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work on formatting and references, mostly

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1 parent f5fc9da commit 05557c5f025b6abb7a63d457ca6a5c57b300b7b0 @bvds committed May 9, 2013
@@ -9,7 +9,7 @@
\begin{document}
-\title{Measuring the moment of learning with an information-theoretic approach}
+\title{Measuring the Moment of Learning with an Information-Theoretic Approach}
\numberofauthors{1}
\author{
\alignauthor
@@ -170,11 +170,11 @@ \subsection{Correct/Incorrect steps}
\section{The step model}
-\begin{figure}
- \centering \includegraphics{step-model.eps}
- \caption{Functional form of the step model.}
- \label{step-model}
-\end{figure}
+%\begin{figure}
+% \centering \includegraphics{step-model.eps}
+% \caption{Functional form of the step model.}
+% \label{step-model}
+%\end{figure}
We need to compare the student log data to some sort of model
of learning. In another paper~\cite{van_de_sande_applying_2013},
@@ -184,7 +184,7 @@ \section{The step model}
%
\begin{equation}
P_\mathrm{step}(j)= \left\{\begin{array}{cc}
- g, & j<l \\
+ g, & j<L \\
1-s, & j\ge L
\end{array} \right.
\end{equation}
@@ -337,12 +337,12 @@ \section{Weighted gain}
A calculation of $w_L \Delta_L$ for an example bit sequence is
shown in Fig.~\ref{weighted-gain-example}. Not surprisingly,
the largest gain occurs at $L=4$, corresponding to the first 1 in the
-bit sequence. Note that the rest of the weighted gains are much smaller.
+bit sequence. The remaining weighted gains are much smaller.
\begin{figure}
\centering \includegraphics{weighted-gain-histogram.eps}
\caption{Histogram of weighted gains $w_L \Delta_L$ for
- all steps in all student-KC sequences in student dataset $\mathcal{A}$.}
+ all steps in all student-KC sequences of dataset $\mathcal{A}$.}
\label{weighted-gain-histogram}
\end{figure}
@@ -388,7 +388,7 @@ \section{Weighted gain}
dataset.
We use the sample standard deviation of the weighted gains $w_L \Delta_L$
to calculate the standard error associated with $Q$.
-An example calculation of $Q$ for a single bit sequence is shown in Fig.~\ref{weighted-gain-example}.
+An example calculation is shown in Fig.~\ref{weighted-gain-example}.
\begin{figure}
\centering \includegraphics{weighted-gain-histogram2.eps}
@@ -464,16 +464,12 @@ \section{Acknowledgments}
Learning Center which is funded by the National Science Foundation
award No. SBE-0836012.
-%
-% The following two commands are all you need in the
-% initial runs of your .tex file to
-% produce the bibliography for the citations in your paper.
\bibliographystyle{abbrv}
-\bibliography{education-modeling}
-%Generated by bibtex from your ~.bib file. Run latex,
-%then bibtex, then latex twice (to resolve references)
-%to create the ~.bbl file. Insert that ~.bbl file into
-%the .tex source file and comment out
-%the command \texttt{{\char'134}thebibliography}.
+%
+% BibTeX does not support journal name abbreviations as a
+% separate field. As a work-around, export from Zotero with
+% switch for abbreviations on and name ``education-modeling-abbr.bib''
+%
+\bibliography{education-modeling-abbrev}
\end{document}
@@ -9,7 +9,7 @@
\begin{document}
-\title{Applying three models of learning to individual student log data}
+\title{Applying Three Models of Learning to Individual Student Log Data}
\numberofauthors{1}
\author{
\alignauthor
@@ -206,9 +206,16 @@ \section{Three models of learning}
so criterion~\ref{crit:perform} is partially satisfied.
Another model that is frequently used in the context of learning is
-the logistic model~\cite{cen_learning_2006,chi_instructional_2011},
+the logistic model~\cite{cen_learning_2006,chi_instructional_2011}.
+Since we are interested in fitting the model to a single student
+and a single KC, these models take on the form
%
\begin{equation}
+ \log\left(\frac{P_\mathrm{logistic}(j)}{1-P_\mathrm{logistic}(j)}\right)=
+ b (j-L)
+\end{equation}
+which can be written as:
+\begin{equation}
P_\mathrm{logistic}(j)= \frac{1}{1+\exp\left(-b (j-L)\right)} \; .
\end{equation}
%
@@ -223,11 +230,11 @@ \section{Three models of learning}
The third model is the ``step model'' which assumes that learning
occurs all at once; this corresponds to the ``eureka learning''
-discussed by \cite{baker_detecting_2011}. It is defined as:
+discussed by \cite{baker_detecting_2011}. It is defined as:
%
\begin{equation}
P_\mathrm{step}(j)= \left\{\begin{array}{cc}
- g, & j<l \\
+ g, & j<L \\
1-s, & j\ge L
\end{array} \right.
\end{equation}
@@ -381,8 +388,17 @@ \subsection{Analysis}
exempli gratia} 001001101, for each student-KC sequence. This bit
sequence is then fit to each of the three models, $P_\mathrm{step}$,
$P_\mathrm{logistic}$, and $P_\mathrm{BKT}$ by maximizing the
-associated log likelihood. %This determines the free parameters in
-each model. We then calculate the AIC score for each fit. Finally,
+associated log likelihood.
+%This determines the free parameters in each model.
+For $P_\mathrm{logistic}$, and $P_\mathrm{BKT}$, the fits were
+calculated using the
+Differential Evolution algorithm~\cite{storn_differential_1997}
+provided by {\em Mathematica}.
+For $P_\mathrm{step}$, the best fit, as a function
+of $s$ and $g$, can be found analytically; one can
+then find the best fit, as a function of $L$,
+by conducting an exhaustive search.
+Next, we calculate the AIC score for each fit. Finally,
we calculate the Akaike weights, $w_\mathrm{logistic}$,
$w_\mathrm{step}$, and $w_\mathrm{BKT}$ for each student-KC
sequence~\cite{burnham_model_2002}.
@@ -586,16 +602,12 @@ \section{Acknowledgments}
Learning Center which is funded by the National Science Foundation
award No. SBE-0836012.
-%
-% The following two commands are all you need in the
-% initial runs of your .tex file to
-% produce the bibliography for the citations in your paper.
\bibliographystyle{abbrv}
-\bibliography{education-modeling}
-%Generated by bibtex from your ~.bib file. Run latex,
-%then bibtex, then latex twice (to resolve references)
-%to create the ~.bbl file. Insert that ~.bbl file into
-%the .tex source file and comment out
-%the command \texttt{{\char'134}thebibliography}.
+%
+% BibTeX does not support journal name abbreviations as a
+% separate field. As a work-around, export from Zotero with
+% switch for abbreviations on and name ``education-modeling-abbr.bib''
+%
+\bibliography{education-modeling-abbrev}
\end{document}
@@ -590,6 +590,7 @@ \section{Conclusion}
a step) may be crucial for Andes.
% Bibliography
+%
\bibliographystyle{acmlarge}
\bibliography{education-modeling}

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