[LON-CAPA-cvs] cvs: modules /gerd/discussions/paper discussions.tex

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www		Sun Apr  3 08:37:34 2005 EDT

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    /modules/gerd/discussions/paper	discussions.tex 
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Index: modules/gerd/discussions/paper/discussions.tex
diff -u modules/gerd/discussions/paper/discussions.tex:1.5 modules/gerd/discussions/paper/discussions.tex:1.6
--- modules/gerd/discussions/paper/discussions.tex:1.5	Sat Apr  2 18:12:05 2005
+++ modules/gerd/discussions/paper/discussions.tex	Sun Apr  3 08:37:34 2005
@@ -117,14 +117,14 @@
 \item[Essay questions] These are ``explain why" questions. A certain scenario is presented, and students are asked to explain why it turns out the way it does. Students are not asked to recall a certain law --- it is given to them. Instead, they are asked to discuss its validity.
 \end{description}
 The three courses did not include estimation, qualitative, and essay problems, even though they could have been 
-mediated through the online system. Table~\ref{classification} shows the classification distribution of the online 
+mediated through the online system. Table~\ref{table:problemcat} shows the classification distribution of the online 
 problems available for this project.
 
 \begin{table*}
 \caption{Classification of the online questions according the classification scheme described in 
 subsection~\ref{subsec:problemcat} (adapted from Redish~\cite{redish}). The columns denote the
 different question types, while the rows denote the features of required representation translation and
-context-based reasoning.\label{classification}}
+context-based reasoning.\label{table:problemcat}}
 \begin{ruledtabular}
 \begin{tabular}{lccccccc|l}
 \hline
@@ -164,14 +164,14 @@
 \end{description}
 The following are examples of how contributions were characterized:
 
-Discussion contributions were always classified as a whole, and since they were mostly fairly short, they mostly fell clearly into one of the classes. If a longer contribution had aspects of more than one class, it was characterized by
+Discussion contributions were always classified as a whole, and since they were fairly short, they mostly fell clearly into one of the classes. If a longer contribution had aspects of more than one class, it was characterized by
 the class that its majority fell into. Discussion contributions by teaching assistants and instructors were not 
-considered. Table~\ref{discclass} shows the distribution of the available discussion contributions.
+considered. Table~\ref{table:disccat} shows the distribution of the available discussion contributions.
 \begin{table}
 \caption{Classification of the online discussion contributions according the classification scheme described in 
 subsection~\ref{subsec:disccat}. The columns denote the different discussion types and subtypes, while the 
 rows denote the 
-features.\label{disclass}}
+features.\label{table:disccat}}
 \begin{ruledtabular}
 \begin{tabular}{lcccccccc|l}
 &\multicolumn{2}{c}{Emotional}
@@ -193,19 +193,61 @@
 The vast majority of discussion contributions had the feature of being solution-oriented, 
 yet a considerable number dealt with the physics
 of the problems. 
-
+\subsection{Computation of Results\label{subsec:comp}}
+Each question was classified according to the types and features described in subsection~\ref{subsec:problemcat}. In addition, its
+difficulty index was computed according to the formula
+\begin{equation}\label{eqn:diffidx}
+\mbox{Difficulty Index}=10\left(1-\frac{N_{\mbox{correct}}{N_{\mbox{attempts}}\right)
+\end{equation}
+where $N_{\mbox{correct}}$ is the total number of correct solution in the course, and $N_{\mbox{attempts}}$ is the total number of
+correct and incorrect solution submissions (the system allows multiple attempts to arrive at the correct solution, see 
+subsection~\ref{subsec:system}). If all submissions were correct, meaning, every student would have solved the problem
+correctly on the first attempt, the difficulty index would be 0. If none of the submissions were correct, the index would be 10.
+
+Each associated discussion contribution was classified according to the types and features described in 
+subsection~\ref{subsec:disccat}. As a measure of the prominance of a class in a given discussion, 
+the number of contributions belonging to it is devided by the total number of contributions. In addition, the following 
+superclasses are considered:
+\begin{description}
+\item[Chat] - all contributions that are unrelated or emotional.
+\item[Emotional climate] - the number of positive non-unrelated contributions minus the number of negative non-unrelated
+contributions. This number would be negative if the problem led to mostly negative emotional comments.
+\irem[Type and feature sums] - number of all related contributions belonging to a certain type, subtype, or feature.
+\end{description}   
 \section{Results}
 \subsection{Influence of Question Difficulty}
+The discussion characteristics of the problems were bined by their 
+difficulty index (equation~\ref{eqn:diffidx}) and the average percentage plotted in figure~\ref{fig:diff}. Only superclasses are
+shown (subsection~\ref{subsec:comp}), namely the emotional climate (crosses), as well as all (questions and answers) related
+procedural 
+(triangles) and conceptual (diamonds) contributions. As an example, the plot is to be interpreted in the following way: within the given
+error boundaries, for a question with difficulty index of six, ten percent of the online discussion is conceptual.
 \begin{figure}
 \includegraphics[width=92mm]{diff}% Here is how to import EPS art
-\caption{\label{fig:diff} A figure caption. The figure captions are
-automatically numbered.}
+\caption{\label{fig:diff}Discussion characteristics as a function of problem difficulty.
+}
 \end{figure}
+In addition, the data was fit using second order (procedural, long dashes) and third order (emotional climate, short dashes; conceptual, solid) polynomials.
+
+The greatest variation is found in the emotional climate of the discussion. As is to be expected, the climate is mostly positive
+for ``easy" questions, but then remains positive for a fairly wide range of problem difficulties until it becomes negative
+at a difficulty index of 7. Only six questions had a difficulty index of 9, and --- surprisingly --- none of these had
+associated emotional comments.
+
+For difficulty indizes beyond 3, the prominance of conceptual discussions increases. Surprisingly, it also increases for easier
+questions. This may be attributed to students feeling more confident discussing easier problems on a conceptual level, or simply
+in there being less of a need of procedural discussions in the worst.
+Overall, the prominance of conceptual discussions is disappointingly low, as it varies between 5 and 16 percent.
+
+Across all difficulties, procedural contributions dominate the discussions, with relatively little significant variance around
+the 40 percent mark. The maximum occurs for questions with a difficulty index of 5. 
 
+In figure~\ref{fig:diffnochat} the same analysis was carried out, but this time excluding all ``chat" contributions 
+(subsection~\ref{subsec:comp}), i.e., only related non-emotional contributions were considered.
 \begin{figure}
 \includegraphics[width=92mm]{diffnochat}% Here is how to import EPS art
-\caption{\label{fig:diffnochat} A figure caption. The figure captions are
-automatically numbered.}
+\caption{\label{fig:diffnochat}Discussion characteristics as a function of problem difficulty, no considering ``chat."
+}
 \end{figure}
 
 \subsection{Influence of Question Types}