adding some files

.project

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+<?xml version="1.0" encoding="UTF-8"?>
+<projectDescription>
+	<name>tps</name>
+	<comment></comment>
+	<projects>
+	</projects>
+	<buildSpec>
+	</buildSpec>
+	<natures>
+	</natures>
+</projectDescription>

Introduction.tex

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+This is a qualitative study.\\
+Its analytic lens is phenomenography.\\
+The research question is what are the conceptions of proof we find in the population of students of computer science (and engineering).

QlistCSE2500.tex

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+Product:
+an assessment list of questions for incoming to discrete math
+
+%\begin{enumerate} 
+
+%\item Matching symbolic representations (i.e., equations in figures) with algorithms in pseudocode:
+
+%Stick breaking:\\
+%Start with a unit length.\\ % stick.\\
+%This unit serves as "what is in stock".\\
+%Every time a fractional part is required, a random fraction of the remaining %stock is taken.// %the stick is broken, one piece will be provided as output of the process, and the remainder will be held for future breaking.\\
+%When it is desired to have $p$ fractions, adding to length 1, $p-1$ iterations will satisfy this.\\
+
+
+\begin{figure}[ht]
+\centering
+\includegraphics[width=0.7
+\linewidth]{./pic8}
+\caption{Equation (1)}
+\end{figure}  
+
+\begin{figure}[ht]\centering
+\[
+ \sum_{i=0}^k \frac{1}{2^i}
+\]
+\caption{Equation (2)}
+\end{figure} 
+
+
+% \begin{algorithm}[H] 
+%  factorization(n)\;
+%  \KwData{an integer $\geq 2$, which becomes bound to the variable n}
+%  \KwResult{a prime factorization of n}
+%  \eIf{$prime(n)$}{
+%    return n
+%    }{
+%   (factor1, factor2) = getFactors(n)\;
+%    return factorization(factor1) $\times$  factorization(factor2)
+%  }  
+%    \caption{pseudocode for obtaining factorization }
+%   \end{algorithm}
+
+
+\begin{multicols}{2}
+\begin{algorithm}[H]
+\caption{  }
+\begin{algorithmic}[1]
+%\IF{$A \rightarrow false$}
+%\STATE $A = false$\\
+%\ENDIF
+\STATE num = rand()*10;\\
+\STATE stock = 1;\\
+\STATE amount = 0;\\
+\STATE frac = 1/2;\\
+getRandomFraction()
+\WHILE{num $>0$} 
+\STATE{stock = stock*frac;
+\STATE amount = stock+amount;\\
+\STATE num = num-1;\\
+} \ENDWHILE
+
+return amount;\\
+\}
+\end{algorithmic}
+
+\end{algorithm}
+
+\columnbreak
+
+\begin{algorithm}[H]
+\caption{  }
+\begin{algorithmic}[1]
+%\IF{$A \rightarrow false$}
+%\STATE $A = false$\\
+%\ENDIF
+\STATE num = rand()*10;\\
+\STATE stock = 1;\\
+\STATE amount = 0;\\
+\STATE frac = 1/2;\\
+getRandomFraction()
+\STATE frac=rand(); \\
+\STATE amount =  stock*frac;\\
+\STATE stock = stock - amount;\\
+return amount;
+\end{algorithmic}
+\end{algorithm}
+
+\end{multicols}
+Circle your choice:\\
+Equation 1 goes with Algorithm 1? Yes, No\\
+Equation 1 goes with Algorithm 2? Yes, No\\
+Equation 2 goes with Algorithm 1? Yes, No\\
+Equation 2 goes with Algorithm 2? Yes, No\\
+
+\newpage
+%\item  Matching figures/diagrams with symbolic representations\\
+Show which equation goes with which diagram, if they can be matched.
+\begin{enumerate} 
+
+
+\item \begin{figure}[ht]
+\centering
+\includegraphics[width=0.7\linewidth]{./pic2GNUPaint}
+\caption{}
+\label{fig:pic2}
+\end{figure}
+
+\item \begin{figure}[ht]
+\centering
+\includegraphics[width=0.7\linewidth]{./pic4}
+\caption{}
+\label{fig:pic4}
+\end{figure}
+\end{enumerate}
+
+\begin{enumerate}
+\item $b^2 + ab = (b+a/2)^2 - (a/2)^2$
+\item $(a+b)^2 + (a-b)^2 = 2(a^2 + b^2)$
+\end{enumerate}
+Circle your choice:\\
+Equation (a) goes with Figure 3? Yes, No\\
+Equation (b) goes with Figure 3? Yes, No\\
+Equation (a) goes with Figure 4? Yes, No\\
+Equation (b) goes with Figure 4? Yes, No\\
+
+\newpage
+%\item  Matching figures/diagrams with pseudocode
+%\begin{enumerate}
+
+\begin{figure}
+\centering
+\includegraphics[width=0.6\linewidth]{./pic9}
+\caption{First}
+\label{fig:pic9}
+\end{figure}
+
+
+
+\begin{figure}
+\centering
+\includegraphics[width=0.6\linewidth]{./pic10GNU}
+\caption{Second}
+\label{fig:pic10}
+\end{figure}
+
+
+
+
+\begin{multicols}{2}
+\begin{algorithm}[H]
+\caption{  }
+\begin{algorithmic}[1]
+\STATE amount = 1;\\
+getAmount(n)\{\\
+\STATE amount = 0;
+\FOR{$i=0$ to $n$}
+\STATE \FOR{$j=0$ to $i$}
+\STATE amount = amount +j;
+\ENDFOR
+\ENDFOR\\
+return amount;\}
+\end{algorithmic}
+\end{algorithm}
+\columnbreak
+
+\begin{algorithm}[H]
+\caption{  }
+\begin{algorithmic}[1]
+\STATE amount = 1;\\
+getAmount(n)\{\\
+\IF{$n=0$}
+            \STATE return (1)
+
+        \ELSE 
+            \STATE return(2*getAmount(n-1)+1)
+        \ENDIF\\
+\} 
+\end{algorithmic}
+
+\end{algorithm}
+
+\end{multicols}
+\newpage
+Circle your choice:\\
+Figure 5 goes with Algorithm 3? Yes, No\\
+Figure 5 goes with Algorithm 4? Yes, No\\
+Figure 6 goes with Algorithm 3? Yes, No\\
+Figure 6 goes with Algorithm 4? Yes, No\\
+
+
+%\item 
+
+%\item  
+
+
+%\end{enumerate}
+%\newpage
+%\item  Comprehending figures\\
+
+%Explain why the figure matches the equation $\frac{a+b}{2} \geq \sqrt{ab}$ with equality if and only if $a=b$
+
+%\begin{figure}
+%\centering
+%\includegraphics[width=0.7\linewidth]{./pic5}
+%\caption{}
+%\label{fig:pic5}
+%\end{figure}
+
+\newpage
+%\item  Comprehending symbolic representation\\
+
+Describe in text what this symbolic statement means:\\
+\[
+\sum_{ k \in \mathbb{N}}^{\infty} (2k+1)
+\]
+\newpage
+%\item  Comprehending pseudocode
+
+Describe in text, what this process is doing:\\
+Challenge question: What is the significance of the process described by this pseudocode?
+
+\begin{algorithm}[H]
+\caption{  }
+\begin{algorithmic}[1]
+\STATE done = false;\\
+\STATE a = 0;\\
+\STATE b = 0;\\
+\STATE c=0;\\
+\STATE n = 2;\\
+\WHILE{!done} 
+\STATE{ \WHILE{$a>0$} 
+\STATE{ a=a+1;
+\WHILE{$b>0$} 
+\STATE{ b=b+1;
+\WHILE{$c>0$} 
+\STATE{ c=c+1;\\
+\WHILE{$n>0$} 
+\STATE{ n=n+1;\\
+\IF{$a^n +b^n = c^n$}
+            \STATE done = true;
+        \ENDIF\\
+
+} \ENDWHILE
+} \ENDWHILE\\
+} \ENDWHILE\\
+} \ENDWHILE
+
+} \ENDWHILE
+
+\end{algorithmic}
+
+\end{algorithm}
+
+\newpage
+  Applying symbolic representation to figure
+
+Label these figures mathematical symbols:\\
+Challenge question: What is the significance of these figures taken together?
+
+\vspace{1cm}
+\begin{figure}[ht]
+\centering
+\includegraphics[width=0.7\linewidth]{./pic1}
+\caption{}
+\label{fig:pic1}
+\end{figure}
+
+
+\newpage
+ Applying  figure to symbolic representation
+
+Draw a figure that expresses:\\
+Through any three points that are not collinear, two can be used to identify a line, and the third can be used, combined with that line, to identify a line parallel to the first line.
+
+\newpage
+  Applying pseudocode to figure
+
+Write pseudocode (e.g., as has been seen earlier in these questions) to count the little squares, according to the method suggested by the shading in the figure: \\
+Hint: the bottom row could be row 1.\\
+$n$ and $k$ could be parameters.%(p. 93)\\
+
+\begin{figure}[ht]
+\centering
+\includegraphics[width=0.7\linewidth]{./p93}
+
+\label{fig:p93}
+\end{figure}
+
+
+\newpage
+   Applying pseudocode to symbolic representation
+
+Write pseudocode for the calculation below:\\
+Hint: ${ n \choose k} $ means, from a set of size $n$ choose (without replacement) $k$ elements.\\
+For example, from a list of friends of size $n$, choose a list of party guests of size $k$. (Without replacement means, you do not send two invitations to the same friend.)
+
+Please say whether the concrete example (friends, guest list) aided your thinking.
+
+${ n \choose k} = {n-1 \choose k-1}+ {n-1 \choose k}$
+\newpage
+ Synthesis: word problems to figures
+
+Draw a figure for this word problem:\\
+Pick an angle between 0 and $\pi/2$ radians, call it $\theta$.\\
+A right triangle can be drawn, the height of which is 1 plus the tangent of $\theta$, the base of which is 1 plus the cotangent of $\theta$.  The angle $\theta$ is adjacent to the base. It will be the case that the hypotenuse of this triangle is the cosecant of $\theta$ plus the secant of $\theta$.
+\newpage
+Synthesis: word problems to symbolic representation\\
+
+Express in symbols this word problem:\\
+The number of moves in a game of size n is given by twice the number of moves in a game of size (n-1), plus one more move.
+\newpage
+ Synthesis: word problems to pseudocode
+
+Write pseudocode for this word problem:\\
+Two trains, initially 40 miles apart on the same track, going opposite directions, are getting closer to each other at the rate of 40 miles per hour. An insect flies from one train to the other and back, at a constant speed of $v$, repeatedly. How far does the insect fly, before the trains collide?

TODOs.tex

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+\newpage
+
+TODOs
+read more on van Hiele levels and their theory
+
+Professor McC asks should this include communication? Is he talking about proofs being communicative, or is he talking about proving that communication occurs among algorithms?
+
+explanations of things :
+DONE phenomenography,
+DONE variation theory, 
+DONE constructivism/Piaget
+DONE social constructivism
+
+how much detail on the description of the population of students in CS, or, interviewed students?
+
+details on data analysis: describing how analysis was done in detail really important. How do you do phenomenography?
+Is "this" (my description of thematic analysis) the way everything was analyzed.
+
+details of semi-structured interview protocols for any interviews

abstract.tex

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+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.

acknowledgments.tex

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+Thank you to all of the members of the department, each of whom has helped me to some degree. Your daily example means a great deal. Scholarship, graciousness, patience and compassion are a few of the qualities with which you inspire us, the students. Thank you to Professor Donald Sheehy for his helpful suggestions and exemplary teaching. Thank you to Professors Shvartsman, Gokhale, and Ammar for support and kindness. Thank you to Professors Russell and Michel for inspiration. Thank you to Debra Mielczarek, Joy Billion and Rebecca Randazzo for exemplary competence and unfailing assistance. Thank you to Professor McCartney for support, example, and astonishing patience. Thank you to Jack, \textit{semper providente prospectu}.