=3, +pages={411-427}, +annote={} +} + + @inbook{Belize, +author={K. Altork}, +title={You never know when you might be a red head in Belize}, +booktitle={Inside Stories: Qualitative Research Reflections}, +publisher={Lawrence Erlbaum Associates}, +year=1998, +pages={111-126}, +annote={This is about the researcher promising a participant, who trusts the researcher, having known her for 15 years, not to make her sound bad, repeatedly, and then making he sound as if she were under the influence of too much alcohol, and mentioned a breakup with a lover, and also did not recheck her data often enough, and embroidered it, entertainingly but it was false.\\ +ethical considerations, improve without fictionalizing}} + +@article {JCOP:JCOP20074, +author = {Arcidiacono, Caterina and Procentese, Fortuna}, +title = {Distinctiveness and sense of community in the historical center of Naples: A piece of participatory action research}, +journal = {Journal of Community Psychology}, +volume = {33}, +number = {6}, +publisher = {Wiley Subscription Services, Inc., A Wiley Company}, +issn = {1520-6629}, +url = {http://dx.doi.org/10.1002/jcop.20074}, +doi = {10.1002/jcop.20074}, +pages = {631--638}, +year = {2005}, +abstract = {Inspired by the impact of an increase in tourism in the Old Center of Naples, Fondazione Laboratorio Mediterraneo, a nonprofit organization that promotes sustainable town development and encourages participation, has undertaken the participatory action research described in this article. The inhabitants' sense of community (McMillan \& Chavis, 1986) with regard to the distinctiveness of the area (Puddifoot, 1995) and its representation are also explored. The collection of socioenvironmental data (Arcidiacono, 1999), 15 semistructured interviews with key people, and photodialogue (Legewie, 2003) are followed by relational activities carried out together with local inhabitants and group associations in the area. The inductive analysis of the established categories and networks has been carried out with the aid of Atlas.ti. Our findings emphasize that the distinctiveness of the Center and the pride of belonging felt by its inhabitants are expressed ambivalently and negatively, evidence of the inhabitants' lack of a sense of community. }, +annote={Nice statement about grounded theory:\\ +When speaking of theory, we do not mean formal theory but substantive theory, theory derived inductively from the study of the phenomenon (i.e., explanation and interpretation of a specific phenomenon whose peculiarity is that it is constructed as a theory). +This is nicer than Pomrenke, because it elaborates the type of interpretation of a phenomenon to make clear that the explanation about a phenomenon is a theory about that phenomenon. +They developed macrocategories, relations and networks among categories, } +} + + @article{Pomrenkec, +author={Marlene Pomrenke}, +title={Using Grounded Theory to Understand Resiliency in Pre-Teen Children of High-Conflict Families}, +journal={Qualitative Report}, +volume=12, +number=3, +year=2007, +pages={356-374}, +annote={ Then a proposition is formed from the coding paradigm. It provides a broader systemic view of the information gained through the study. the example given in the paper is a finding, saying in effect that coherence in families helps children be resilient, which takes the research question and answers it with the word coherence, defining that as blending, extending, adapting. It also takes the word community from the research question, and defines that to be friends, teachers, counselors (pay the researcher) and extra curricular activities. + + The proposition ties the coding paradigm together. (Maybe this means the proposition is a proposed interrelationship of the codes obtained by coding the data and postulating various interrelationships, and observing a most favored interrelationship.)}} + + @article{Pomrenkeb, +author={Marlene Pomrenke}, +title={Using Grounded Theory to Understand Resiliency in Pre-Teen Children of High-Conflict Families}, +journal={Qualitative Report}, +volume=12, +number=3, +year=2007, +pages={356-374}, +annote={ Data gained from describing these interactions was used as a background to explore the phenomenon of resilience within the children of these families. From this background, specific categories related to protective factors emerged. For example, ideas associated with the external support systems fo the children emerged as a category. + (so she says) + Part of this analysis included discovering the relationships amongst and then between the categories. For example, included in the category of ``post-separation changes'' were ideas associated with the differences in communication as well as how the parents coped with the separation. the relationships defined within this category allowed for a thorought examination of the issues and how they then fit with other categories. Grounded theory methodology allows for the development of specific relationships between categories as a way to substantiate an emerging hypothesis from the data. The final phase of the research analysis consisted of constructing a proposition and sutstantive-level theory about the interactions of family members and how this relates to the phenomenon of resilience. + + Steps in open coding\\ + 1. ideas expressed are coded\\ + 2. codes clustered into categories of related ideas\\ + some categories cover the space of ideas,\\ + others, now called subcategories, explain scope, nature and level, are of less interest or relevance\\ + + Steps in axial coding\\ + goal is to identify ``the central phenomenon'' from the categories, and define how this distinguished category is related to the others\\ + there is an approach called ``contant comparison'', used to identify the central phenomenon and initial categories are refined in this process. The stuff being compared is at first the raw text, then later applies to data within categories. Categories are reviewed and changed, resulting in the categories being more complex and inclusive. Categories were merged. Ultimately one category achieves a central role, and connections between it and the remaining categories are drawn and these relationships are described. + + then there is also the concept of coding paradigm. Coding paradigm includes the notions of causal relationships. implying antecedents, and causal chains are linked into the phenomenon. (Post hoc ergo propter hoc might be a problem here.) The putative causal chain is considered in its context, and there is the notion of intermediaries, called intervening conditions or intervening interactions, in the context, (presumably this could be the empty set, though that is not clear from this writing) These intervening interactions help to determine the consequences. So, there is inherent in grounded theory procedure the notion that there are consequences, there are causes, there can be intermediary contributing contextual factors, and moreover, the grounded theory procedure is intended to reveal these. Furthermore, ideas gained through conducting the process give rise to more questions. (Isay It sounds like detective work.) these questions can be asked in a different context with the participants in an attempt to gain furhter understanding of the phenomenon. + + The determination of the core category occurs during ``selective coding'', and relating this distinguished core category to the others. This determines the ``shape'' of the final theory. It involves noting patterns. The example in this article takes the research question, which was of the form ``How does A cause B?'' + + Because axial coding does this same process, of choosing, in turn, each category and placing it centrally and relating it to the other categories, it sounds as if selecting coding is just picking the one of these axial coding trials that generated the most appealing set of relationships. Selective coding also uses the subcategories to see how they affect the (at this point, chosen) central (core category) phenomenon. + + At the end of the selective coding portion of this paper, it has added detail to the initial research question (which is really a premise), modifying it to, the particular means by which family and community interactions promote resilience in children (Isay, when they do) is discuss together, try to trust one another, try to cohere. Then, this conjecture is supported with evidence, namely that in those extended families that do not cohere well, the children are not as resilient. + + }} + +@article{Pomrenke, +author={Marlene Pomrenke}, +title={Using Grounded Theory to Understand Resiliency in Pre-Teen Children of High-Conflict Families}, +journal={Qualitative Report}, +volume=12, +number=3, +year=2007, +pages={356-374}, +annote={This article was selected for the class as a good article but I'm having a bad reaction to it. +The researcher works as a counsellor, and the conclusion is self-serving, namely, if the state would pay counsellors to get these children connected with their other relatives, then the kids will be able to withstand the aggression of the parents. The initial research question is biased, because it contains a suggested solution ``How family and community interations promote resilient behaviours in children within this population''. It would be a lot more useful to have a question with fewer premises, for example, can we distinguish which children in which contexts are not going to be able to survive from the ones who will be able to ``tough it out''? The recently murdered children in the high profile case in Canada (Shafia) shows that this would be a useful research area.\\ +This article has a helpful collection of references on social constructivism:\\ +Social constructioninsm ``references knowledge neigher in the observed nor the observer, but rather in the place between the two, in the social arena among interpreting subjects'' (Pare, 1995, p. 5). ``Social construction theory sees meaning as a fluid process of constrantly changing narratives that are socialy derived and exist in language'' (Slovik and Griffith, 1992, p. 232). It emphasizes social interaction as a basis for creating meaning. Social constructionism uses ``The intersubjective influence of language and culture, as well as the hermeneutical tradition of textual interpretation'' (Pare, p. 5). If our exerience is regarded as the basis of meaning, discussing this experience through our language gives us a way of understanding the meaning of the experience. ``People consider and reconsider reality through their conceptions of and experience with it. It is not discovered; rather, it is created and recreated'' (Laird, 1995, p. 152). ``Realities are socially constructed, constituted through language and organized and maintained throug narrative'' (Freedman and Combs, 1996, p. 22). In other words, realities are organized and maintained through stories. These stories represent how people know themselves and their worlds. Within this study the stories told be the children represented their ideas of resilience and how they managed to adapt to the ongoing parental conflict. \\ + +There is also a summary of grounded theory:\\ +Grounded theory is a method of social inquiry associated with a qualitative approach to research. This inductive research process utilized generalized knowledge that is derived from specific observations of phenomena from the field. In turn, this can be used to build theory. For example, grounded theorists aim to create theoretical categories from collected data and then analyze relationships between key categories (charmaz 1990). In dded the main purpose of using a grounded theory approach is to develop theory through understandin concepts that are related by means of statements of relationships (Strauss and Corbin, 1990). Using the concepts from gournded theory, this study starts from understanding the experience of the research participants (i.e., how they construct their worlds). The data analysis stage focused on finding recurrent themes or issues in the data, and finally into developing or refining a theory about the phenomenon. + + Within the grounded theory approach developed by Strauss and Corbin (1990) there are three basic elements. They are referred to as concepts, categories and propositions. According to Strauss and Corbin, it is from the conceptualization of the data, not the actual data per se, that theory is developed. Within this study, the research consdiered the interactions of family members in the context of high-conflict separated parents. + + The article goes on to say that the idea of external support systems emerged from the data, which in my mind is highly suspect, because the research question stipulates that community support systems are involved. In effect the research question establishes the category, and any statement the childrem might make matching what is sought is used as evidence that the sought item is found. For example, if we postulate a research question that children say ``x'', and we observe children reciting the alphabet, we obtain evidence that children do indeed say ``x'', but the result is misleading. + + }} + +@misc{GrenierTrust, +key={EDCI6000Trust}, +author={Robin Grenier}, +title={Criteria for establishing trustworthiness}, +howpublished={classnotes}, +annote={Trustiworthiness is her favorite of this kind of term\\ +Credibility(in preference to internal validity) extent to which the results appear to be acceptable representations of the data\\ +Transferability (in preference to external validity/generalizability) extent to which the findings from one study in one context will apply to other contexts\\ +Dependability(in preference to reliability) extent to which findingd are unique to time and place, the stability or consistency of explanations (same in beginning to end, across participants vs based on subset of participants)\\ +Confirmability (in preference to objectivity) extent to which interpretations are the result of the participants and the phenomenon as opposed to the researcher bias\\ +strategies for promoting trustworthiness, see Johnson 1997\\ +\begin{tabular}{|p{2cm}|p{12cm}|}\hline +Strategy & Description\\ \hline \hline +Researcher as ``Detective'' & A metaphor: consider potential cause/effect, systematically eliminate, until one left and is beyond reasoable doube\\ +Extended fieldwork & collect over an extended period of time\\ +low inference & stay close to participants words\\ +triangulation& cross-check, multiple procedures and/or sources, want corroboration\\ +data triangulation&multiple sources\\ +method triangulation&multiple methods\\ +investigator triangulation & multiple investigators\\ +theory triangulation & multiple theories, perspectives\\ +participant feedback & feedback and discussion of researcher's interpretations, with participants and others in participant community\\ +peer review & discussion of researcher's interpretations, with peers, including devil's advocate\\ +negative case sampling & locating and examining cases that disconfirm researcher's expectations and tentative explanation\\ +reflexivity & self-awareness, critical self-reflection, by researher on his or her potential biases and predispositions\\ +pattern matching & predicting a series of results that forma pattern then determinint the degree to which the actual results fit the predicted patther\\ +\hline +\end{tabular} +}} + +@book{RichieLewis2003, +author={J. Ritchie and J. Lewis}, +title={Qualitative Research Practice: A Guide for Social Science Students and Researchers}, +year=2003, +publisher={Thousand Oaks, CA : Sage Publications}, +annote={key elements commonly agreed to give qualitative research its distinctive character include samples that are small in scale and purposeively selected on the basis of salient criteria\\ +this book has a very nice introduction\\ +}} + +@book{Navigator, +author={David A. Westbroook}, +title={Navigators of the contemporary: why ethnography matters}, +year=2008, +publisher={The University of Chicago Press}} + + +@article{multiculture, +author={Kathleen Gregory}, +title={Native-view Pardigms: Multiple Cultures and Culture conflicts in Organizations}, +year=1983, +journal={Adminstrative Science Quarterly}, +annote={}} + +@book{Reissman, +author={Catherine Kohler Riessman}, +title={Narrative Analysis}, +year=1993, +publisher={Thousand Oaks, CA: Sage}, +annote={}} + +@article{Cary, +author={Lisa J. Cary}, +title={Unexpected Stories: Life Histoyr and the Limits of Representation}, +year=1999, +journal={Qualitative Inquiry}, +volume=5, +pages={411-427}, +publisher={Sage Publications, Inc.}, +annote={}} + +@article{suddaby, +author={Roy Suddaby}, +title={From the Editors: What Grounded Theory is not}, +journal={Academy of Management Journal}, +year=2006, +volume=49, +number=4, +pages={633-642}, +annote={}} + +@article{FQS466b, + author = {Barbara Kawulich}, + title = {Participant Observation as a Data Collection Method}, + journal = {Forum Qualitative Sozialforschung / Forum: Qualitative Social Research}, + volume = {6}, + number = {2}, + year = {2005}, + annote={DeWalt and DeWalt (2002) where people stand or sit, whose opinions are respected, who has power and who does not, sometimes counting is useful, try also to remember nonverbal expressions and gestures, include spatial maps in field notes\\ +Wocott(2001): be tolerant of ambiguity\\ +Geertz(1973): thick description. This essay is available through UConn library electronic access. +``From one point of view, that of the textbook, doing ethnography is establishing rapport, selecting informants, transcribing texts, taking genealogies, mapping fields, keeping a diary, and so on. But it is not these things, techniques and received procedures, that define the enterprise. What defines it is the kind of intellectual effort it is: an elaborate venture in, to borrow a notion from Gilbert Ryle, 'thick description'.'' +``But the point is that between what Ryle calls the 'thin description' of what the rehearser (parodist, winker, twitcher \ldots) is doing ('rapidly contracting his right eyelids') and the 'thick description' of what he is doing ('practicing a burlesque of a friend faking a wink to deceive an innocent into thinking a conspiracy is in motion') lies the object of ethnography: a stratified hierarchy of meaningful structures in terms of which twitches, windks, fake-winks, parodies, rehearsals of parodies are produced, perceived and interpreted, and without which they would not (not even the zero-form twitches, which, \textit{as a cultural category}, are as much nonwinks as winks are nontwitches) exist, no matter what anyone did or didn't do with his eyelids.'' +``\ldots culture is not a power, something to which social events, behaviors, institutions or processes can be causally attributed; it is a context, something within which they can be intelligibly--that is thickly--described'' (Isay thick description tuus means a description that conveys connotations as well as denotations, conveys not just a depiction of an event, but its ramifications in the culture) +A good interpretation of anything--a poem, a person, a history, a ritual, an institution, a society--takes us into the heart of that of which it is the interpretation.\\ +Notes on silent television, and on radio are good practice.\\ +Field notes are to be taken as soon as possible after observations occur, without intervening conversations or drinking.\\ +Patton (2002) does not discuss basic or generic interpretive, buth find under his discussion of social construction and constructivism\\ +basic/generic is not guided by an established philosophic assumption, and to avoid a common error, +we should carefully explain processes, procedures and analysis in relation to the purpose of the study (Patton 2002)\\ +description is a key attribute of this approach\\}} + +@misc{Grenier, +key={EDCI6000}, +author={Robin Grenier}, +title={Considerations for Making Choices Regarding Sample Size in Qualitative Studies}, +howpublished={classnotes}, +annote={process of selecting participants is generally evolving based on patterns, categories and dimensions emerging from the data, researchers see out participant who may be able to provide deeper insights, so when number of participants is fixed, it might happen that sample sizes have to be increased, and small-scale sampling}} + +@misc{GrenierGT, +key={EDCI6000GT}, +author={Robin Grenier}, +title={GroundedTheory}, +howpublished={classnotes}, +annote={start with initial generative questions, expect them to be modified\\ +from gathered data, identify core theoretical concepts\\ +develop linkages between core theoretical concepts and data\\ +maybe take months, expect to evolve toward one central core category\\ +Use these strategies:\\ +Coding, to categorize data, describe implications and details of categories\\ +first open coding=see data in minute detail and develop initial categories\\ +later selective coding=code systematically with respect to a core concept\\ +Memoing: process of recording ideas as they evolve, think of as extensive marginal notes and comments\\ +early memos are open, later memos focus in on the core concept\\ +Integrative diagrams, discussion sessions: diagrams are any useful graphic, directed graphs are allowed, +multiple people talking to increase insight\\ +this process eventually approaches conceptually dense theory because new observations lead to new linkages, which review the theory and stimulate more data collection, so one core category is identified and described in detail, ``Essentially the project ends when the researcher decides to quit.'', i.e., nothing new they want to add, finished product is extremely well-considered explanation for some phenomenon of interest --the grounded theory. This theory can be explained in words and is usually presented with much of the contextually relevant detail collected. +}} + +@article{FQS466, + author = {Barbara Kawulich}, + title = {Participant Observation as a Data Collection Method}, + journal = {Forum Qualitative Sozialforschung / Forum: Qualitative Social Research}, + volume = {6}, + number = {2}, + year = {2005}, + keywords = {participant observation; qualitative research methods; field notes}, + abstract = {Observation, particularly participant observation, has been used in a variety of disciplines as a tool for collecting data about people, processes, and cultures in qualitative research. This paper provides a look at various definitions of participant observation, the history of its use, the purposes for which it is used, the stances of the observer, and when, what, and how to observe. Information on keeping field notes and writing them up is also discussed, along with some exercises for teaching observation techniques to researchers-in-training. +URN: urn:nbn:de:0114-fqs0502430}, + issn = {1438-5627}, + url = {http://www.qualitative-research.net/index.php/fqs/article/view/466}, + annote={Participant observation has been applied to education, + citing Bernard, 1994, that a certain amount of deception and impression management is needed\\ + establishing rapport and learning to act in such a way as to blend into the community, so its members will act naturally, then remove so as to be able to concentrate on the collected data\\ + not only passive observation but also natural conversations and other methods\\ + characterized by having an open, nonjudgmental attitiude, \\ + Fine (2003) is cited as stating that the observer is expected to become part of the group being studied to the extent that the members themselves include the observer in the activity\\ +DeMunck and Sobo 1988 say a source of richly detailed description, \\ +DeWalt and DeWalt 2002 say improves the quality of data collections and interpretation and facilitates the development of new research questions or hypotheses\\ +Johnson and Sackett (1998) point out that what researchers find interesting to report on can govern the amount of effort they put into attending to it, producing a skewed representation of the culture, so systematic procedures are advocated\\ +DeWalt and DeWalt (2002) note that gender, sexuality, ethnicity, class and theoretical approach may affect observation, analysis and interpretation\\ +Schensul, Schensul and LeCompt (1999) mention appearance, ethnicity, age, gender and class as things affecting acceptance of the observer into the community\\ +DeWalt, DeWalt and Wayland(1998) mention researcher bias, as does Ratner (2002) as a source of distortion of research results. Reflection on oneself is to be used to attempt to reduce this effect.\\ +Schensul, Schensul and LeCompt (1999) suggest that accurate observation field notes without imposing preconceived categories from the researcher's theoretical perspective, to allow categories representative of the culture under study to emerge.\\ +Gold (1958) has extended Junker's four theoretical stances: Complete participant, participant as observer, observers as participant and complete observer, which differ in degree of visibility of the research activity, and degree of visibility of the researcher, and the membership in the group of the person participating and researching.\\ +The impact of the visible presence of the participant observer has been the concern of many. Merriam 1998, according to Kawulich, states that this is not the appropriate question; instead the question is how the observer is to account for those effects in explaining the data. (My thought on this is, it is a feedback control system of unknown order, and accounting for the effects is no simple matter.) +DeWalt and DeWalt(2002) and also Spradley (1980, pp. 58-62) and Adler and Adler(1987) all describe degrees of pariticpation and observation for the researcher role.\\ +DeWalt and DeWalt(2002) state that in the report, the role taken by the researcher ``should be made clear''.\\ +What to observe: observe enough to be able to sort the regular from the irregular\\ +look for variation, to see the viewpoints\\ +look for exceptions, negative cases\\ +when finding data felicitous for the theoretical purposes, take note of the context, so as to be able to seek similar opportunities; be persistent\\ +Wolcott(2001) Making good use of the opportunity for what's wanted to learn, and also, is what's wanted to learn the best thing to be learned from this opportunity?\\ +DeMunck and Sobo, rapport is over time, it involves establishing a trusting relationship with the community, \\ +active listening, showing respect and empathy, being truthful, showing a committment to th well-being of the community\\ +How to observe: take notes on what is seen and heard\\ +get (e.g., through interviews) hits about participants' insights about what's relevant\\ +focus of different activities, to help delineate what's different among them\\ +Merriam 1988 observation guide: includes physical environment, activities, interactions in the setting, their frequency and duration and subtle factors such as informal, unplanned activities, symbolic meaning, nonverbal communication, physical clues and absence of expected happenings, who speaks to whom, who listens, and silences, and how the researcher's role affects (though I think this is difficult to disentangle) those one is observing\\ +need to occupy the context enough to achieve prolonged engagement, so as to achieve trustworthy findings see Lincoln and Guba 1994, time, interaction, (Isay quality time?)\\ +Fennell: ask the informants to treat the researcher like a child who knew nothing, inviting researcher to activities that were important for understanding culture\\ +Kottak 1994, enculturation is a process of learning and transmitting culture\\ +DeWalt and DeWalt, informal interviewing, recording detailed field notes, \\ +Angrosino and DePerez (2000) structured observation process\\ +Bernard(1994) going into the field with prepared questions, checklist of data\\ + } +} + +@article{doi:10.1191/1478088706qp063oab, +author = {Braun, Virginia and Clarke, Victoria}, +title = {Using thematic analysis in psychology}, +journal = {Qualitative Research in Psychology}, +volume = {3}, +number = {2}, +pages = {77-101}, +year = {2006}, +doi = {10.1191/1478088706qp063oa}, +URL = {http://www.tandfonline.com/doi/abs/10.1191/1478088706qp063oa}, +eprint = {http://www.tandfonline.com/doi/pdf/10.1191/1478088706qp063oa}, +annote = {Phase 1 familiarize = read actively, search for meaning, start taking notes\\ +put into written form\\ +Phase 2 initial coding= identify a feature of data, develop a sense of what is a unit of meaning, which is different, samller than the unit of analysis or theme\\ +equal attention to each data item\\ +identify interesting aspects in the data items that may form the basis of repeated patterns (themes)\\ +make sure all data extracts are coded, and collate the coded extracts\\ +text segments can have many codes\\ +a satisfactory thematic 'map' that will eventually be produced, an overall conceptualization of the data patterns, and relationship between them\\ +phase 3 searching for themes\\ +starts with long list of codes\\ +refocus at higher level of abstraction, themes\\ +analyze codes, think how to combine them into themes, maybe visuals,\\ +different levels of themes, relationships among themes\\ +Phase 4: reviewing themes\\ +have a set of candidate themes, will refine them\\ +is there enough data, or really not theme\\ +can two be combined?\\ +need to split a theme into 2?\\ +consider internal homgeneity and external heterogenity\\ +do all the coded extracts collated here belong together here?\\ +fix first, then proceed: do candidate themes capture the contours of the coded extracts?\\ +part 2 of phase 4 is review the themes with respect to one another, and for the dataset\\ +phase 5, defining and naming themes, starts with thematic map\\ +identify the essence of the theme by organizing the collated extracts into a coherent and internally consistent account, with accompanying narrative, identify what is of interest and why\\ +for each theme, write a detailed analysis, tell its story and see how it fits into the overall story\\ +concise punchy names, immediately communicative\\ +phase 6: report\\ +tell the compulicated story of your data in a way that convinces the reader of the merit and validity of your analysis,\\ +choose particularly vivid examples,\\ +embed withing an analytic narrative that compellingly illustrates the story your are telling about your data\\ +go beyond descriptoin, make an argument in relation to the research question\\ +good example: each theme is clearly linked back to the overall research question, but each is distinct\\ +Ask: what does this theme mean?\\ +what are the assumptions underpinning it?\\ +what are the implications of this theme?\\ +what conditions are likely to have given rise to it?\\ +why do people talk about this thing in this way?\\ +}} + + + +@article{Shaw01122008, +author = {Shaw, Ian}, +title = {Ethics and the Practice of Qualitative Research}, +volume = {7}, +number = {4}, +pages = {400-414}, +year = {2008}, +doi = {10.1177/1473325008097137}, +abstract ={This article stems from a concern that relying only on codes of research ethics risks compartmentalizing ethical aspects of research, and shutting them off into a preamble to research. I explore ways in which the practice of qualitative research ethics is presented afresh and contextualized in distinct forms at every stage of research. I develop three linked arguments. First, the ethics of qualitative research design pose distinctive demands on principles of informed consent, confidentiality and privacy, social justice, and practitioner research. I focus on consent for its topicality, not because it is more important or difficult and social justice. Second, fieldwork ethics raise special considerations regarding power, reciprocity and contextual relevance. Third, ethical issues raised by the analysis and uses of qualitative inquiry evoke illustrative questions regarding the ethics of narrative research and the utilization of research.}, +URL = {http://qsw.sagepub.com/content/7/4/400.abstract}, +eprint = {http://qsw.sagepub.com/content/7/4/400.full.pdf+html}, +journal = {Qualitative Social Work} , +annote={ethics of qual. researhc design pose distinctive demands upon principles of informed consent, condigentiality and privacy, social justice and prctitioner research,\\ +fieldwork ethics raise special considerations regarding power, recipricity and contextual relevance\\ +ethical issues raised by the analysis and uses of qualitative inquiry evoke illustrative questions regarding the ethics of narrative research and the utilization of research\\ +applies, in distinct forms, at each stage of research\\ +there are personal ethics and research ethics, intellectual, professional and corporate ethics\\ +Design: informed consent, confidentiality, privacy, social justice, practitioner research\\ +fieldwork: special considerations of power, reciprocity and contextual relevance\\ +analysis and use: narrative research, utilization of research\\ +participants face the consequent risk of involuntary disclosure, and unwittingly the researcher becomes a covert investigator\\ +covert evaluation is a dangerous example of covert social research\\ +informed consent implies that the researcher knows before the event, though not so\\ +issue of genuine voluntariness of consent\\ +primarily researchers and secondarily advocates for participants\\ +principles for moral basis of evaluation: moral equality, moral autonomy, impartiality and reciprocity, justice as prior\\ +fair evaluation agreement: participants:\\ +not be coerced\\ +be able to argue their position\\ +accept the terms under which the agreement is reached\\ +negotiate. This is not simply a coincidence among individual choices\\ +not pay excessive attention to one's own interests\\ +adopnt an agreement that affects all equally\\ +select a policy for evaluation that is in the interests of the group to which it applies\\ +have equal and full information on relevant facts\\ +avoid undue risk to participants arising from incompetent and arbitrary evaluations\\ +examiners of research bids look for data about ethics issues\\ + } +} + +@book{Yin1994, +author={Robert K. Yin}, +title={Case Study Research, Design and Methods}, +edition=2, +publisher={Sage Publications}, +annote={ +This book is about case studies for research and publication, rather than for teaching in, e.g., law school. +The types of research question for which case study is the appropriate technique are those questions starting with ``How'', and ``Why'', so perhaps ``How did we figure out that the relevant items to students learning the pumping lemma include use of the contrapositive, and negation of statements using quantifiers?'', or ``Why didn't Makan learn the pumping lemma until now?'' +Case study adds direct observation and systematic interviewing to methods available with historical data (primary and secondary documents, cultural and physical artifacts). +Reviewing literature on a topic serves to develop sharper and more insightful questions on it. +from p.15: ``And, yes, case studies have a distinctive place in evaluation research (gives references). there are at least five different applications. The most important is to explain the causal links in real-life interventions that are too complex for the survey or experimental strategies. In evaluation language, the explanations would link program implementation with program effects. \\ +the case study strategy may be used to explore those siutation in which the intervention being evaluated has no clear, single set of outcomes.\\ +Case study research is remarkably hard.\\} +} \ No newline at end of file diff --git a/literatureQualRes2.bib b/literatureQualRes2.bib new file mode 100644 index 0000000..63e8d0a --- /dev/null +++ b/literatureQualRes2.bib @@ -0,0 +1,91 @@ + +@article{doi:10.1191/1478088706qp063oa, +author = {Braun, Virginia and Clarke, Victoria}, +title = {Using thematic analysis in psychology}, +journal = {Qualitative Research in Psychology}, +volume = {3}, +number = {2}, +pages = {77-101}, +year = {2006}, +doi = {10.1191/1478088706qp063oa}, +URL = {\url{http://www.tandfonline.com/doi/abs/10.1191/1478088706qp063oa}}, +eprint = {url\{http://www.tandfonline.com/doi/pdf/10.1191/1478088706qp063oa}}, +abstract = {Thematic analysis is a poorly demarcated, rarely acknowledged, yet widely used qualitative analytic method within psychology. In this paper, we argue that it offers an accessible and theoretically flexible approach to analysing qualitative data. We outline what thematic analysis is, locating it in relation to other qualitative analytic methods that search for themes or patterns, and in relation to different epistemological and ontological positions. We then provide clear guidelines to those wanting to start thematic analysis, or conduct it in a more deliberate and rigorous way, and consider potential pitfalls in conducting thematic analysis. Finally, we outline the disadvantages and advantages of thematic analysis. We conclude by advocating thematic analysis as a useful and flexible method for qualitative research in and beyond psychology.}, +annote={} +} +@misc{notsecret, +author={Victoria Bellottti and James Bertrand}, +title={The (not-so) secret weapon: Just-in-time wisdom with ethnography, PARC forum}, +howpublished={}}%\url={www.parc.com/event/1179/not-so-secret-weapon.html}}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +@article {springerlink:10.1007/s10882-005-3688-1, + author = {Burstein, Karen and Bryan, Tanis and Chao, Pen-Chiang}, + affiliation = {Southwest Institute for Families and Children with Special Needs Scottsdale Arizona}, + title = {Promoting Self-Determination Skills Among Youth with Special Health Needs Using Participatory Action Research}, + journal = {Journal of Developmental and Physical Disabilities}, + publisher = {Springer Netherlands}, + issn = {1056-263X}, + keyword = {Behavioral Science}, + pages = {185-201}, + volume = {17}, + issue = {2}, + url = {http://dx.doi.org/10.1007/s10882-005-3688-1}, + note = {10.1007/s10882-005-3688-1}, + abstract = {A team of 20 high school and college students with physical and/or health and orthopedic impairments was engaged in participatory action research (PAR) to systematically test strategies to solve problems they confronted in their daily lives. PAR goals were set by the participating youth with special health needs (YSHN) who were involved in every step of the research process from problem identification to dissemination of results. In the study reported here, all participants made progress in analyzing their personal needs, selecting a goal, and implementing a strategy to achieve the goal. In addition, the YSHN identified a common goal of visiting public venues, such as shopping malls, and conducted PAR projects to assess the accessibility of such venues. The results indicate that PAR is a viable method for involving YSHN with varied skills, limitations, and experiences to address personal issues as well as barriers they all confront. PAR appears to be a promising methodology for assisting YSHN in their quest for self-determination and the IDEA (1997) mandate to include adolescents in decision making.}, + year = {2005}, + annote={This was recommended by Professor Grenier as a source on participatory action research (a methodology, but also called a method).\\ + There is a difference between participatory action research and the participant observer role. Participatory action research not only has researchers taking part in activities, which is enough for participant observer, but it is also the case, due to ``action'', that the activity in which the participation occurs is not just as activity that is part of a culture getting described. The activity is intended to foster change. In this case, the activity is tried and its feasibility and helpfulness assessed. It is the case with CSE2102 that we are trying to effect change, namely create a course designed to suit needs (societal need for more computer discipline -trained people, plus job security needs of students). Most if not all of the students enrolled in CSE2102 are not thinking of themselves as researchers in this activity. Also, the thing that is being changed is not considered to be an infliction of a wrong by a power, so the question, is it participatory action research remains. Creswell2012 p. 582 makes clear that participatory action research conttributes to emancipation or change in society, so it does not seem to apply to CSE2102 innovation.} +} + + + + + + + + +@article{doi:10.1191/1478088706qp063oabc, +author = {Braun, Virginia and Clarke, Victoria}, +title = {Using thematic analysis in psychology}, +journal = {Qualitative Research in Psychology}, +volume = {3}, +number = {2}, +pages = {77-101}, +year = {2006}, +doi = {10.1191/1478088706qp063oa}, +URL = {http://www.tandfonline.com/doi/abs/10.1191/1478088706qp063oa}, +eprint = {http://www.tandfonline.com/doi/pdf/10.1191/1478088706qp063oa}, +annote = {pitfalls\\ +1. fail to analyze, make analytic points about the data\\ +2. use the data collection questions as the themes\\ +3. weak or unconvincing analysis--not rich description, interpretation\\ +failure to provide adequate examples, e.g., only 1 or 2\\ +analysis is deliberate an self-consiously artful creation by the researcher, and must be constructed to persuade the reader of the plausibility of an argument\\ +4. mismatch between data and analytic claims\\ +5. mismatch between theory and analytic claims, research question and form of thematic analysis, +interpretation has to be consistent with theoretical framework\\ +There are criteria for assessing qualitative research, +and they are not uncontroversial\\ +rigor: be systematic, with a method that makes sense with the way of conceptualizing the data\\ +\begin{tabular}{|p{1cm}|l|p{5cm}|}\hline +Process & No. & Criteria\\ hline +Transcription & 1 & the data have been transcribed to an appropriate level of detail, and the transcripts have been checked against the source for accuracy\\ +Coding & 2 & Each data item has been given equal attention\\ +& 3 & Themes have not been generate from a few vivid examples (anecdotal)\\ +& 4 & All relevant extracts for each theme have been collated\\ +& 5 & Themes have been checked against each other and back to the original data set\\ +& 6 & Themes are interally coherent, consistent, and distinctive\\ +Analysis & 7 & Data have been analyzed-interpreet-made senso of-rather than just paraphrased or described\\ +& 8 &Analysis and data match each other - the extracts illustrate the analytic claims\\ +& 9& Analysis tells a convincing and well-organized sotry about the data and topic\\ +& 10 & A good balance between analytic anrrative and illustrative extracts is provided\\ +Overall & 11 & Enough time has been allocated to complete all phases of the analysis adquately without rushing a phase or giving it a once-voer-lightly\\ +Written report & 12 & The assumtions about, and specific appraoch to, thematic analysis are clearly explicated\\ +& 13 & There is a good fit between what you cleaim you do, and what you show you have done -- i.e., described method and reported analysis are consistent.\\ +& 14 & The language an concepts used in the report are consistent with the epistemological postion of the analysis\\ +& 15 & the researcher is positioned as active in the research process themes do not just emerge.\\ +\end{tabular}}} + + diff --git a/literatureQualRes3.bib b/literatureQualRes3.bib new file mode 100644 index 0000000..d1f27f2 --- /dev/null +++ b/literatureQualRes3.bib @@ -0,0 +1,80 @@ + +%verification strategies +@article{Morse-Barrett-Mayan-Olson-Spiers-Hon-2002, +title={Verification Strategies for Establishing Reliability and Validity in Qualitative Research}, + volume={1}, + url={http://ejournals.library.ualberta.ca/index.php/IJQM/article/viewArticle/4603}, + number={2}, + journal={International Journal}, + publisher={University of Alberta}, + author={Morse, Janice M and Barrett, Michael and Mayan, Maria and Olson, Karin and Spiers, Jude and Hon, Dnurs}, + editor={Smith, Lorenzo M and Pourboghrat, Farhang and Yoon, Jeong-Whan and Stoughton, Thomas BEditors}, year={2002}, + pages={1--19}, +annote={Noting shift away from researcher trying for reliability and validity to reader or consumer (Isay ``caveat emptor'') deciding about transferability, shift is also away from thinking about how to make the research reliable and valid by methodology, to evaluating trustworthiness and utility implemented after the conduct of the research, the authors argue that reliability and validity remain appropriate concepts. +Moreover, they argue that techniques for this should happen during, rather than after, the research. They also prefer teminology from what they call mainstream science.\\ +When confidence values became readily available in quantitative social research, this was considered by qualitative social research and two responses occurred, one, these things don't apply to qualitative research, and two, some new criteria for reliability and validity are appropriate to qualitative, such as trustworthiness. +According to LincolnGuba, aspects of trustworthiness are credibility, transferability, dependability and confirmability, each having methodological strategies for their achievement in some degree, such as audit trail, member checks when coding, categorizing, confirming results with participants, peer debriefing etc, (LG 1981, 1982, 1985). Later, LG developed authenticity criteria unique to constructivist assumptions, and could be used beyond methodological dimensions (LG1989). Their work is fundamental to standards of quality for qualitative. Strategies for reliability and validity took back stage to these criteria. The study urges the restoring of the strategies built in to each phase of research, not (only) evaluation afterwards. +specific strategies recommended by LG81\\ +}} + +@article{Morse-Barrett-Mayan-Olson-Spiers-Hon-2002, +title={Verification Strategies for Establishing Reliability and Validity in Qualitative Research}, + volume={1}, + url={http://ejournals.library.ualberta.ca/index.php/IJQM/article/viewArticle/4603}, + number={2}, + journal={International Journal}, + publisher={University of Alberta}, + author={Morse, Janice M and Barrett, Michael and Mayan, Maria and Olson, Karin and Spiers, Jude and Hon, Dnurs}, + editor={Smith, Lorenzo M and Pourboghrat, Farhang and Yoon, Jeong-Whan and Stoughton, Thomas BEditors}, year={2002}, + pages={1--19}, +annote={negative cases\\ +peer debriefing\\ +prolonged engagement\\ +persistent observation\\ +audit trails\\ +member checks\\ +of the investigator\\ +responsive and adaptable to changing circumstances, +holistic, having processional immediacy, sensitivity and ability for clarification and summarization\\ +They challenge the assumption that study is rigorous if the evaluation, based on the existence of audit trails, member checks, memos, says so. They explain why audit trail is not convincing. They explain why memberchecking is not necessarily helpful and can be harmful. They cite Morse 1999 who says these criteria, alternative to reliability and validity, undermine the issue of rigor. Comparison of post hot with verification strategies that were used to shape and direct the research during development. Think evaluate vs. ensure.\\ +Recommended strategies to ensure rigor:\\ +investigator responsiveness\\ +methodological coherence\\ +theoretical sampling\\ +sampling adequacy\\ +an active analytic stance\\ +saturation\\ +Except for investigator responsiveness, they do not define, or give citations, for any of the above. +Verification refers to mechanisms used during research process to incrementally contribute to reliability and validity and therefore rigor. +Creswell 1997 and Kvale 1989 are cited here. +Identify and correct errors before they are built into the model, before subvert analysis.\\ +Systematically check data, move back and forth between design and implementation\\ +monitor and confirm constantly\\ +many research decisions may underlie the sampling selection, which requires responsiveness to the needs of developing variation, verification and the developing theory\\ +Investigator responsiveness\\ +research is only as good as the investigator\\ +creativity, sensitivity, flexibility, skill in using verification strategies that determine the reliability and validity of the evolving study.\\ +E.g., form conjecture, form new question, perform purposive sampling, i.e., future participant recruitment, +want sampling strategies to ensure replication and confirmation.\\ +responsiveness to whether the categorization scheme actually holds or appears thin and muddled\\ +remain open, use sensitivity, creativity and insight, be willing to relinquish ideas with poor support\\ +lack of responsiveness is the greatest hidden threat\\ +Examples: overly adhering to instructions vs. being guided by data\\ +inability to abstract, synthesize or get beyond technicalities\\ +working deductively from previously held assumptions or theoretical framework\\ +following instructions rote, rather than using instructions strategically in decision making\\ +To do while conducting inquiry:\\ +ensure methodological coherence (still undefined, see below)\\ +sampling sufficiency(see below)\\ +develop dynamic relationship between:\\ +sampling\\ +data collection\\ +analysis\\ +thinking theoretically\\ +theory development\\ +(see Meadows and Morse, 2001, for detailed explanation of these strategies)\\ +Methodological coherence\\ +aim is to get research question connected to components of method\\ +question has to match method has to match data has to match analytic procedure\\ +thngs may not go according to plan, including sampling\\ +coherence is about all of these things matching throughout the process of the research\\}} \ No newline at end of file diff --git a/literatureQualRes4.bib b/literatureQualRes4.bib new file mode 100644 index 0000000..970cc6b --- /dev/null +++ b/literatureQualRes4.bib @@ -0,0 +1,80 @@ +@article{doi:10.1191/1478088706qp063oa, +author = {Braun, Virginia and Clarke, Victoria}, +title = {Using thematic analysis in psychology}, +journal = {Qualitative Research in Psychology}, +volume = {3}, +number = {2}, +pages = {77-101}, +year = {2006}, +doi = {10.1191/1478088706qp063oa}, +URL = {http://www.tandfonline.com/doi/abs/10.1191/1478088706qp063oa}, +eprint = {http://www.tandfonline.com/doi/pdf/10.1191/1478088706qp063oa}, +abstract = { Thematic analysis is a poorly demarcated, rarely acknowledged, yet widely used qualitative analytic method within psychology. In this paper, we argue that it offers an accessible and theoretically flexible approach to analysing qualitative data. We outline what thematic analysis is, locating it in relation to other qualitative analytic methods that search for themes or patterns, and in relation to different epistemological and ontological positions. We then provide clear guidelines to those wanting to start thematic analysis, or conduct it in a more deliberate and rigorous way, and consider potential pitfalls in conducting thematic analysis. Finally, we outline the disadvantages and advantages of thematic analysis. We conclude by advocating thematic analysis as a useful and flexible method for qualitative research in and beyond psychology. }, +annote={Thematic analysis\\ +discusses theory and method, clarifies similarities and differences between different approaches that share some features with thematic approach\\ +is a foundational method, is the first researchers should learn, provides core skills\\ +consider a dichotomy: 1. tied to a particular theoretical framework or epistemological position\\ +2. not\\ +In 1 we find tightly constrained methods and less tightly constrained methods\\ +In 2, methods independent of theoretical framework and epistemology\\ +Thematic analysis is an experiential method, compatible with constructionist paradigm\\ +flexible, and not trying to limit that flexibility\\ +want to explain it without limiting it\\ +researchers should make their epistemological and theoretical perspectives clear\\ +so, will provide 6-phase guide, potential pitfalls, what makes good, and advantages and disadvantages\\ +Definitions: data corpus is all data collected\\ +data set is all data being used\\ +data item is each piece\\ +data extract is individual coded item\\ +patterns = themes\\ +we want to identify, analyze and report themes.\\ +organize, described data set, interpret aspects of research topic\\ +``emerging'' denies the active role the researcher always plays in indentifying patterns/themes, selecting those of interest and reporting them\\ +Thematic analysis can be a method that works both to reflect reality and to unpick or unravel the surface of reality. \\ +A good thematic analysis will make transparent the assumptions about the nature of the data, what they represent in terms of the world, reality,\\ +Thematic analysis involves choices that need to be explicitly considered and discussed, +before analysis, sometimes before collection\\ +theme: captures something important about the data in relation to the research question, and represents some level of patterned response or meaning, and researcher judgement determines what is a theme\\ +key theme: theme that is important to the research question\\ +furthermore there is no right or wrong method to measure prevalence, +even if do choose to use prevalence in technique for determining theme\\ +goal could be, provide a rich thematic descirption of entire data set\\ +inductive vs. theoretical thematic analysis\\ +inductive is bottom up, start with data, see if it connects to research question, but not in an epistemological vacuum\\ +theoretical is deductive is top down, where the research question is much more influential about what is noticed as a theme\\ +themes can be at semantic or explicit level vs. being at latent or interpresetive level\\ +but pick one of those two\\ +semantic: words mean surface meanings\\ +organize data,\\ +describe\\ +interpret: attempt to theorize the significance and broader meanings, implications\\ +see Patton1990\\ +latent level thematic analysis\\ +identify features that give the described themes their particular form and meaning\\ +latter tradition typically constructionist paradigm, and find overlap with discoure analysis\\ +here broader assumptions, structures, meanings are theorized as underpinnings of what is actually articulated\\ +compatible with psychoanalytic modes of interpretation\\ +Epistemology: essentialist/realist vs. constructionist\\ +essentialistrealist is simple, one way\\ +constructionist, where meaning and experience are socially produced, seeks to theorize the sociocultural contexts, and structural conditions, that enable the individual accounts\\ +latent is more constructionist, can overlap thematic discourse analysis\\ +not all laten is constructionist\\ +searching for repeated patterns of meaning\\ +step-by-step\\ +look for patterns of meaning and issues of potential interest\\ +want to report the content and meaning of these themes\\ +analysis involves moving back and forth between the dataset and the coded extracts and writing analysis\\ +when to be involved with the literature?\\ +some say early, so as to have nuanced anticipation of possible themes (possibly more theoretical)\\ +some say late, so that not predisposed to favor one idea over another (more inductive)\\ +\begin{tabular}{|p{2cm}|p{9cm}|}\hline +Phase&Description\\ \hline \hline +Data familiarization & transcribe, read, \ldots reread, note down initial ideas\\ +initial codes & code interesting features entire dataset, collating data relevant to each code\\ +search for themes & collating, gathering\\ +review themes & checking if themes work in relation to coded extracts and entire data set, generating a thematic map\\ +defining and naming themes & ongoing analysis refines the specifics of each theme and the overall story the analysis tells, generating clear defniitions and names for each theme\\ +producing the report & selection of vivid compelling extract examples, relate the analysis to the research question and literature, producing scholarly report\\ +\hline +\end{tabular} +}} diff --git a/literatureQualRes5.bib b/literatureQualRes5.bib new file mode 100644 index 0000000..8d94ebb --- /dev/null +++ b/literatureQualRes5.bib @@ -0,0 +1,58 @@ + +@article{Morse-Barrett-Mayan-Olson-Spiers-Hon-2002b, +title={Verification Strategies for Establishing Reliability and Validity in Qualitative Research}, volume={1}, url={http://ejournals.library.ualberta.ca/index.php/IJQM/article/viewArticle/4603}, number={2}, journal={International Journal}, publisher={University of Alberta}, author={Morse, Janice M and Barrett, Michael and Mayan, Maria and Olson, Karin and Spiers, Jude and Hon, Dnurs}, editor={Smith, Lorenzo M and Pourboghrat, Farhang and Yoon, Jeong-Whan and Stoughton, Thomas BEditors}, year={2002}, pages={1--19}, +annote={Appropriate sample +participants who best represent or have knowledge of topic, resulting in\\ +efficient and effective saturation of categories\\ +detect sampling adequacy by saturation and replication (Morse 1991). +Sampling adequacy means sufficient data are present to account for all aspects of the phenomenon.\\ +Seeking negative cases is essential, becuase aspects that are initially less than obvious will be indicated.\\ +Saturating data, by definition, ensures replication in categories. \\ +The replication verifies (ok) and ensures comprehension (not so sure) and completeness.\\ + +Collecting and analyzing data concurrently is essential for reliability and validity. (so they say, and in exploring a search tree where not allowed to retrace your steps, would be important, but we are not in that situation) + +Thinking theoretically:\\ +ideas emerging from data are reconfirmed in new data (Isay or maybe they are not)\\ +produces new ideas, must be (back) verified in the data already collected\\ +requires macro-micro perspectives, samll steps, no cognitive leaps, constantly checking and rechecking\\ + +Theory development\\ +more with deliberation between a micro perspective of the data and a macro conceptual/theoretical understanding\\ +Theory is developed throughtwo mechanisma\\ +outcome of research (not adopted as a framework)\\ +template for comparison and further development of the theory\\ +valid theories are well-developed and informed, comprehensive, logical, parsimonious, and consistent\\ +Glaser 1978 and Morse 1997 are references. + +Attending to rigor throughout the research process will have important ramifications for qualitative inquiry, +verification and attention to rigor will be evident in the quality of the text. Excellent inquiry is stunning: the arguments are sophisticated in that they are complex yet elegant, focused yet profound, surprising yet obvious.}} +@article{Birks01012008, +author = {Birks, Melanie and Chapman, Ysanne and Francis, Karen}, +title = {Memoing in qualitative research}, +volume = {13}, +number = {1}, +pages = {68-75}, +year = {2008}, +doi = {10.1177/1744987107081254}, +abstract ={This paper explores memoing in the context of qualitative research methodologies. The functions of memos in the research process are discussed and a number of techniques for employing memo writing to enhance the research experience and outcomes are examined. Memoing is often discussed in the literature as a technique employed in grounded theory research, yet there is limited exploration of the value of memo writing in qualitative methodologies generally. Memoing serves to assist the researcher in making conceptual leaps from raw data to those abstractions that explain research phenomena in the context in which it is examined. Memos can be effectively employed by both the novice and experienced researcher as a procedural and analytical strategy throughout the research process. Data exploration is enhanced, continuity of conception and contemplation is enabled and communication is facilitated through the use of memoing. While guidelines exist to aid in the production and use of memos, memoing remains a flexible strategy wherein the process of construction and nature of content is determined by the preferences and abilities of the researcher and the aims and focus of the specific research study.}, +URL = {http://jrn.sagepub.com/content/13/1/68.abstract}, +eprint = {http://jrn.sagepub.com/content/13/1/68.full.pdf+html}, +journal = {Journal of Research in Nursing} , +annote={techniques for employing memo writing\\ +helps the leap from raw data to abstraction\\ +often employed in grounded theory, also useful in basic inductive\\ +qual: contextually situated meaning\\ +} +} + +@article{marton2006sameness, + title={Sameness and difference in transfer}, + author={Marton, Ference}, + journal={The Journal of the Learning Sciences}, + volume={15}, + number={4}, + pages={499--535}, + year={2006}, + publisher={Taylor \& Francis} +} \ No newline at end of file diff --git a/literatureQualRes6.bib b/literatureQualRes6.bib new file mode 100644 index 0000000..38f426a --- /dev/null +++ b/literatureQualRes6.bib @@ -0,0 +1,124 @@ + @article{Johnson2007, +author = {Johnson, R. Burke and Onwuegbuzie, Anthony J. and Turner, Lisa A.}, +title = {Toward a Definition of Mixed Methods Research}, +volume = {1}, +number = {2}, +pages = {112-133}, +year = {2007}, +doi = {10.1177/1558689806298224}, +abstract ={The purpose of this article is to examine how the field of mixed methods currently is being defined. The authors asked many of the current leaders in mixed methods research how they define mixed methods research. The authors provide the leaders' definitions and discuss the content found as they searched for the criteria of demarcation. The authors provide a current answer to the question, What is mixed methods research? They also briefly summarize the recent history of mixed methods and list several issues that need additional work as the field continues to advance. They argue that mixed methods research is one of the three major "research paradigms" (quantitative research, qualitative research, and mixed methods research). The authors hope this article will contribute to the ongoing dialogue about how mixed methods research is defined and conceptualized by its practitioners.}, +URL = {http://mmr.sagepub.com/content/1/2/112.abstract}, +eprint = {http://mmr.sagepub.com/content/1/2/112.full.pdf+html}, +journal = {Journal of Mixed Methods Research} +} + + + +@misc{Bernard1994, +key={B94}, +howpublished={\url{http://safetynet.aap.org/}}} + +@misc{Fine2003, +key={fine2003}, +howpublished={\url{http://safetynet.aap.org/}}} + +@misc{JohnsonSackett1998, +key={JS}, +howpublished={\url{http://safetynet.aap.org/}}} + +@misc{Senschul1999, +key={s99}, +howpublished={\url{http://safetynet.aap.org/}}} + +@misc{DeMunck, +key={dem}, +howpublished={\url{http://safetynet.aap.org/}}} + + +@misc{Kottak1994, +key={K}, +howpublished={\url{http://safetynet.aap.org/}}} + +@misc{SeymourHewitt2000, +key={SH}, +howpublished={\url{http://safetynet.aap.org/}}} + +@misc{saturate, +author={Jonathan Sillito}, +title={Saturate Application}, +howpublished={\url{http://www.saturateapp.com/}}} + +@misc{surveymonkey, +author={unknown }, +title={Survey Monkey Application}, +howpublished={\url{http://www.surveymonkey.com/}}} + +@misc{Play, +author={Kamran Sedig}, +title={From Play to Thoughtful Learning: A Design Strategy to Engage Children with Mathematical Representations}, +journal={Journal of Computers in Mathematics and Science Teaching}, + volume=27, + number= 1 , +pages={65-101}, +year=2008, +annote={game like starts like geometry}} + +@ARTICLE{6155163, +author={Goldman, Glenn}, +journal={Computer Graphics and Applications, IEEE}, +title={Digital Media and the Beginning Designer}, +year={2012}, +volume={32}, +number={2}, +pages={14 -21}, +abstract={Use and creation of computer graphics can be effectively taught to beginning design students in the context of discipline-specific design projects. In particular, a case study of the pedagogy implemented by the New Jersey Institute of Technology's College of Architecture + Design provides examples of how teachers harness the students' desire to create and provide educational opportunities for undergraduates to learn about the use of digital media in the processes and products of design. Employing a carefully constructed sequence, students are exposed to (and use) computer applications for raster imaging, vector drawing, 3D modeling and rendering, and eventually building information modeling and time-based sequential representation all while producing original work through analysis and synthesis.}, +keywords={}, +doi={10.1109/MCG.2012.35}, +ISSN={0272-1716},} + +@article {MEET:MEET14504701336, +author = {Given, Lisa M. and Julien, Heidi and Ouellette, Dana and Smith, Jorden}, +title = {Evidence-based information literacy instruction: Curriculum planning from the ground up}, +journal = {Proceedings of the American Society for Information Science and Technology}, +volume = {47}, +number = {1}, +publisher = {Wiley Subscription Services, Inc., A Wiley Company}, +issn = {1550-8390}, +url = {http://dx.doi.org/10.1002/meet.14504701336}, +doi = {10.1002/meet.14504701336}, +pages = {1--2}, +year = {2010}, +abstract = {The purpose of this longitudinal research study is to assess the information literacy (IL) skills of grade 12 students as they transition to university in order to determine their preparedness for academic work in the digital age. This poster reports the results of the first phase of this study which included a university-wide information literacy instruction (ILI) audit, as well as the administration of the quantitative Information Literacy Test (ILT) to 103 grade 12 students. Results indicate a gap between the expectations and skills required in secondary and post-secondary education. The results of this study contribute new knowledge to the research literature on IL, by providing a unique understanding of the information literacy skills possessed by grade 12 students as they transition to university. This will also be important for professional practice by providing librarians tasked with ILI with evidence enabling construction of tailored curriculum to address specific IL deficits shown by new students.}, +} + +%Piaget constructivism +@inbook{Piagetf, +author={Jean Piaget}, +year= 1967, +title={Logique et Connaissance scientifique}, +booktitle={Encyclop\'edie de la Pl\'eiade}, +publisher={Gallimard}} + +@book{Piagete, +author={Jean Piaget}, +year=1950, +title={The Psychology of Intelligence}, +publisher={New York: Routledge}} + +%SeymourPapert, constructionism +@book{Papert, +title={Constructionism}, +editor={ Papert and Harel}, +publisher={Norwood, NJ: Ablex Publishing Company}, +year= 1991} + +@book{1978Glaser, +author={Glaser, B. G.}, +year=1978, +title={Theoretical Sensitivity}, +address={Mill Valley, CA.}, +publisher={The Sociology Press}} + +% Constructivist Grounded Theory (Bryant \& Charmaz, 2010). + +Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Grounded theory procedures and techniques (2nd ed.). Newbury Park, CA: Sage. \ No newline at end of file diff --git a/literatureproof.bib b/literatureproof.bib new file mode 100644 index 0000000..d5960e6 --- /dev/null +++ b/literatureproof.bib @@ -0,0 +1,242 @@ +@misc{criticalThinking, +howpublished={\url{www.criticalthinking.org/pages/defining-critical-thinking/410} viewed September 26, 2013} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2013 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{bussey2013variation, + title={Variation theory: A theory of learning and a useful theoretical framework for chemical education research}, + author={Bussey, Thomas J and Orgill, MaryKay and Crippen, Kent J}, + journal={Chemistry Education Research and Practice}, + volume={14}, + number={1}, + pages={9--22}, + year={2013}, + publisher={Royal Society of Chemistry} +} +@article{sun2013assessment, + title={Assessment of Prospective Teachers’ Multiple Proof Construction of a Trapezoid Area Formula}, + author={Sun, Xuhua}, + journal={New Waves-Educational Research \& Development}, + volume={16}, + number={1}, + year={2013} +} + +@article{malmi2013doctoral, + title={Doctoral studies in computing education research: part 1}, + author={Malmi, Lauri}, + journal={ACM Inroads}, + volume={4}, + number={4}, + pages={18--19}, + year={2013}, + publisher={ACM} +} +@article{hellqvist2013students, + title={Students’ experiences of participation in the disciplines Computer Science, Physics, and Earth Sciences as an aspect of novice students’ identity}, + author={Hellqvist, Magnus and Lindblad, Andreas and Peters, Anne-Kathrin}, + year={2013} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2012 +% % % % % % % % % % % % % % % % % % % % % % % % +@incollection{jones2012proof, + title={Proof, proving, and teacher-student interaction: Theories and contexts}, + author={Jones, Keith and Herbst, Patricio}, + booktitle={Proof and proving in mathematics education}, + pages={261--277}, + year={2012}, + publisher={Springer} +} +@article{kinnunen2012phenomenography, + title={Phenomenography and grounded theory as research methods in computing education research field}, + author={Kinnunen, P{\"a}ivi and Simon, Beth}, + journal={Computer Science Education}, + volume={22}, + number={2}, + pages={199--218}, + year={2012}, + publisher={Taylor \& Francis} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2011 +% % % % % % % % % % % % % % % % % % % % % % % % + +@article{bauldryappendix, + title={Appendix {C}: Projects in Real Analysis}, + author={Bauldry, William C}, + journal={Introduction to Real Analysis: An Educational Approach}, + pages={239--251}, + year=2011, + publisher={Wiley Online Library} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2010 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{rundgren2010critical, + title={CRITICAL FEATURES OF VISUALIZATIONS OF TRANSPORT THROUGH THE CELL MEMBRANE -- AN EMPIRICAL STUDY OF UPPER SECONDARY AND TERTIARY STUDENTS' MEANING-MAKING OF A STILL IMAGE AND AN ANIMATION}, + author={Rundgren, Carl-Johan and Tibell, Lena AE}, + journal={International Journal of Science and Mathematics Education}, + volume={8}, + number={2}, + pages={223--246}, + year={2010}, + publisher={Springer} +} +@techreport{thune2010students, + title={Students' Conceptions of Computer Programming}, + author={Thun{\'e}, Michael and Eckerdal, Anna}, + institution={Uppsala Universitet}, + year={2010} +} +% % % % % % % % % % % +% 2009 +% % % % % % % % % % % +@article{thune2009variation, + title={Variation theory applied to students’ conceptions of computer programming}, + author={Thun{\'e}, Michael and Eckerdal, Anna}, + journal={European Journal of Engineering Education}, + volume={34}, + number={4}, + pages={339--347}, + year={2009}, + publisher={Taylor \& Francis} +} + +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2007 +% % % % % % % % % % % % % % % % % % % % % % % % + +@inproceedings{suhonen2007applications, + title={Applications of variation theory in computing education}, + author={Suhonen, Jarkko and Davies, Janet and Thompson, Errol and others}, + booktitle={Proceedings of the Seventh Baltic Sea Conference on Computing Education Research-Volume 88}, + pages={217--220}, + year={2007}, + organization={Australian Computer Society, Inc.} +} + + +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2005 +% % % % % % % % % % % % % % % % % % % % % % % % +@inproceedings{eckerdal2005novice, + title={Novice {J}ava programmers' conceptions of object and class, and variation theory}, + author={Eckerdal, Anna and Thun{\'e}, Michael}, + booktitle={ACM SIGCSE Bulletin}, + volume={37}, + number={3}, + pages={89--93}, + year={2005}, + organization={ACM} +} +@inproceedings{eckerdal2005does, + title={What does it take to learn 'programming thinking'?}, + author={Eckerdal, Anna and Thun{\'e}, Michael and Berglund, Anders}, + booktitle={Proceedings of the first international workshop on Computing education research}, + pages={135--142}, + year={2005}, + organization={ACM} +} +@article{marton2005unit, + title={On the unit of description in phenomenography}, + author={Marton, Ference and Pong, Wing Yan}, + journal={Higher Education Rresearch \& Development}, + volume={24}, + number={4}, + pages={335--348}, + year={2005}, + publisher={Taylor \& Francis} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2003 +% % % % % % % % % % % % % % % % % % % % % % % % + +@article{hazzan2003students, + title={How students attempt to reduce abstraction in the learning of mathematics and in the learning of computer science}, + author={Hazzan, Orit}, + journal={Computer Science Education}, + volume={13}, + number={2}, + pages={95--122}, + year={2003}, + publisher={Taylor \& Francis} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 2002 +% % % % % % % % % % % % % % % % % % % % % % % % +@book{krantz2002handbook, + title={Handbook of logic and proof techniques for computer science}, + author={Krantz, Steven George}, + year={2002}, + publisher={Springer} +} +@article{reid2002students, + title={Students' conceptions of statistics: A phenomenographic study}, + author={Reid, Anna and Petocz, Peter}, + journal={Journal of Statistics Education}, + volume={10}, + number={2}, + pages={1--28}, + year={2002} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1997 +% % % % % % % % % % % % % % % % % % % % % % % % +@book{marton1997learning, + title={Learning and awareness}, + author={Marton, Ference and Booth, Shirley A}, + year={1997}, + publisher={Routledge} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 1993 +% % % % % % % % % % % % % % % % % % % % % % % % +@article{ramsden1993theories, + title={Theories of learning and teaching and the practice of excellence in higher education}, + author={Ramsden, Paul}, + journal={Higher Education Research and Development}, + volume={12}, + number={1}, + pages={87--97}, + year={1993}, + publisher={Taylor \& Francis} +} +@book{saljo1979learning, + title={Learning in the learner's perspective. {I}. Some common-sense conceptions}, + author={Saljo, Roger}, + year={1979}, + publisher={ERIC Clearinghouse} +} +@article{wyndhamn1997word, + title={Word problems and mathematical reasoning—A study of children's mastery of reference and meaning in textual realities}, + author={Wyndhamn, Jan and S{\"a}lj{\"o}, Roger}, + journal={Learning and Instruction}, + volume={7}, + number={4}, + pages={361--382}, + year={1997}, + publisher={Elsevier} +} +@article{marton1976qualitative, + title={ON QUALITATIVE DIFFERENCES IN LEARNING -- {II} {O}UTCOME AS A FUNCTION OF THE LEARNER'S CONCEPTION OF THE TASK}, + author={Marton, Ference and S{\"a}alj{\"o}, R}, + journal={British Journal of Educational Psychology}, + volume={46}, + number={2}, + pages={115--127}, + year={1976}, + publisher={Wiley Online Library} +} + +@article{svensson1997theoretical, + title={Theoretical foundations of phenomenography}, + author={Svensson, Lennart}, + journal={Higher Education Research \& Development}, + volume={16}, + number={2}, + pages={159--171}, + year={1997}, + publisher={Taylor \& Francis} +} \ No newline at end of file diff --git a/macros.tex b/macros.tex new file mode 100644 index 0000000..1e38d92 --- /dev/null +++ b/macros.tex @@ -0,0 +1 @@ +%%%% Add any personal macros here. \ No newline at end of file diff --git a/materials.tex b/materials.tex new file mode 100644 index 0000000..7a62228 --- /dev/null +++ b/materials.tex @@ -0,0 +1 @@ +Ball states\cite[p. 38]{loewenberg2003mathematical} "The creation of materials, tools and processes that can be widely used in mathematics education is an important component of a problem-centered program of research and development. In fields such as medicine, agriculture, and computer science, this type of research-based development is key to advances in the technologies of each practice." diff --git a/p93.png b/p93.png new file mode 100644 index 0000000..097722e Binary files /dev/null and b/p93.png differ diff --git a/parking.tex b/parking.tex new file mode 100644 index 0000000..761fc60 --- /dev/null +++ b/parking.tex @@ -0,0 +1,65 @@ +\section{Mathematization Related Proofs Using the Pumping Lemma for Regular Languages} +We taught the introduction to the theory of computing course from Sipser's +third edition\cite{sipser2012introduction}, using chapters 1 through 5 and 7. The pumping lemmas were +given emphasis in class, help sessions and tutoring, in homework, exams, and +in review. We treated the pumping lemma in the context of logic, emphasizing +the inversion of quantifiers. We discovered that some students seem to +tire of attending to statements with more than one quantifier, consistent with +Devlin \cite{devlin2012mathematical}. We also treated the pumping lemma with diagrams of machines +from Sipser's book\cite{sipser2012introduction}. We encouraged student collaboration on all learning +activities, including homework. +For grading, we used only work (exams) known to be individual. +To encourage active learning \cite{prince2004does} beyond using the classroom response system, +we assigned participation in a discussion of a specified question, weekly. We +discovered that students preferred to have their contributions to these discussions +be anonymous to other students. + +\section{Proofs by Induction} + +We carried out a qualitative study, inspired by the ideas of Marton et al.\cite{marton1981phenomenography,svensson1997theoretical,marton1997learning,marton2005unit}] on phenomenography and variation theory. We are using qualitative +techniques because we seek to be able to describe the nature of the various +understandings achieved by the students, rather than the relative frequency +with which any particular understanding is obtained. Phenomenography and +its extension, variation theory, are applicable to this study, because the variety +of outcomes in student understanding can be used to guide future offerings of +the course. +Marton and other researchers, e.g., Bussey, using phenomenography and variation +theory \cite{bussey2013variation} direct attention to the information intended by the instructor +for delivery to the student and the information received by the student. These +are not necessarily the same: the student may take in material with a different +emphasis than intended by the lecturer, such as specifics of an example that are +unimportant for illustration of the intended point. Items that seem obvious to +the instructor might not be to the student. Bussey et al. observe that “variation +theory is a useful framework for guiding qualitative educational research studies +that attempt to identify gaps between teaching and learning.” \cite{bussey2013variation}We attempt +to address the third goal identified by Bussey et al., ``describe the variation in +student understanding of a given object of learning after the learning event +has taken place''. We want to identify what Suhonen et al. \cite{suhonen2007applications} call ``critical +aspects'', in the area of proof by mathematic induction, those that seem to be conceptually +difficult, or are seen not to have been grasped by the students. +We used semi-structured interviews with students to learn their conceptualizations +of proof. + + +\section{Conceptions of Domain, range, mapping, relation, function, +equivalence in Proofs} +\section{Conceptions of Definitions, Language, Reasoning in Proofs} +\section{Conceptions of Equivalence, Abstraction in Proofs} + +\section{Instructive Problems} +``Instructive problem'':begin with a problem situation that embodies key aspects of the topic, and mathematical techniues are developed as reasonable responses'' This note was made the weekend I was reading research in collegiate mathematics education 3, and I left no reference. + +\section{List of Questions for Initial (Before course) Assessment for Discrete Structures} +This list of questions is designed to elicit data about the mental representations students have prepared for encountering the teaching they are about to receive in the discrete structures course. + +Discrete structures is the course in the curriculum that (re)acquaints students with proof, which will be used in other courses, including Algorithms and Introduction to the Theory of Computing, and possibly Data Structures, depending upon how it is taught, and possible Software Engineering, depending upon how it is taught. + +The purpose of the instrument is to determine what level of skill with proof exists in the students, as they arrive. +The problems include problem situations posed in a variety of representations: words, and/or symbolically, and/or by figures and/or as pseudocode. +The students are asked to, in some cases, match the problems that are expressed in multiple ways, and in some cases provide the missing representation form. + +This instrument was developed using inspiration from Gibson\cite{gibson1998students}, as well as Nelson\cite{nelson1993proofs}. + +%these came out of chapter 4 +\section{Mathematical Definitions, Language, Reasoning} +\section{Equivalence Classes, Generic Particular, Abstraction in Proofs} \ No newline at end of file diff --git a/pic1.png b/pic1.png new file mode 100644 index 0000000..efbe370 Binary files /dev/null and b/pic1.png differ diff --git a/pic10.png b/pic10.png new file mode 100644 index 0000000..012ec1d Binary files /dev/null and b/pic10.png differ diff --git a/pic2.png b/pic2.png new file mode 100644 index 0000000..6190b1c Binary files /dev/null and b/pic2.png differ diff --git a/pic3.png b/pic3.png new file mode 100644 index 0000000..be266bf Binary files /dev/null and b/pic3.png differ diff --git a/pic4.png b/pic4.png new file mode 100644 index 0000000..a4f2f9b Binary files /dev/null and b/pic4.png differ diff --git a/pic5.png b/pic5.png new file mode 100644 index 0000000..cc33ba1 Binary files /dev/null and b/pic5.png differ diff --git a/pic6.png b/pic6.png new file mode 100644 index 0000000..333e08f Binary files /dev/null and b/pic6.png differ diff --git a/pic7.png b/pic7.png new file mode 100644 index 0000000..b89d44e Binary files /dev/null and b/pic7.png differ diff --git a/pic8.png b/pic8.png new file mode 100644 index 0000000..26b6ded Binary files /dev/null and b/pic8.png differ diff --git a/pic9.png b/pic9.png new file mode 100644 index 0000000..3445001 Binary files /dev/null and b/pic9.png differ diff --git a/preamble.tex b/preamble.tex new file mode 100644 index 0000000..84d4bf7 --- /dev/null +++ b/preamble.tex @@ -0,0 +1,74 @@ +%There are portions of this file which are editable, and portions which should not be adjusted. I've clearly labeled the section where your customizations should be written. + +%%%%%%%%%%%%%%%%%%%% +%% Do not edit!!! %% +%%%%%%%%%%%%%%%%%%%% +\usepackage{ + amsmath, + amsthm, + amssymb, + fancyhdr, + setspace, +} +\usepackage[ + paper=letterpaper, + left=1.5in, + top=1in, + bottom=1in, + right=1in, + includehead, + includefoot +] +{geometry} +\usepackage[titles]{tocloft} +\setlength{\cftbeforechapskip}{2ex} +\setlength{\cftbeforesecskip}{0.5ex} +\renewcommand{\cftchapfont}{\bfseries} +\renewcommand{\cftchapaftersnum}{.} +\renewcommand{\cftsecfont}{} +\renewcommand{\cftchappagefont}{\mdseries} +\renewcommand\cftchappresnum{Ch.\,} +\setlength{\cftchapnumwidth}{3.75em} +\usepackage{sectsty} +\allsectionsfont{\singlespacing} +\pagestyle{fancy} +\rhead{\thepage} +\cfoot{} +\lhead{} +\chead{} +\renewcommand{\headrulewidth}{0pt} +\renewcommand{\footrulewidth}{0pt} + +%%%%%%%%%%%%%%%%%%%% +%%%%% Editable %%%%% +%%%%%%%%%%%%%%%%%%%% + +%\usepackage{} +\usepackage{graphicx} +\usepackage{url} +\usepackage[center,small,sc]{caption} + +\usepackage{color} +\usepackage{algorithm2e} +\usepackage{algorithmic} +\usepackage{float} +\usepackage{multicol} + +\theoremstyle{plain} +\newtheorem{thm}{Theorem}[section] +\newtheorem{lemma}[thm]{Lemma} +\newtheorem{prop}[thm]{Proposition} +\newtheorem{cor}[thm]{Corollary} +\theoremstyle{definition} +\newtheorem{dfn}[thm]{Definition} +\newtheorem{ex}[thm]{Example} +\newtheorem{remark}[thm]{Remark} +\numberwithin{equation}{section} +\numberwithin{figure}{section} +\numberwithin{table}{section} + +%%%%%%%%%%%%%%%%%%%% +%% Do not edit!!! %% +%%%%%%%%%%%%%%%%%%%% +\input{macros.tex} +\doublespacing \ No newline at end of file diff --git a/thesis2.tex b/thesis2.tex new file mode 100644 index 0000000..887c1a4 --- /dev/null +++ b/thesis2.tex @@ -0,0 +1,74 @@ +%%%---- Do not adjust ----%%% +\documentclass[12pt,oneside]{book} +\input{preamble.tex} +%%%-----------------------%%% + +%Add your data to the following commands. +%%%%%%%%%%%%%%%%%%%%% +\newcommand{\mythesistitle}{Categories of Conceptions of Proofs by\\Students of Computer Science} +\newcommand{\myname}{Th\'er\`ese Mary Smith} +\newcommand{\myyear}{2016} +\newcommand{\degreeone}{S.B. Physics, Massachusetts Institute of Technology, Cambridge, +Massachusetts, USA, 1975} +\newcommand{\degreeoneshort}{S.B.\ Physics} +\newcommand{\degreetwo}{M.S. Biomedical Engineering, Iowa State University of Science and +Technology, Ames, Iowa, USA, 1982} +\newcommand{\degreetwoshort}{M.S.\ BME} +\newcommand{\degreethree}{M.S. Computer Science and Engineering, University of Connecticut, Storrs, +Connecticut, USA, 2014} +\newcommand{\degreethreeshort}{M.S.\ CSE} +\newcommand{\majoradvisor}{Robert McCartney} +\newcommand{\associateone}{Sanguthevar Rajasekaran} +\newcommand{\associatetwo}{Jinbo Bi} +%%%%%%%%%%%%%%%%%%%%% + +%%%---- Do not adjust ----%%% +\begin{document} +\input{frontmatter.tex} +\singlespacing +\tableofcontents +\thispagestyle{plain} +\mainmatter +\doublespacing +%%%-----------------------%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%---- Input content ----%%% +\input{ch1.tex} %intro +\input{ch2.tex} %design of the study +\input{ch3.tex} %research perspective and epistemological framework +\input{ch4.tex} %methodology +\input{ch5.tex} %data +\input{ch6.tex} %data analysis and interpretation +\input{ch7.tex} %what got produced by analysis +\input{ch8.tex} %validity and reliability +\input{ch9.tex} %related work +\input{ch10.tex} %conclus +\input{ch11.tex} %future work +%\input{TODOs.tex} +%... etc. +%%%-----------------------%%% + +\newpage +\addcontentsline{toc}{chapter}{Bibliography} +\bibliography{literature,literatureClickersTheory,literatureFIE,literatureproof,literatureQualRes,literatureQualRes2,literatureQualRes3,literatureQualRes4,literatureQualRes5,literatureQualRes6,litMathPhenom,litSEEval,litSEQual,litVertical2} %{} +\bibliographystyle{amsplain} +\newpage +%\appendix{Materials} +%\input{materials.tex} +%\newpage +%\appendix{Incoming Assessment for Object Oriented Software} +%\input{incomingOO.tex} +%\newpage +\appendix{Incoming Assessment for Discrete Math} +\input{QlistCSE2500.tex} +%\newpage +%\appendix{Incoming Assessment for Algorithms} +%\input{incomingAlgos.tex} +%\newpage +%\appendix{Incoming Assessment for Introduction to the Theory of Computation} +%\input{incomingTheory.tex} %in which proofs of correctness of resource util. +\end{document} \ No newline at end of file