# bvds/andes

work on formatting and references, mostly

 @@ -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