From 72a22cac1712f57b355c23b7e1be75da068b7f61 Mon Sep 17 00:00:00 2001 From: theresesmith Date: Mon, 10 Aug 2015 10:04:53 -0400 Subject: [PATCH] save the thesis --- .classpath | 6 + .gitignore | 1 + .project | 17 + .settings/org.eclipse.jdt.core.prefs | 11 + CSE2500IncomingAssessment.tex | 240 +++++ TODOs.tex | 4 + abstract.tex | 9 + acknowledgments.tex | 1 + ch1.tex | 150 ++++ ch10.tex | 242 ++++++ ch2.tex | 143 +++ ch3.tex | 123 +++ ch4.tex | 169 ++++ ch5.tex | 282 ++++++ ch6.tex | 353 ++++++++ ch7.tex | 175 ++++ ch8.tex | 385 ++++++++ ch9.tex | 64 ++ chp7p1.png | Bin 0 -> 19406 bytes frontmatter.tex | 118 +++ incomingAlgos.tex | 67 ++ incomingDiscrete.tex | 239 +++++ incomingOO.tex | 11 + incomingTheory.tex | 67 ++ litMathPhenom.bib | 48 + litSEEval.bib | 176 ++++ litSEQual.bib | 526 +++++++++++ litVertical.bib | 968 +++++++++++++++++++++ literature.bib | 1204 ++++++++++++++++++++++++++ literatureClickersTheory.bib | 114 +++ literatureFIE.bib | 646 ++++++++++++++ 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create mode 100644 literatureQualRes4.bib create mode 100644 literatureQualRes5.bib create mode 100644 literatureQualRes6.bib create mode 100644 literatureproof.bib create mode 100644 macros.tex create mode 100644 materials.tex create mode 100644 p93.png create mode 100644 pic1.png create mode 100644 pic10.png create mode 100644 pic10GNU.png create mode 100644 pic2.png create mode 100644 pic2GNUPaint.png create mode 100644 pic3.png create mode 100644 pic4.png create mode 100644 pic5.png create mode 100644 pic6.png create mode 100644 pic7.png create mode 100644 pic8.png create mode 100644 pic9.png create mode 100644 preamble.tex create mode 100644 thesis.tex create mode 100644 useConceptionsGuidePrep.tex diff --git a/.classpath b/.classpath new file mode 100644 index 0000000..fb565a5 --- /dev/null +++ b/.classpath @@ -0,0 +1,6 @@ + + + + + + diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..ae3c172 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +/bin/ diff --git a/.project b/.project new file mode 100644 index 0000000..ee63325 --- /dev/null +++ b/.project @@ -0,0 +1,17 @@ + + + forThesis + + + + + + org.eclipse.jdt.core.javabuilder + + + + + + org.eclipse.jdt.core.javanature + + diff --git a/.settings/org.eclipse.jdt.core.prefs b/.settings/org.eclipse.jdt.core.prefs new file mode 100644 index 0000000..7341ab1 --- /dev/null +++ b/.settings/org.eclipse.jdt.core.prefs @@ -0,0 +1,11 @@ +eclipse.preferences.version=1 +org.eclipse.jdt.core.compiler.codegen.inlineJsrBytecode=enabled +org.eclipse.jdt.core.compiler.codegen.targetPlatform=1.7 +org.eclipse.jdt.core.compiler.codegen.unusedLocal=preserve +org.eclipse.jdt.core.compiler.compliance=1.7 +org.eclipse.jdt.core.compiler.debug.lineNumber=generate +org.eclipse.jdt.core.compiler.debug.localVariable=generate +org.eclipse.jdt.core.compiler.debug.sourceFile=generate +org.eclipse.jdt.core.compiler.problem.assertIdentifier=error +org.eclipse.jdt.core.compiler.problem.enumIdentifier=error +org.eclipse.jdt.core.compiler.source=1.7 diff --git a/CSE2500IncomingAssessment.tex b/CSE2500IncomingAssessment.tex new file mode 100644 index 0000000..97488ae --- /dev/null +++ b/CSE2500IncomingAssessment.tex @@ -0,0 +1,240 @@ +\documentclass[]{article} +\usepackage{hyperref} +\usepackage{amsthm} +\usepackage[cmex10]{amsmath} +\interdisplaylinepenalty=2500 +\usepackage{amssymb} +\usepackage{graphicx} +%opening +\title{CSE2500 Incoming Assessment} +\author{} + +\begin{document} + +\maketitle + + + + +\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) + + +\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} + +\end{document} diff --git a/TODOs.tex b/TODOs.tex new file mode 100644 index 0000000..4301fe5 --- /dev/null +++ b/TODOs.tex @@ -0,0 +1,4 @@ +\newpage + +TODOs +read more on van Hiele levels and their theory \ 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..3ec4a5b --- /dev/null +++ b/acknowledgments.tex @@ -0,0 +1 @@ +Thank you to Professor Donald Sheehy for his helpful suggestions and exemplary teaching. \ No newline at end of file diff --git a/ch1.tex b/ch1.tex new file mode 100644 index 0000000..ee4349c --- /dev/null +++ b/ch1.tex @@ -0,0 +1,150 @@ +\chapter{Introduction} + +\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} + +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. + + $$While there are many aspects of students' conceptualizations of proofs that are interesting, we concentrate our attention onto proofs that seem to be useful in showing the correctness, progress, termination, safety and resource utilization of algorithms.$$ +It is important for students of computer science, and of computer science and +engineering (called, in the following, computer science) to comprehend and +apply simple 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. 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, 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. +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. +Phenomenology has also been invoked by mathematician Alan Schoenfeld in modeling teachin behavior. +His lesson segments are chosen for phenomological 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 judgement 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 metacognitive behavior'' +He had, earlier on the same page, described metacognitive behavior as reflecting and acting on what you know. +By contrast, 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. 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} + +We propose to research these questions: +\begin{itemize} +\item What do students think a proof is? (We want to know, do they understand deduction, abstraction, where are they on van Hiele levels ) +\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} + +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. + + +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 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 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..43318a1 --- /dev/null +++ b/ch10.tex @@ -0,0 +1,242 @@ +\chapter{Future Work} +Neuroscience ( and some study in software engineering) leads to believe helping students pay attention and remember intrinsic reward, the sense of pleasantness, helps students 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 thinkg 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..ae51b27 --- /dev/null +++ b/ch2.tex @@ -0,0 +1,143 @@ +\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 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{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 student 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. + +\subsection{Parts of the Study} +Part of the study was devoted to proofs. +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. + +\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{Instrument for Initial (Before course) Assessment for Discrete Structures} +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}. + diff --git a/ch3.tex b/ch3.tex new file mode 100644 index 0000000..5594c29 --- /dev/null +++ b/ch3.tex @@ -0,0 +1,123 @@ +\chapter{Research Perspective and Epistemological Framework}\footnote{In the psychological sense, rather than that of Brouwer} + +Part of the research perspective is formed by the goals for what students 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." + +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." + + + + +Marton developed the phenomenographic research perspective +\section{Phenomenography} +First there was phenomenography, which focused on the interface between the +student and the material. +\section{Variation Theory} +Then there was variation theory. +\section{Constructivism} +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 + +From McGowan, Tall 2013 Jour Math Behav ``\ldots an instrucotr 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 mathmatically more appropriate way Thompson 1994 p. 32. +Thomposn P N 1994 Students, functions and the undergraduate curriculur in Dubinsky, Schoenfeld and Kaput Research in collegiate mathematics education I, CBMS issue in math education vol 4 pp 21-44. + + +\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{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] + +Thoug it is easy to assume that communication between practitioners is carried out verbally, there are examples of proofs without words \cite{nelson1993proofs}. +\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. + +\section{Cognitive Science} +Leslie Valiant, in Circuits of the Mind, Oxford University Press [p. 103] 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)." +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." + + +\section{Neuroscience} +\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}. +\subsection{Brain Imaging} +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}). diff --git a/ch4.tex b/ch4.tex new file mode 100644 index 0000000..f940658 --- /dev/null +++ b/ch4.tex @@ -0,0 +1,169 @@ +\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} +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. We used homework +to observe student attempts at proofs. We used later interviews to explore the +understanding of proof by mathematical induction and the use of recursive +algorithms. We plan to use homework to observe student familiarity/facility +with dferent (specific) proof techniques: induction, construction, contradiction, +and what students think it takes to make an argument valid. We plan to +conduct interviews to investigate the remaining questions mentioned earlier. +\section{Sample Selection} +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. +\section{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 woment, +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. +\section{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. +\section{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{Definition, Language, Reasoning} +\section{Equivalence Classes, Generic Particular, Abstraction in Proofs} +\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. + +\section{Interviews} +\section{Documents} +\subsection{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. +\section{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} +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 focussed 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. +\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} \ No newline at end of file diff --git a/ch5.tex b/ch5.tex new file mode 100644 index 0000000..ffd481a --- /dev/null +++ b/ch5.tex @@ -0,0 +1,282 @@ +\chapter{Results} + +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. \ No newline at end of file diff --git a/ch6.tex b/ch6.tex new file mode 100644 index 0000000..f832047 --- /dev/null +++ b/ch6.tex @@ -0,0 +1,353 @@ +\chapter{Data Analysis and Interpretation} +\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{ Maybe duplicative?} +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 fromusing 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 + +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 $x = 0^a, y = 0^b1^a$\\ +$x = 0^{p-h}, y = 0^h$\\ +$x = 0^i, y = 0^i, z = 0^i1^j$ +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. +Figure 5.3.2: Categories of Student Conceptualizations of Proof by Induction +that Recursion Works +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} +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{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 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 [?], and the well-known empirical +misconception [?]. 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. [?]. +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]. '’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[?] 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.(Say something about how this is consistent with the procedural conceptualization, bifurcation in Tall's writing.) 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[?] 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. +Figure 5.3.4: Categories of Student Conceptualizations of Proof by Induction +that Recursion Works +\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{Helping Students Discern Abstraction} +\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..323554f --- /dev/null +++ b/ch7.tex @@ -0,0 +1,175 @@ +\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 diff --git a/ch8.tex b/ch8.tex new file mode 100644 index 0000000..24c565a --- /dev/null +++ b/ch8.tex @@ -0,0 +1,385 @@ +\chapter{Related Work} +\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.)" +\section{Abstraction} +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. +\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{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} +\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) +\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. +Thagard and Stewart~\cite{thagard2011aha} consider combinations of mental representations at the level of cognitive neuroscience. +They hypothesize a process of convolution. + +Thagard and Stewart~\cite[p. 12]{thagard2011aha} supply reasons why single neurons are thought insufficient to represent a concept, consistent with Valiant~\cite{valiant2000circuits}. +\section{ Neuroscience} + +``An odor present during learning \ldots enhances these memories when the participant +is re-exposed to the odor during slow-wave sleep after learning[?]'' +``There is strong evidence that eIF2$\alpha$ phosphorylation and the integrated stress +response are important regulators of hippocampal synaptic plasticity, with dual +effects of inducing long-term depression while suppressing long-term potentiation +and the different types of learning associated with each phenomenon. +``[?] + +``Adult neurogenesis plays an important role in learning and memory (Clelland et al., 2009, Deng et al. 2010 and Mattson 2012)'' from Brandhorst et al., A Periodic Diet that Mimics Fasting Promotes Multi-System Regeneration, Enhanced Cognitive Performance, and Healthspan, Cell Metabolism 7 July 2015 +Kowatari et al.'s\cite{kowatari2009neural} results supported the idea that ``training increases creativity via reorganized intercortical interactions''. +\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.'' +\ \ No newline at end of file diff --git a/ch9.tex b/ch9.tex new file mode 100644 index 0000000..33a9e17 --- /dev/null +++ b/ch9.tex @@ -0,0 +1,64 @@ +\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. +\section{ Perspective on Future Directions} \ No newline at end of file diff --git a/chp7p1.png b/chp7p1.png new file mode 100644 index 0000000000000000000000000000000000000000..6d950eb0385062660b7914c9c1d167189395948f GIT binary patch literal 19406 zcmeIabyQUCyD*IPs30IBT_OrfigYU}E!`m9j5I@vNViCrk}@=i)Bq|qv~+{O&@nQ^ zFbwhS8F`-HI`OXeJMVkGKfbljA1wCF-ut?*`|7$U{H2NZ2ey;o+53e$o;KcMA@cHKJ7kaLEctow( zze}B<&lY%iistgt&o#Y_w`b>z`Q-f&yJ!L;w1x|Kg2HuG87j~DmSW)s)emwDPTot( z&#r_&`S_!PFe)zmNjDYj!KGER_bkty-7F}t(=oAfThO17sm0oeN@ZkN+-EFoC~j!n zz~nZLO%>ah?i~16%4Zp!mV&fU{$r3>4A@E{_Cx?c$|E%HIv!qy)H_i;yf<|B;g|66 zw&HGqTaE|E>A?dON57WrBz`E~Yof%%n|Mlv{K1&)f6efr@nyU>e)r&)uKhP()S!MH 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zd0X`R;%glQ$ofjQRU)EQJI6l}fA@8>^QnpT+imVJYji>PsMTY=bqkjdX-~SR zld$sLCBI7DR-2dXQ$R|L76oZN9*c%=bIcjBR}^*)2G_J%I{Vq_ZFNCgONM{uK}qWO zfs#6a3lY%YW89jV08Yey0~)n>4%jZj2G(%?hl`KEH@Ij1Z!S){8KAUt^+&&gh{cam z&Tk-+7Q_;O66(ME!K&K;7I?2h0keaLCjyk+fL~)_1S)WN-*!$=0p|f_k8kKUo{EJ4 Qck$$9RHVx!U%mZ*0K10;i--$)\{\\ + disp(i);\\ +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item for ($i=n;i>0;i--$)\{\\ + disp(i);\\ +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item +i=n; +while ($i>n$)\{\\ + disp(i);\\ + i--; +\}\\ +Assuming there is no problem with disp, how do we prove that this loop terminates? +\item +i=n; +while ($$)\{\\ + 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..ba028e8 --- /dev/null +++ b/incomingDiscrete.tex @@ -0,0 +1,239 @@ +Product: +an assessment instrumentlist 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/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/litVertical.bib b/litVertical.bib new file mode 100644 index 0000000..3f7a7a0 --- /dev/null +++ b/litVertical.bib @@ -0,0 +1,968 @@ +% +%2015 +% +@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{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} +} +@book{kemmerer, +author={David Kemmerer}, +title={Cognitive Neurscience of Language}, +publisher={Psychology Press}, +year={2015} +} +@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} +} + +% +%2014 +% +@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} +} +@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} +} +% +%2013 +% +@book{hiebert2013conceptual, + title={Conceptual and procedural knowledge: The case of mathematics}, + author={Hiebert, James}, + year={2013}, + publisher={Routledge} +} +@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{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} +} +% +%2012 +% +@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{gentner2012analogical, + title={Analogical reasoning}, + author={Gentner, Dedre and Smith, Linsey}, + journal={Encyclopedia of human behavior}, + pages={130--136}, + year={2012}, + publisher={Elsevier Oxford, UK} +} +@book{gries2012science, + title={The science of programming}, + author={Gries, David}, + year={2012}, + publisher={Springer Science \& Business Media} +} +@book{sipser2012introduction, + title={Introduction to the Theory of Computation}, + author={Sipser, Michael}, + year={2012}, + publisher={Cengage Learning} +} +% +%2011 +% +@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}} +} +% +%2010 +% +@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{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} +} +% +%2010 +% +@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}, +} +% +%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{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} +} + +% +%2008 +% +@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{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{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} +} +% +%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{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} +} +% +%2006 +% +@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} +} + +@book{viete2006analytic, + title={The analytic art}, + author={Vi{\`e}te, Fran{\c{c}}ois and Witmer, T Richard}, + year={2006}, + publisher={Courier Corporation} +} +% +%2005 +% +@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{marton2005unit, + title={On the unit of description in phenomenography}, + author={Marton, Ference and Pong, Wing Yan}, + journal={Higher education research \& development}, + volume={24}, + number={4}, + pages={335--348}, + year={2005}, + publisher={Taylor \& Francis} +} +% +%2004 +% +@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{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} +} +% +%2003 +% +@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} +} +@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} +} +@book{rosen2003, + title={Discrete Mathematics and Its Applications, 5th ed.}, + author={Rosen, Kenneth H}, + year={2003}, + publisher={McGraw Hill} +} +% +%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} +} +% +%2001 +% +@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} +} +@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} +} +% +%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} +} +@book{valiant2000circuits, + title={Circuits of the Mind}, + author={Valiant, Leslie G}, + year={2000}, + publisher={Oxford University Press} +} +% +%1999 +% +@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} +} +@book{Mattuck, +author={Mattuck, Arthur}, +year={1999}, +title={Introduction to Analysis}, +publisher={Prentice Hall} +} +% +%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{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{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{rota1997phenomenology, + title={The phenomenology of mathematical beauty}, + author={Rota, Gian-Carlo}, + journal={Synthese}, + volume={111}, + number={2}, + pages={171--182}, + year={1997}, + publisher={Springer} +} +@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} +} +% +%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} +} +% +%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{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{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}, + annote={costs money} +} +% +%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} +} +% +%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} +} +% +%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{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} +} +% +%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 +% +@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} +} +% +%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} +} +% +%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..3fe8c61 --- /dev/null +++ b/literature.bib @@ -0,0 +1,1204 @@ +@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}, 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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{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{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{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 +% % % % % % % % % % % +@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} +} +% % % % % % % % % % % +% 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} +} + +@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.} +} + + +% % % % % % % % % % % % % % % % % % % % % % % % % +% 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{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} +} +@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 +% % % % % % % % % % % % % % % % % % % % % % % % +@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{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} +} +@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 +% % % % % % % % % % % % % % % % % % % % % % % % +@book{marton1997learning, + title={Learning and awareness}, + author={Marton, Ference and Booth, Shirley A}, + year={1997}, + publisher={Routledge} +} +@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{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} +} +@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{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} +} +% % % % % % % % % % % % % % % % % % % % % % % % % +% 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} +} \ 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. 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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} + +\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/thesis.tex b/thesis.tex new file mode 100644 index 0000000..25d45ce --- /dev/null +++ b/thesis.tex @@ -0,0 +1,73 @@ +%%%---- 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} %results +\input{ch6.tex} % data analysis and interpretation +\input{ch7.tex} %validity and reliability +\input{ch8.tex} %related work +\input{ch9.tex} %conclus +\input{ch10.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,litVertical} %{} +\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{incomingDiscrete.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 diff --git a/useConceptionsGuidePrep.tex b/useConceptionsGuidePrep.tex new file mode 100644 index 0000000..7356595 --- /dev/null +++ b/useConceptionsGuidePrep.tex @@ -0,0 +1,263 @@ +\documentclass[]{article} + +%opening +\title{} +\author{} + +\begin{document} + +\maketitle + +\begin{abstract} + +\end{abstract} + +\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 a 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 know which mathematical tools we wish to use, and on the other hand we have an idea of the extent of the students' conceptualizatons. 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 rigourous description of these processes. +Path algebra ought to be accessible. to the students. +We could introduce (typed) lanbda 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. + +\subsubsection{Instructions} +Having the use of typed lanbda calculus for path algebra, we can then use it to describe the effect of instructions in the context of Floyd-Hoare triples. + +\subsubsection{Derivation} +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{Use of Bridging Material} +The material on mathemtatical tools we wish to use should be introduced at a level that addresses the conceptualizataions 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 point 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 highlight the critical aspects that distinguish one 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 becomes 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 \ref{} 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 to match well with the phenomenography of Rota\cite{}, who found that short proofs were more beautiful and more memorable, we prefer this style. + + + +\subsubsection{Symbolization} +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. + +\paragraph{Self-assessment Questions} +%if you do well on questions, you can skip to next +%symbols are used in Floyd-Hoare triples, so use them in self-assessment questions +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 ($\neg$d)(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 variables 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. +\paragraph{Material} +Variables, which can be individual letters, or names, either in computer programs or in mathematical statements, are used to represent ideas. +In programs, meaningful variable names have been shown to increase the speed and correctness of comprehension.~\cite{}%teaching and learning formal methods +In mathematical statements, single letter variable names have been shown to improve the skill of abstraction.\cite{} + +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 program language, such as MATLAB, that supports vector variables, you will have seen single variables that can refer to many individual values at once. Likewise, you may have worked with arrays of one or more dimensions; reflecting on this, the array name (without specified indices) can be thought 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 students 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{Gries} %in TLFM +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 processes that can be carried out confidently are not used due to lack of a means to determine whether the process is appropriate to circumstances. + +\paragraph{Self-assessment Questions} +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 of the recursive algorithm map to the induction step. 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 deLorean.\\ +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 the above simple algorithm, we could have $A_{TM}$.\\ +We cannot get $A_{TM}$.\\ +So, we cannot have $E_{TM}$ and the above simple algorithm.\\ +We can have the simple algorithm,$M$.\\ +So, it must be that we cannot get $E_{TM}$. + +In symbols:\\ +$\neg A_{TM}$\\ +$M \land E_{TM} \rightarrow A_{TM}$\\ +$\neg A_{TM} \rightarrow \neg (M \land E_{TM})$\\ +$\neg (M \land E_{TM})$\\ +$\neg M \lor \neg E_{TM}$\\ +$M$\\ +$\neg E_{TM}$ + + + + +\paragraph{Material} + + +\subsection{Perceptual} +\paragraph{Self-assessment Questions} + +\paragraph{Material} + +\subsection{Transformational} +\paragraph{Self-assessment Questions} + +\paragraph{Material} + +\subsection{Axiomatic} +\paragraph{Self-assessment Questions} + +\paragraph{Material} +To detect + +\section{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 +\subsection{Math for Proof} +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, +\subsection{Proof of what} +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 +\subsection{Autogenerated Code, Proof by Construction} +The construction technique needs to be proven. +BL, statecharts, Wise computing +\subsection{Levels of Abstraction} +This goes with composition of system. +Unlike 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 +so, make the space from the defined things, and situate the defined things in the space +invariant as an example of abstraction, i.e., many different operational sequences covered by one invariant +\subsection{Types, Systems of Types, Operations} +What impact does provability have on these? +structure in types +data structures meets provability +(reursive data structures, 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 +\subsection{Definition, Denotation, Operational, Axiomatic} +models, 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 +\subsection{Formal Methods} +Z VDM, Larch +algebraic specification language +would we want to use Tempo instead of OBJ? +A formal method has an assertion language, for example, 1st order predicate logic +A formal method has a specification language, which in turn has a syntax and a semantics. +The syntax contains rules for formulating syntactically correct (legal) terms + +\bibliographystyle{alpha} +\bibliography{literature} + +\end{document}