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Index: modules/gerd/correlpaper/correlations.tex
diff -u modules/gerd/correlpaper/correlations.tex:1.12 modules/gerd/correlpaper/correlations.tex:1.13
--- modules/gerd/correlpaper/correlations.tex:1.12 Thu Sep 28 11:18:57 2006
+++ modules/gerd/correlpaper/correlations.tex Fri Sep 29 15:13:27 2006
@@ -69,11 +69,16 @@
The MPEX ``Product Warning Label'' continues, that ``this survey is primarily intended to evaluate the impact of one or more semesters of instruction on an overall class''~\cite{mpexwarning}, and recommends using the outcomes, in combination with evaluations of student learning of content, as a means to improve overall course instruction. In this paper, we are asking the question if the evaluation of student online discussion behavior can be used as a means to get to assess the attitudes and beliefs of an individual student, and if in turn, these can be used to predict the success of an individual student in the learning of physics content. An obvious application would be the early detection of students at risk.
+In particular:
+\begin{itemize}
+\item We classify the online homework discussion contributions from one course
+\item We deploy the MPEX for comparison as a pre- and post-test
+\item We are using the pre- and post-FCI, as well as the final exam and course grades, as a measure of student learning
+\end{itemize}
+
\section{\label{background}Background}
Online discussions are a rich source of feedback to the instructor~\cite{kortemeyer05feedback}, and their quality and character was found to be correlated with the type and difficulty of the associated problems~\cite{kortemeyer05ana}, i.e., data exists regarding the influence of {\it problem} characteristics on associated discussions. Unfortunately, less data exists on the correlation between {\it student} characteristics and discussion behavior, because usually only very few student characteristics are known, with the exception of the students' overall performance in the course. Thus, one of the few findings was the fact that certain discussion behavior, most prominently exhibited on ``non-sanctioned'' discussion sites external to the course, is negatively correlated with performance in the course~\cite{kashy03,kortemeyer05ana}. Also, Hogan~\cite{hogan99} assessed eight graders' epistemological frameworks through interviews and then analyzed their discussion behavior in a science course with a particular focus on collaboration, finding a number of correlations.
-In this study, we aim to answer the question if and how student discussion characteristics are related to their beliefs, attitudes, and expectations, as measured by the MPEX. We investigate correlations with the MPEX, and compare correlations with measures of student learning.
-
\section{\label{setting}Setting}
The project was carried out in an introductory calculus-based physics course with initially 214 students. Most of the students in this course plan on pursuing a career in a medical field. The course had three traditional lectures per week. It did not use a textbook, instead, all course materials were available online. Topics were introductory mechanics, as well as sound and thermodynamics. There was twice-weekly online homework: one small set as reading problems due before the topic was dealt with in class (implementing JiTT~\cite{jitt}), and a larger set of traditional end-of-the-chapter style homework at the end of each topic. The online problems in the course were randomized using the LON-CAPA system, i.e., different students would receive different versions of the same problem (different graphs, numbers, images, options, formulas, etc)~\cite{loncapa,kashyd01}. The students had weekly recitation sessions, and a traditional lab was offered in parallel. The course grade was determined from the students' performance on biweekly quizzes, the final exam, the recitation grades, and the homework performance.
@@ -82,17 +87,14 @@
In LON-CAPA, discussions boards are directly underneath each online homework problem, i.e., each problem has its own discussion board on the same web page. Since problems in LON-CAPA are randomized, such that each student has different options, numbers, graphs, equations, or even scenarios (e.g., accelerating to the left or to the right), the students cannot simply exchange the correct answer, and are encouraged to freely discuss the problems with each other. Figure~\ref{newfig1} shows a screenshot of such a problem and its associated discussion.
\begin{figure*}
\includegraphics[width=18cm]{newfig1}
-\caption{\label{newfig1}Example of an online homework problem with associated student discussions. The problem is past its due date, so the correct answer is shown. If it were still open, the students would have one text answer box, into which they would enter the value with physical units.}
+\caption{\label{newfig1}Example of an online homework problem with associated student discussions. The problem is past its due date, so the correct answer is shown. If it were still open, the students would have one text answer box, into which they would enter the value with physical units. The students in this example chose to post anonymously, however, the student name is still available to faculty.}
\end{figure*}
-The author analyzed the online student discussions that were associated with the online homework given in his course, using the scheme first suggested in Ref.~\cite{kortemeyer05ana}. There were a total of 2405 such online discussion contributions over the course of the semester.
-
-Each contribution was classified by the author according to the classification scheme of Ref.~\cite{kortemeyer05ana}, however, with the additional refinement that each contribution could be member of more than one class, and that the contributions were weighted by their length. For example, a certain contribution might include both a procedural solution-oriented question and a surface-level mathematical answer, and would thus receive 50\% membership in both classes, weighted by its total length. The student names were not available during classification in order to avoid bias.
+The author analyzed the online student discussions that were associated with the online homework given in his course, using the scheme first suggested in Ref.~\cite{kortemeyer05ana}. The student names were not available during classification in order to avoid bias.
+There were a total of 2405 such online discussion contributions over the course of the semester.
-The analysis was carried out based on discussion superclasses~\cite{kortemeyer05ana}, for example, all conceptual classes were combined, independent of their features. A given contribution can thus belong to more than one superclass.
-
-The following list shows the superclasses taken into consideration, as well as illustrative examples that have partial membership in each superclass, taken from this course:
+The following list shows the classifications taken into consideration, as well as illustrative examples that would receive the respective classification.
\begin{itemize}
\item Discussion contributions were classified as {\it surface} if they
@@ -185,8 +187,15 @@
That's why we float on the moon...
\end{quote}
\end{itemize}
+
+One particular contribution could receive more than one classification. Each contribution was weighed by its length when calculating the overall discussion behavior of an individual student. For additional details, see Ref.~\cite{kortemeyer05ana}, where the above classes were referred to as ``superclasses.''
+
Note that correctness of the contribution was not considered. For example, in the last physics-related example, the fact that the student confused the gravitational constant and the gravitational acceleration was not taken into account.
+Interrater reliability was assessed by asking a graduate student in physics education research at another university to read
+Ref.~\cite{kortemeyer05ana} and classify a randomly selected subset of 104 contributions. Without further training, the overall reliability was 81 percent. As it turned out, though, this value did vary by class: the conceptual and mathematical classes had an interrater reliability of 91 and 96 percent, respectively, while the solution-oriented class had a reliability of only 58 percent. Looking at the prominence of contributions in certain classes, the author classified 60 percent and the graduate student only 38 percent as ``solution-oriented.'' The discrepancy might be due to the fact that the author in his course attempts to strongly discourage this behavior and thus may be more prone to detect and label it than an individual who is not connected with the course. The discrepancy could likely be resolved with training.
+
+
As already found in Ref.~\cite{kortemeyer05ana}, most students are quite prolific in their online discussions, but a few students only made a small number of contributions, leading to small statistics on their actual discussion behavior. For each of the discussion correlations, we thus also carried out a second calculation limited to students who contributed at least five entries over the course of the semester.
\subsection{\label{mpex}The MPEX}
@@ -218,134 +227,45 @@
\end{quote}
\end{itemize}
-
-
\subsection{\label{performance}Measures of Student Learning}
As a measure of student conceptual understanding and learning, we deployed the revised Force Concept Inventory (FCI)\cite{fci} at the beginning and the end of the course, again with voluntary participation. As an additional measure of student performance, the performance on the final exam and the course grade for each student were taken into consideration. For the grade we used the raw percentage score, not the number grades, since it provides finer grained information about the overall student performance in the course.
-\section{\label{hypo}Hypotheses}
-Between the measures described in section~\ref{measures}, a number of correlations are to be expected:
-\begin{enumerate}
-\item Student responses to clusters on the MPEX should correlate with corresponding discussion behavior patterns
-\item Student performance on the FCI should correlate positively with desirable and negatively with undesirable discussion behavior
-\item Student performance on the FCI should positively correlate with performance on the MPEX
-\end{enumerate}
-Somewhat less general, since dependent on the grading mechanism implemented by the instructor, corresponding correlations should exist with the final exam and the course grade.
-\section{\label{results}Results}
-In this section, we present the correlations among the different instruments and measures.
-\subsection{Correlation Table}
-Table~\ref{fullresults} shows the complete correlation results of the study. In the columns of the table, we listed:
-grade performance;
-final exam performance;
-final (post) FCI score;
-FCI gain;
-final (post) MPEX score;
-MPEX gain;
-prominence of solution-oriented discussion contributions;
-prominence of math-related discussion contributions;
-prominence of physics-related discussion contributions;
-prominence of surface-level discussion contributions;
-prominence of procedural discussion contributions;
-prominence of conceptual discussion contributions.
-
-In the rows of the table, we listed:
-grade performance;
-final exam performance;
-final (post) FCI score;
-FCI gain;
-final (post) MPEX score;
-MPEX gain;
-MPEX Independence Cluster score;
-MPEX Coherence Cluster score;
-MPEX Concept Cluster score;
-MPEX Reality Link Cluster score;
-MPEX Math Link Cluster score;
-MPEX Effort Cluster score.
-
-Correlations with $|R|<0.1$ are indicated by a dash, correlations with $|R|>0.5$ are printed boldface. The values in brackets are the result of calculations limited to students with at least five discussion contributions over the course of the semester.
-
-\begin{table*}
-\caption{\label{fullresults}Complete correlation results ($R$-values). In the columns we list the grade performance, final exam performance, FCI scores and gains, MPEX scores and gains, as well as the prominences of different online discussion characteristics. In the rows we list the grade performance, final exam performance, FCI scores and gains, MPEX scores and gains, as well as the performance on the different MPEX clusters. Calculated correlations whose absolute value was lower than 0.1 are indicated by "---." Correlations with an absolute value higher than 0.5 have been printed in boldface. The values given in brackets have been calculated including only students who contributed more than five discussion entries over the course of the semester. As an example, the correlation between the prominence of solution-oriented discussion contributions of students who made more than five contributions over the course of the semester and the FCI gain is -0.44, indicating that students who make more solution-oriented discussion contributions have a lower gain on the FCI between the beginning and the end of the semester.}
-\begin{ruledtabular}
-\begin{tabular}{rllllllllllll}
- &Grade&Final&FCI &FCI &MPEX&MPEX&Solution &Math &Physics &Surface &Proce-&Concep-\\
- & &Exam&Final &Gain &Final &Gain & & & & &dural &tual\\
-Grade & & &{\bf 0.56}&0.45 &0.3 &0.27 &--- (--0.25)&--0.15 (---)&0.22 (0.33)&--- (--0.25)&--- (---)&0.2 (0.28)\\
-Final & & && & & & & & & & & \\
-Exam & & & 0.46 & 0.39 & 0.27 & 0.26&--- (--0.16)&--- &0.15 (0.22)&--- (--0.18)&--- (0.1)&0.12 (0.16)\\
-FCI & & && & & & & & & & & \\
- Final &{\bf 0.56} &0.46 & & &0.24 &--- &--0.37 ({\bf--0.58})&0.13 (0.1)&0.34 ({\bf 0.51})&--- (--0.41)&--- (---)&0.25 (0.35)\\
-FCI & & && & & & & & & & & \\
-Gain & 0.45 &0.39 & & &0.17 &--- &--0.28 (--0.44)&0.14 (---)&0.22 (0.4)&--0.1 (--0.34)&--- (---)&0.31 (0.34)\\
-MPEX & & && & & & & & & & & \\
-Final & 0.3 & 0.27 & 0.24 &0.17 & & &--0.12 (---)&--- (---)&0.17 (0.16)&--- (---)&--- (0.12)&0.13 (0.11)\\
-MPEX & & && & & & & & & & & \\
-Gain & 0.27 &0.26 & --- & --- & & &--- (---)&--- (---)&--- (0.18)&0.14 (---)&--0.14 (---)&--- (---)\\
-Indepen- & & && & & & & & & & & \\
-dence&0.25 &0.25&0.23 &0.1 & & &--- (---)&--- (0.13)&--- (---)&--- (---)&--- (---)&--- (0.15)\\
-Cohe- & & && & & & & & & & & \\
-rence &0.36 &0.31&0.2 &0.23 & & &--- (---)&--- (0.11)&0.18 (0.18)&--- (--0.18)&--- (0.24)&0.1 (0.17)\\
-Con-& & && & & & & & & & & \\
-cepts &0.25 &0.24 &0.21 &0.13 & & &--- (---)&--- (---)&0.11 (0.14)&--- (---)&--- (---)&0.14 (0.15)\\
-Reality & & && & & & & & & & & \\
-Link&--- &0.1&0.15 &--- & & &--0.12 (---)&--- (--0.16)&--- (---)&--0.2 (---)&0.11 (---)&--- (---)\\
-Math & & && & & & & & & & & \\
-Link &0.15 &---&0.13 &--- & & &--- (---)&--- (--0.14)&--- (---) &0.1 (---)&--- (---)&--- (---)\\
-Effort &0.15&0.15 &--- &0.11 & & &--0.14 (--0.19)&--- (---)&0.19 (0.2)&--0.14 (--0.12)&--- (---)&0.22 (0.15)
-\end{tabular}
-
-\end{ruledtabular}
-\end{table*}
-
-Of particular interest is the lower right corner of Table~\ref{fullresults}, as it lists the correlations between student attitudes and expectations (as measured by the MPEX clusters) with the prominence of discussion behavior classes. One would have expected strong correlations between for example the score on the Concepts Cluster and the prominence of conceptual discussion contributions ($R=0.14 [-0.08 - 0.34] (0.15 [-0.13 - 0.41]); n=84 (51)$), or the comfort level with the usage of mathematics as a language and the corresponding lack of purely mathematical contributions ($|R|<0.1$, and $R=-0.14 [-0.4 - 0.14]$ ($n=51$) when including only students with more than five contributions overall). However, the 95\% confidence intervals (given in square brackets) include zero. The Coherence and Effort Clusters are most strongly correlated with discussions, the Math Link Cluster -- surprisingly -- the least.
-
-The upper right and the lower left corner list the correlations of student discussion behavior and the MPEX, respectively, with measures of student learning. Correlations are again low, but of comparable magnitude, where the MPEX appears to be slightly more correlated with grade and final exam performance, while the discussion is more correlated with the FCI. In fact, some of the strongest correlations in the study occur between the prominence of solution-oriented and physics-related discussions and the FCI. We will analyze correlations with grades in more detail in subsection~\ref{gradecorrel}, and with the FCI in subsection~\ref{fcicorrel}.
-
-The Coherence Cluster of the MPEX appears to be more strongly correlated to other performance indicators than the other clusters. Out of that cluster, agreement with the statement "In doing a physics problem, if my calculation gives a result that differs significantly from what I expect, I'd have to trust the calculation" (53\% unfavorable responses) has $R=-0.3 [-0.47 - -0.11]$ ($n=97$) with the grade in the course, $R=-0.3 [-0.47 - -0.11]$ ($n=97$) with the final FCI Score, and $R=0.3 [0.09 - 0.48]$ ($n=84$) with solution-oriented discussion postings. Out of the Concepts Cluster, agreement with the single statement "The most crucial thing in solving a physics problem is finding the right equation to use" (45\% unfavorable responses) correlates with $R=-0.3 [-0.47 - -0.11]$ ($n=96$) with the final FCI score and also with $R=-0.3 [-0.48 - -0.09]$ ($n=85$) with the FCI Gain, i.e., stronger than the cluster it belongs to.
-
-Going beyond the analysis of the large discussion superclasses, when considering the intersection of student discussion characteristics, only a few relatively strong correlations can be found. For example, the prominence of discussion contributions that were both conceptual and physics-related correlates with $R=0.2 [0.05 - 0.33]$ ($n=173$) with the grade in the course, and with $R=0.29 [0.09 - 0.46]$ ($n=95$) and $R=0.3 [0.09 - 0.48]$ ($n=84$) with the final FCI Score and Gain, respectively. The prominence of contributions that are both solution-oriented and surface-level correlates with $R=-0.29 [-0.46 - -0.09]$ ($n=95$) and $R=-0.13 [-0.34 - 0.08]$ ($n=84$) with the FCI Score and Gain, respectively.
-
-
+\section{\label{results}Results}
+\subsection{\label{MPEXDiscussion}Correlations between Discussion Behavior and MPEX}
+To directly compare the attitudes and beliefs measures, we calculated correlations between the prominence of discussion behavior classes and the MPEX clusters, and generally found them to be very low. As an example, the correlation between the score on the Concepts Cluster and the prominence of conceptual discussion contributions turned out to be $R=0.14 [-0.08 \to 0.34]; n=84$ when considering all students, and $R=0.15 [-0.13 \to 0.41]; n=51$ when only considering those who made at least five discussion contributions -- the 95\% confidence intervals (given in square brackets) include zero. Thus, we conclude that discussion behavior and the individual MPEX cluster scores are -- if at all -- only weakly correlated.
+\subsection{\label{learningcorrel}Correlations between Discussions, MPEX, and Learning}
+Correlations between the MPEX and measures of student learning are generally weak. Considering final exam and course grade, $R=0.36 [0.17 \to 0.52]$ ($n=97$) between the score on the Coherence cluster and the course grade percentage is the highest correlation found. Dancy~\cite{dancy02} found similarly low correlations with the performance on homework, tests, and final exams: direct comparison with the performance on the final exams found $R=0.37$ for the correlation with the total MPEX score ($R=0.27$ here), $R=0.39$ with the Independence Cluster ($R=0.25$ here), $R=0.24$ with the Coherence Cluster ($R=0.36$ here), $R=0.29$ with the Concept Cluster ($R=0.25$ here), $R=-.02$ with the Reality Link cluster ($R=0.1$ here), $R=0.3$ with the Math Link cluster (no significant correlation found here), and no significant correlation with the Effort Cluster ($R=0.1$ here). As a caveat already pointed out in section~\ref{setting}, however, the course grade is based on a number of factors, some of which are simply a matter of diligence or effort.
-\subsection{\label{gradecorrel}Correlations with the Overall Course Grade and Final Exam}
-Figure~\ref{fcimpexgrade} shows the correlation between the final FCI and MPEX scores with the final course grade percentage. With an $R$ of $0.56 [0.41 - 0.68]$ ($n=110$) and $0.30 [0.11 - 0.47]$ ($n=97$), respectively, these -- particularly for the MPEX -- turned out lower than expected. As pointed out in section~\ref{setting}, however, the course grade is based on a number of factors, some of which are simply a matter of diligence or effort.
-
-\begin{figure*}
-\includegraphics[width=9cm]{fcipostgrade}\includegraphics[width=9cm]{mpexpostgrade}
-\caption{\label{fcimpexgrade}Correlation between the FCI score (left; $R=0.56 [0.41 - 0.68] $; $n=110$) and the MPEX score (right; $R=0.3 [0.11 - 0.47] $; $n=97$) with the course grade percentage. 58\% was the minimum percentage to pass the course. More students participated in the FCI than in the MPEX.}
-\end{figure*}
-
-Correlations with the MPEX were generally weak, with $R=0.36 [0.17 - 0.52]$ ($n=97$) between the score on the Coherence cluster and the course grade percentage being the highest value. Dancy~\cite{dancy02} found similarly low correlations with the performance on homework, tests, and final exams: direct comparison with the performance on the final exams found $R=0.37$ for the correlation with the total MPEX score ($R=0.27$ here), $R=0.39$ with the Independence Cluster ($R=0.25$ here), $R=0.24$ with the Coherence Cluster ($R=0.36$ here), $R=0.29$ with the Concept Cluster ($R=0.25$ here), $R=-.02$ with the Reality Link cluster ($R=0.1$ here), $R=0.3$ with the Math Link cluster (no significant correlation found here), and no significant correlation with the Effort Cluster ($R=0.1$ here).
-Figure~\ref{physicsgrade} shows the correlation between the prominence of physics-related discussions and the course grade percentage (for better statistics, only students who contributed at least five discussion entries over the course of the semester were considered). The correlation is stronger than with the MPEX Score, yet smaller than with the FCI.
+Figure~\ref{mpexfci} shows how the final MPEX and FCI scores correlated with each other, i.e, $R=0.24 [0.04 \to 0.42]$ ($n=97$).
+Coletta and Philips~\cite{coletta05} found a strong correlation between the FCI Gain and the MPEX Score ($R=0.52 [0.24 \to 0.72]; n=37$), while the same correlation turned out much lower in this study ($R=0.17 [-0.05 \to 0.37]; n=84$ here). The correlations reported here are in the same range that
+Perkins et al.~\cite{perkins04} found when investigating the influence of beliefs on conceptual learning, using the CLASS~\cite{adams04} and the Force and Motion Conceptual Evaluation (FMCE)~\cite{thornton98} instruments.
\begin{figure}
-\includegraphics[width=9cm]{physicsgrade}
-\caption{\label{physicsgrade}Correlation of percentage physics-related discussions with grade percentage ($R=0.33 [0.15 - 0.49]$; $n=111$).}
+\includegraphics[width=9cm]{fcipostmpexpost}
+\caption{\label{mpexfci}Correlation of the final FCI score with the MPEX score ($R=0.24 [0.04 \to 0.42]$; $n=97$).}
\end{figure}
-\subsection{\label{fcicorrel}Correlations with the FCI}
-Figure~\ref{mpexfci} shows how the final FCI and MPEX scores correlated with each other, i.e, $R=0.24 [0.04 - 0.42]$ ($n=97$).
-Coletta and Philips~\cite{coletta05} found a strong correlation between the FCI Gain and the MPEX Score ($R=0.52 [0.24 - 0.72]; n=37$), while the same correlation turned out much lower in this study ($R=0.17 [-0.05 - 0.37]; n=84$ here). The correlations reported here are in the same range that
-Perkins et al.~\cite{perkins04} found when investigating the influence of beliefs on conceptual learning, using the CLASS~\cite{adams04} and the Force and Motion Conceptual Evaluation (FMCE)~\cite{thornton98} instruments.
-
-Correlations with discussion characteristics turned out somewhat stronger. Figure~\ref{fciphysics} shows how the percentage of a particular student's discussion contribution that was classified as "physics-related" correlates with their final FCI score ($R=0.34 [0.15 - 0.51]$; $n= 95$). As already in Fig.~\ref{physicsgrade}, an additional analysis was carried out that was limited to students for which better statistics were available, which let to a stronger correlation ($R=0.51[0.29 - 0.68]$; $n=57$).
+Figure~\ref{physicsgrade} shows the correlation between the prominence of physics-related discussions and the course grade percentage (for better statistics, only students who contributed at least five discussion entries over the course of the semester were considered). The correlation is stronger than with the MPEX Score, yet smaller than with the FCI.
\begin{figure}
-\includegraphics[width=9cm]{fcipostmpexpost}
-\caption{\label{mpexfci}Correlation of the final FCI score with the MPEX score ($R=0.24 [0.04 - 0.42]$; $n=97$).}
+\includegraphics[width=9cm]{physicsgrade}
+\caption{\label{physicsgrade}Correlation of percentage physics-related discussions with grade percentage ($R=0.33 [0.15 \to 0.49]$; $n=111$).}
\end{figure}
+Figure~\ref{fciphysics} shows how the percentage of a particular student's discussion contribution that was classified as "physics-related" correlates with their final FCI score ($R=0.34 [0.15 \to 0.51]$; $n= 95$). As already in Fig.~\ref{physicsgrade}, an additional analysis was carried out that was limited to students for which better statistics were available, which let to a stronger correlation ($R=0.51[0.29 \to 0.68]$; $n=57$). While physics-related discussions positively correlate with FCI scores and grades (Fig.~\ref{physicsgrade}), solution-oriented discussions negatively correlate (Fig.~\ref{solutionfci}; $R=-0.58 [-0.73 \to -0.38]$; $n=57$).
+
\begin{figure*}
\includegraphics[width=9cm]{fcipostphysics}\includegraphics[width=9cm]{fcipostphysicsT}
-\caption{\label{fciphysics}Correlation between the FCI score and the percentage of that student's discussion that was classified as "physics" ($R=0.34 [0.15 - 0.51]$; $n= 95$). The figure on the right only includes students who contributed more than five discussion entries over the course of the semester ($R=0.51 [0.29 - 0.68]$; $n=57$).}
+\caption{\label{fciphysics}Correlation between the FCI score and the percentage of that student's discussion that was classified as "physics" ($R=0.34 [0.15 \to 0.51]$; $n= 95$). The figure on the right only includes students who contributed more than five discussion entries over the course of the semester ($R=0.51 [0.29 \to 0.68]$; $n=57$).}
\end{figure*}
-While physics-related discussions positively correlate with FCI scores and grades (Fig.~\ref{physicsgrade}), solution-oriented discussions negatively correlate (Fig.~\ref{solutionfci}; $R=-0.58 [-0.73 - -0.38]$; $n=57$).
\begin{figure}
\includegraphics[width=9cm]{fcipostsolutionT}
-\caption{\label{solutionfci}Correlation of percentage solution-oriented discussions with final FCI score ($R=-0.58 [-0.73 - -0.38]$; $n=57$).}
+\caption{\label{solutionfci}Correlation of percentage solution-oriented discussions with final FCI score ($R=-0.58 [-0.73 \to -0.38]$; $n=57$).}
\end{figure}
+
+
\section{Discussion of the Correlation Results}
Correlations between Grade, Final Exam, FCI, MPEX, and student discussion behavior have turned out lower than expected. The strongest correlations exist with the final score on the FCI, namely $R=0.56$ with the grade percentage in the course, $R=0.51$ with the prominence of physics-related discussions, and $R=-0.58$ with the prominence of solution-oriented discussions.
@@ -398,7 +318,7 @@
The expected correlation between MPEX clusters and the prominence of different classes of student discussion behavior is largely missing. The reason for this lack of correlation could not completely be determined in the framework of this study: it might be that the mechanisms -- even in related areas -- measure different things, or that at least one of them in fact measures very little, or that, as indicated by an additional survey, the students did not bother responding to the MPEX with sufficient diligence.
\begin{acknowledgments}
Supported in part by the National Science Foundation under NSF-ITR 0085921 and NSF-CCLI-ASA 0243126. Any opinions, findings, and conclusions or recommendations expressed in this
-publication are those of the author and do not necessarily reflect the views of the National Science Foundation. The author would like to thank the students in his course for their participation in this study.
+publication are those of the author and do not necessarily reflect the views of the National Science Foundation. The author would like to thank the students in his course for their participation in this study, as well as Deborah Kashy for assistance with the statistical analysis of the data.
\end{acknowledgments}
\bibliography{correlations}% Produces the bibliography via BibTeX.
--www1159557208--