# [LON-CAPA-cvs] cvs: modules /gerd/correlpaper correlations.tex

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Index: modules/gerd/correlpaper/correlations.tex
diff -u modules/gerd/correlpaper/correlations.tex:1.1 modules/gerd/correlpaper/correlations.tex:1.2
--- modules/gerd/correlpaper/correlations.tex:1.1	Fri Jul  7 18:23:08 2006
+++ modules/gerd/correlpaper/correlations.tex	Mon Jul 10 11:59:52 2006
@@ -34,7 +34,7 @@

\begin{document}

-\preprint{APS/123-QED}
+%\preprint{APS/123-QED}

\title{Correlations between FCI, MPEX, Student Discussion Behavior,\\
and Grade Performance in an Introductory Physics Course}% Force line breaks with \\
@@ -52,11 +52,7 @@
%  but any date may be explicitly specified

\begin{abstract}
-An article usually includes an abstract, a concise summary of the work
-covered at length in the main body of the article. It is used for
-secondary publications and for information retrieval purposes. Valid
-PACS numbers may be entered using the \verb+\pacs{#1}+ command.
-\end{abstract}
+In the Physics Education Research community, the Force Concept Inventory (FCI) and the Maryland Physics Expectations Survey are frequently used instruments to assess students' conceptual understanding of and attitudes and expectations toward physics. In this paper, we investigate how these instruments correlate with each other, and how they correlate with the characteristics of students' contributions to online discussions and their overall performance in the course.\end{abstract}

\pacs{01.40.Fk}% PACS, the Physics and Astronomy
% Classification Scheme.
@@ -64,510 +60,135 @@
%display desired
\maketitle

-break was forced \lowercase{via} \textbackslash\textbackslash}
+\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 for the topic was dealt with in class, and a larger set of traditional end-of-the-chapter style homework at the end of each topic. The students had weekly recitation sessions, and a traditional lab was offered in parallel. The course grade was determined from the students' performance on the biweekly quizzes, the final exam, the recitation grades, and the homework performance.

-This sample document demonstrates proper use of REV\TeX~4 (and
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-documentation included in the distribution or available at
-\url{http://publish.aps.org/revtex4/}.
-
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-this format, \verb+#1+, \verb+#2+, etc. stand for required
-author-supplied arguments to commands. For example, in
-\verb+\section{#1}+ the \verb+#1+ stands for the title text of the
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-
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-apssamp}) after the first pass of \LaTeX\ produces the file
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-(Refs.~\onlinecite{epr,feyn54,witten2001}). Note that the references
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-
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-
-\section{Math and Equations}
-Inline math may be typeset using the \verb+$+ delimiters. Bold math -symbols may be achieved using the \verb+bm+ package and the -\verb+\bm{#1}+ command it supplies. For instance, a bold$\alpha$can -be typeset as \verb+$\bm{\alpha}$+ giving$\bm{\alpha}$. Fraktur and -Blackboard (or open face or double struck) characters should be -typeset using the \verb+\mathfrak{#1}+ and \verb+\mathbb{#1}+ commands -respectively. Both are supplied by the \texttt{amssymb} package. For -example, \verb+$\mathbb{R}$+ gives$\mathbb{R}$and -\verb+$\mathfrak{G}$+ gives$\mathfrak{G}$- -In \LaTeX\ there are many different ways to display equations, and a -few preferred ways are noted below. Displayed math will center by -default. Use the class option \verb+fleqn+ to flush equations left. - -Below we have numbered single-line equations; this is the most common -type of equation in \textit{Physical Review}: -\begin{eqnarray} -\chi_+(p)\alt{\bf [}2|{\bf p}|(|{\bf p}|+p_z){\bf ]}^{-1/2} -\left( -\begin{array}{c} -|{\bf p}|+p_z\\ -px+ip_y -\end{array}\right)\;, -\\ -\left\{% - \openone234567890abc123\alpha\beta\gamma\delta1234556\alpha\beta - \frac{1\sum^{a}_{b}}{A^2}% -\right\}% -\label{eq:one}. -\end{eqnarray} -Note the open one in Eq.~(\ref{eq:one}). - -Not all numbered equations will fit within a narrow column this -way. The equation number will move down automatically if it cannot fit -on the same line with a one-line equation: -$$-\left\{ - ab12345678abc123456abcdef\alpha\beta\gamma\delta1234556\alpha\beta - \frac{1\sum^{a}_{b}}{A^2}% -\right\}. -$$ - -When the \verb+\label{#1}+ command is used [cf. input for -Eq.~(\ref{eq:one})], the equation can be referred to in text without -knowing the equation number that \TeX\ will assign to it. Just -use \verb+\ref{#1}+, where \verb+#1+ is the same name that used in -the \verb+\label{#1}+ command. - -Unnumbered single-line equations can be typeset -using the \verb+$+, \verb+$+ format: -$g^+g^+ \rightarrow g^+g^+g^+g^+ \dots ~,~~q^+q^+\rightarrow -q^+g^+g^+ \dots ~.$ - -\subsection{Multiline equations} - -Multiline equations are obtained by using the \verb+eqnarray+ -environment. Use the \verb+\nonumber+ command at the end of each line -to avoid assigning a number: -\begin{eqnarray} -{\cal M}=&&ig_Z^2(4E_1E_2)^{1/2}(l_i^2)^{-1} -\delta_{\sigma_1,-\sigma_2} -(g_{\sigma_2}^e)^2\chi_{-\sigma_2}(p_2)\nonumber\\ -&&\times -[\epsilon_jl_i\epsilon_i]_{\sigma_1}\chi_{\sigma_1}(p_1), -\end{eqnarray} -\begin{eqnarray} -\sum \vert M^{\text{viol}}_g \vert ^2&=&g^{2n-4}_S(Q^2)~N^{n-2} - (N^2-1)\nonumber \\ - & &\times \left( \sum_{i<j}\right) - \sum_{\text{perm}} - \frac{1}{S_{12}} - \frac{1}{S_{12}} - \sum_\tau c^f_\tau~. -\end{eqnarray} -\textbf{Note:} Do not use \verb+\label{#1}+ on a line of a multiline -equation if \verb+\nonumber+ is also used on that line. Incorrect -cross-referencing will result. Notice the use \verb+\text{#1}+ for -using a Roman font within a math environment. - -To set a multiline equation without \emph{any} equation -numbers, use the \verb+\begin{eqnarray*}+, -\verb+\end{eqnarray*}+ format: -\begin{eqnarray*} -\sum \vert M^{\text{viol}}_g \vert ^2&=&g^{2n-4}_S(Q^2)~N^{n-2} - (N^2-1)\\ - & &\times \left( \sum_{i<j}\right) - \left( - \sum_{\text{perm}}\frac{1}{S_{12}S_{23}S_{n1}} - \right) - \frac{1}{S_{12}}~. -\end{eqnarray*} -To obtain numbers not normally produced by the automatic numbering, -use the \verb+\tag{#1}+ command, where \verb+#1+ is the desired -equation number. For example, to get an equation number of -(\ref{eq:mynum}), -$$-g^+g^+ \rightarrow g^+g^+g^+g^+ \dots ~,~~q^+q^+\rightarrow -q^+g^+g^+ \dots ~. \tag{2.6'}\label{eq:mynum} -$$ - -A few notes on \verb=\tag{#1}=. \verb+\tag{#1}+ requires -\texttt{amsmath}. The \verb+\tag{#1}+ must come before the -\verb+\label{#1}+, if any. The numbering set with \verb+\tag{#1}+ is -\textit{transparent} to the automatic numbering in REV\TeX{}; -therefore, the number must be known ahead of time, and it must be -manually adjusted if other equations are added. \verb+\tag{#1}+ works -with both single-line and multiline equations. \verb+\tag{#1}+ should -only be used in exceptional case - do not use it to number all -equations in a paper. - -Enclosing single-line and multiline equations in -\verb+\begin{subequations}+ and \verb+\end{subequations}+ will produce -a set of equations that are numbered'' with letters, as shown in -Eqs.~(\ref{subeq:1}) and (\ref{subeq:2}) below: -\begin{subequations} -\label{eq:whole} -$$-\left\{ - abc123456abcdef\alpha\beta\gamma\delta1234556\alpha\beta - \frac{1\sum^{a}_{b}}{A^2} -\right\},\label{subeq:1} -$$ -\begin{eqnarray} -{\cal M}=&&ig_Z^2(4E_1E_2)^{1/2}(l_i^2)^{-1} -(g_{\sigma_2}^e)^2\chi_{-\sigma_2}(p_2)\nonumber\\ -&&\times -[\epsilon_i]_{\sigma_1}\chi_{\sigma_1}(p_1).\label{subeq:2} -\end{eqnarray} -\end{subequations} -Putting a \verb+\label{#1}+ command right after the -\verb+\begin{subequations}+, allows one to -reference all the equations in a subequations environment. For -example, the equations in the preceding subequations environment were -Eqs.~(\ref{eq:whole}). - -\subsubsection{Wide equations} -The equation that follows is set in a wide format, i.e., it spans -across the full page. The wide format is reserved for long equations -that cannot be easily broken into four lines or less: -\begin{widetext} -$$-{\cal R}^{(\text{d})}= - g_{\sigma_2}^e - \left( - \frac{[\Gamma^Z(3,21)]_{\sigma_1}}{Q_{12}^2-M_W^2} - +\frac{[\Gamma^Z(13,2)]_{\sigma_1}}{Q_{13}^2-M_W^2} - \right) - + x_WQ_e - \left( - \frac{[\Gamma^\gamma(3,21)]_{\sigma_1}}{Q_{12}^2-M_W^2} - +\frac{[\Gamma^\gamma(13,2)]_{\sigma_1}}{Q_{13}^2-M_W^2} - \right)\;. \label{eq:wideeq} -$$ -\end{widetext} -This is typed to show the output is in wide format. -(Since there is no input line between \verb+\equation+ and -this paragraph, there is no paragraph indent for this paragraph.) -\section{Cross-referencing} -REV\TeX{} will automatically number sections, equations, figure -captions, and tables. In order to reference them in text, use the -\verb+\label{#1}+ and \verb+\ref{#1}+ commands. To reference a -particular page, use the \verb+\pageref{#1}+ command. - -The \verb+\label{#1}+ should appear in a section heading, within an -equation, or in a table or figure caption. The \verb+\ref{#1}+ command -is used in the text where the citation is to be displayed. Some -examples: Section~\ref{sec:level1} on page~\pageref{sec:level1}, -Table~\ref{tab:table1}, and Fig.~\ref{fig:epsart}. - -\section{Figures and Tables} -Figures and tables are typically floats'' which means that their -final position is determined by \LaTeX\ while the document is being -typeset. \LaTeX\ isn't always successful in placing floats -optimally. - -Figures may be inserted by using either the \texttt{graphics} or -\texttt{graphix} packages. These packages both define the -\verb+\includegraphics{#1}+ command, but they differ in how optional -arguments for specifying the orientation, scaling, and translation of the -figure. Fig.~\ref{fig:epsart} shows a figure that is small enough to -fit in a single column. It is embedded using the \texttt{figure} -environment which provides both the caption and the imports the figure -file. +\section{\label{measures}Measures and Instruments} + +We deployed the revised Force Concept Inventory (FCI)\cite{fci} and the he Maryland Physics Expectations Survey (MPEX)\cite{mpex} both at the beginning and the end of the mechanics semester. Participation was voluntary. We calculated the score (for the MPEX in comparison to the expert responses given in Ref.~\cite{mpex}) on the final deployment, as well as, for students who participated in both of each instrument, the gain. The same analysis was done for the clusters of the MPEX: +\begin{itemize} +\item{\it Independence:} student takes responsibility for contructing their own understanding rather than takes what is given by authorities (teacher, materials) without evaluation +\item{\it Coherence:} student believes that physics needs to be considered as a connected, consistent framework rather than a set of unrelated facts or pieces'' +\item{\it Concepts:} student stresses the understanding of the underlying ideas and concepts rather than the memorization and usage of formulas +\item{\it Reality Link:} student believes that the ideas learned in physics are relevant and useful in a wide variety of real contexts rather than having little to do with experiences outside the classroom +\item{\it Math Link:} student considers mathematics as a convenient way of representing physical phenomena rather than viewing physics and mathematics as having little or no relationship +\item{\it Effort:} student makes the effort to use the available information and tries to make sense of it +\end{itemize} + +We also analyzed the online student discussions that were associated with the online homework given in the 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. As a refinement, the contributions were weighted by their length, and one particular contribution could belong to more than one class. For each student, the percentage of their contributions falling into the following classes~\cite{kortemeyer05ana} was calculated: + +\begin{itemize} + +\item Discussion contributions were classified as {\it surface} if they +dealt with surface features of the problem or were surface level requests +for help. + +\item {\it Procedural} contributions describe or inquire about mechanisms +of solving a problem without mentioning the underlying concepts or +reasoning. + +\item {\it Conceptual} contributions deal with the underlying concepts of +the problem. + +\item {\it Solution-oriented} -- the goal of the contribution is to arrive at +the correct answer without mentioning or dealing with the mathematics or +physics of the problem. + +\item {\it Mathematical} -- the contribution deals mostly with the +mathematical aspects of the problem. + +\item {\it Physics} -- the contribution deals mostly with the physics-related aspects +of the problem. + +\end{itemize} + +Online student discussions were earlier found to be 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 problems given~\cite{kortemeyer05ana}. This followup study was motivated in part by the hope and expectation to find strong correlations with student attitudes and expectations. + +As an additional measure of student performance, the final grade percentage for each student was taken into consideration. +\section{\label{results}Results} +Figure~\ref{fcimpexgrade} shows the correlation between the final FCI and MPEX scores with the final course grade percentage. With an$rof 0.56 and 0.30, 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. +Figure~\ref{mpexfci} shows how the final FCI and MPEX scores correlated with each other. +\begin{figure*} +\includegraphics[width=9cm]{fcipostgrade}\includegraphics[width=9cm]{mpexpostgrade} +\caption{\label{fcimpexgrade}Correlation between the FCI score (left) and the MPEX score (right) 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*} \begin{figure} -% \includegraphics{fig_1}% Here is how to import EPS art -\caption{\label{fig:epsart} A figure caption. The figure captions are -automatically numbered.} +\includegraphics[width=9cm]{fcipostmpexpost} +\caption{\label{mpexfci}Correlation of the final FCI score with the MPEX score.} \end{figure} - -Fig.~\ref{fig:wide} is a figure that is too wide for a single column, -so instead the \texttt{figure*} environment has been used. +Correlations with discussion characteristics turned out somewhat stronger, particularly with the FCI. 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. An additional analysis was carried out including only students who contributed more than five discussion entries over the course of the semester, and for whom thus their discussion behavior can be determined with better statistics. \begin{figure*} -% \includegraphics{fig_2}% Here is how to import EPS art -\caption{\label{fig:wide}Use the figure* environment to get a wide -figure that spans the page in \texttt{twocolumn} formatting.} +\includegraphics[width=9cm]{fcipostphysics}\includegraphics[width=9cm]{fcipostphysicsT} +\caption{\label{fciphysics}Correlation between the FCI score (left) and the percentage of that student's discussion that was classified as "physics." The figure on the right only includes students who contributed more than five discussion entries over the course of the semester.} \end{figure*} +\begin{figure} +\includegraphics[width=9cm]{physicsgrade} +\caption{\label{physicsgrade}Correlation of percentage physics-related discussions with grade percentage.} +\end{figure} -The heart of any table is the \texttt{tabular} environment which gives -the rows of the tables. Each row consists of column entries separated -by \verb+&+'s and terminates with \textbackslash\textbackslash. The -required argument for the \texttt{tabular} environment -specifies how data are displayed in the columns. For instance, entries -may be centered, left-justified, right-justified, aligned on a decimal -point. Extra column-spacing may be be specified as well, although -REV\TeX~4 sets this spacing so that the columns fill the width of the -table. Horizontal rules are typeset using the \verb+\hline+ -command. The doubled (or Scotch) rules that appear at the top and -bottom of a table can be achieved enclosing the \texttt{tabular} -environment within a \texttt{ruledtabular} environment. Rows whose -columns span multiple columns can be typeset using the -\verb+\multicolumn{#1}{#2}{#3}+ command (for example, see the first -row of Table~\ref{tab:table3}). - -Tables~\ref{tab:table1}-\ref{tab:table4} show various effects. Tables -that fit in a narrow column are contained in a \texttt{table} -environment. Table~\ref{tab:table3} is a wide table set with the -\texttt{table*} environment. Long tables may need to break across -pages. The most straightforward way to accomplish this is to specify -the \verb+[H]+ float placement on the \texttt{table} or -\texttt{table*} environment. However, the standard \LaTeXe\ package -\texttt{longtable} will give more control over how tables break and -will allow headers and footers to be specified for each page of the -table. A simple example of the use of \texttt{longtable} can be found -in the file \texttt{summary.tex} that is included with the REV\TeX~4 -distribution. - -There are two methods for setting footnotes within a table (these -footnotes will be displayed directly below the table rather than at -the bottom of the page or in the bibliography). The easiest -and preferred method is just to use the \verb+\footnote{#1}+ -command. This will automatically enumerate the footnotes with -lowercase roman letters. However, it is sometimes necessary to have -multiple entries in the table share the same footnote. In this case, -there is no choice but to manually create the footnotes using -\verb+\footnotemark[#1]+ and \verb+\footnotetext[#1]{#2}+. -\texttt{\#1} is a numeric value. Each time the same value for -\texttt{\#1} is used, the same mark is produced in the table. The -\verb+\footnotetext[#1]{#2}+ commands are placed after the \texttt{tabular} -environment. Examine the \LaTeX\ source and output for -Tables~\ref{tab:table1} and \ref{tab:table2} for examples. - -\begin{table} -\caption{\label{tab:table1}This is a narrow table which fits into a -narrow column when using \texttt{twocolumn} formatting. Note that -REV\TeX~4 adjusts the intercolumn spacing so that the table fills the -entire width of the column. Table captions are numbered -automatically. This table illustrates left-aligned, centered, and -right-aligned columns. } -\begin{ruledtabular} -\begin{tabular}{lcr} -Left\footnote{Note a.}&Centered\footnote{Note b.}&Right\\ -\hline -1 & 2 & 3\\ -10 & 20 & 30\\ -100 & 200 & 300\\ -\end{tabular} -\end{ruledtabular} -\end{table} - -\begin{table} -\caption{\label{tab:table2}A table with more columns still fits -properly in a column. Note that several entries share the same -footnote. Inspect the \LaTeX\ input for this table to see -exactly how it is done.} -\begin{ruledtabular} -\begin{tabular}{cccccccc} - &r_c$(\AA)&$r_0$(\AA)&$\kappa r_0$& - &$r_c$(\AA) &$r_0$(\AA)&$\kappa r_0$\\ -\hline -Cu& 0.800 & 14.10 & 2.550 &Sn\footnotemark[1] -& 0.680 & 1.870 & 3.700 \\ -Ag& 0.990 & 15.90 & 2.710 &Pb\footnotemark[2] -& 0.450 & 1.930 & 3.760 \\ -Au& 1.150 & 15.90 & 2.710 &Ca\footnotemark[3] -& 0.750 & 2.170 & 3.560 \\ -Mg& 0.490 & 17.60 & 3.200 &Sr\footnotemark[4] -& 0.900 & 2.370 & 3.720 \\ -Zn& 0.300 & 15.20 & 2.970 &Li\footnotemark[2] -& 0.380 & 1.730 & 2.830 \\ -Cd& 0.530 & 17.10 & 3.160 &Na\footnotemark[5] -& 0.760 & 2.110 & 3.120 \\ -Hg& 0.550 & 17.80 & 3.220 &K\footnotemark[5] -& 1.120 & 2.620 & 3.480 \\ -Al& 0.230 & 15.80 & 3.240 &Rb\footnotemark[3] -& 1.330 & 2.800 & 3.590 \\ -Ga& 0.310 & 16.70 & 3.330 &Cs\footnotemark[4] -& 1.420 & 3.030 & 3.740 \\ -In& 0.460 & 18.40 & 3.500 &Ba\footnotemark[5] -& 0.960 & 2.460 & 3.780 \\ -Tl& 0.480 & 18.90 & 3.550 & & & & \\ -\end{tabular} -\end{ruledtabular} -\footnotetext[1]{Here's the first, from Ref.~\onlinecite{feyn54}.} -\footnotetext[2]{Here's the second.} -\footnotetext[3]{Here's the third.} -\footnotetext[4]{Here's the fourth.} -\footnotetext[5]{And etc.} -\end{table} +While physics-related discussions positively correlate with FCI scores and grades (Fig.~\ref{physicsgrade}), solution-oriented discussions negatively correlated (Fig.~\ref{solutionfci}). +\begin{figure} +\includegraphics[width=9cm]{fcipostsolutionT} +\caption{\label{solutionfci}Correlation of percentage solution-oriented discussions with final FCI score.} +\end{figure} +Table~\ref{fullresults} shows the complete results of the study, including correlations with gains on FCI and MPEX. In the columns, the table shows Grade percentage, Final Exam percentage, final FCI Score, FCI Gain, final MPEX Score, MPEX Gain, and discussion characteristics, in the rows, again Grade, Final Exam, FCI, MPEX, as well as the individual scores on the final MPEX clusters. \begin{table*} -\caption{\label{tab:table3}This is a wide table that spans the page -width in \texttt{twocolumn} mode. It is formatted using the -\texttt{table*} environment. It also demonstates the use of -\textbackslash\texttt{multicolumn} in rows with entries that span -more than one column.} +\caption{\label{fullresults}Complete correlation results ($r-values). 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.} \begin{ruledtabular} -\begin{tabular}{rlllllllllll} - &Grade&FCI &FCI &MPEX&MPEX&Solution &Math &Physics &Surface &Procedural&Conceptual\\ - & &Final &Gain &Final &Gain & & & & & &\\ -Grade & &{\bf 0.56}&0.45 &0.3 &0.27 &--- (--0.25)&--0.15 (---)&0.22 (0.33)&--- (--0.25)&--- (---)&0.2 (0.28)\\ -FCI Final &{\bf 0.56} & & &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 & & &0.17 &--- &--0.28 (--0.44)&0.14 (---)&0.22 (0.4)&--0.1 (--0.34)&--- (---)&0.31 (0.34)\\ -MPEX Final & 0.3 & 0.24 &0.17 & & &--0.12 (---)&--- (---)&0.17 (0.16)&--- (---)&--- (0.12)&0.13 (0.11)\\ -MPEX Gain & 0.27 & --- & --- & & &--- (---)&--- (---)&--- (0.18)&0.14 (---)&--0.14 (---)&--- (---)\\ -Independence&0.25 &0.23 &0.1 & & &--- (---)&--- (0.13)&0.12 (---)&--- (---)&--- (---)&--- (0.15)\\ -Coherence &0.36 &0.2 &0.23 & & &--- (---)&--- (0.14)&0.18 (0.15)&--- (---)&--- (0.12)&0.1 (---)\\ -Concepts &0.25 &0.21 &0.13 & & &--- (---)&--- (---)&0.11 (0.14)&--- (---)&--- (-)&0.14 (0.18)\\ -Reality Link&--- &0.15 &--- & & &--0.12 (---)&--- (---)&--- (---)&--0.2 (--0.14)&0.11 (0.15)&--- (---)\\ -Math Link &0.15 &0.13 &--- & & &--- (---)&--- (-0.14)&--- (---) &0.1 (---)&--- (---)&--- (---)\\ -Effort &0.15 &--- &0.11 & & &--0.14 (--0.19)&--- (---)&0.19 (0.2)&--0.14 (--0.12)&--- (---)&0.22 (0.15) +\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)&0.12 (---)&--- (---)&--- (---)&--- (0.15)\\ +Cohe- & & && & & & & & & & & \\ +rence &0.36 &0.31&0.2 &0.23 & & &--- (---)&--- (0.14)&0.18 (0.15)&--- (---)&--- (0.12)&0.1 (---)\\ +Con-& & && & & & & & & & & \\ +cepts &0.25 &0.24 &0.21 &0.13 & & &--- (---)&--- (---)&0.11 (0.14)&--- (---)&--- (---)&0.14 (0.18)\\ +Reality & & && & & & & & & & & \\ +Link&--- &0.1&0.15 &--- & & &--0.12 (---)&--- (---)&--- (---)&--0.2 (--0.14)&0.11 (0.15)&--- (---)\\ +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*} -\begin{table} -\caption{\label{tab:table4}Numbers in columns Three--Five have been -aligned by using the d'' column specifier (requires the -\texttt{dcolumn} package). Non-numeric entries (those entries without -a .'') in a d'' column are aligned on the decimal point. Use the -D'' specifier for more complex layouts. } -\begin{ruledtabular} -\begin{tabular}{ccddd} -One&Two&\mbox{Three}&\mbox{Four}&\mbox{Five}\\ -\hline -one&two&\mbox{three}&\mbox{four}&\mbox{five}\\ -He&2& 2.77234 & 45672. & 0.69 \\ -C\footnote{Some tables require footnotes.} - &C\footnote{Some tables need more than one footnote.} - & 12537.64 & 37.66345 & 86.37 \\ -\end{tabular} -\end{ruledtabular} -\end{table} +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) hasr=-0.3$($N=97$) with the grade in the course,$r=-0.3$($N=97$) with the final FCI Score, and$r=0.3$($N=84$) 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$r=-0.3$($N=96$) with the final FCI score and also with$r=-0.3$($N=85$) with the FCI Gain, i.e., stronger than the cluster it belongs to. -\textit{Physical Review} style requires that the initial citation of -figures or tables be in numerical order in text, so don't cite -Fig.~\ref{fig:wide} until Fig.~\ref{fig:epsart} has been cited. +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$r=0.2$($N=173$) with the grade in the course, and with$r=0.29$($N=95$) and$r=0.3$($N=84$) with the final FCI Score and Gain, respectively. The prominence of contributions that are both solution-oriented and surface-level correlates with$r=-0.29$($N=95$) and$r=-0.13$($N=84$) with the FCI Score and Gain, respectively. -\begin{acknowledgments} -We wish to acknowledge the support of the author community in using -REV\TeX{}, offering suggestions and encouragement, testing new versions, -\dots. -\end{acknowledgments} +\section{Discussion of the 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. -\appendix +Correlations with the MPEX were generally weak, with$r=0.36$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 concepts 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). -\section{Appendixes} +Coletta and Philips~\cite{coletta05} found a strong correlation between the FCI Gain and the MPEX Score ($r=0.52; N=37$), while the same correlation turned out much lower in this study ($r=0.17; N=84$here). -To start the appendixes, use the \verb+\appendix+ command. -This signals that all following section commands refer to appendixes -instead of regular sections. Therefore, the \verb+\appendix+ command -should be used only once---to setup the section commands to act as -appendixes. Thereafter normal section commands are used. The heading -for a section can be left empty. For example, -\begin{verbatim} -\appendix -\section{} -\end{verbatim} -will produce an appendix heading that says APPENDIX A'' and -\begin{verbatim} -\appendix -\section{Background} -\end{verbatim} -will produce an appendix heading that says APPENDIX A: BACKGROUND'' -(note that the colon is set automatically). - -If there is only one appendix, then the letter A'' should not -appear. This is suppressed by using the star version of the appendix -command (\verb+\appendix*+ in the place of \verb+\appendix+). - -\section{A little more on appendixes} - -Observe that this appendix was started by using -\begin{verbatim} -\section{A little more on appendixes} -\end{verbatim} - -Note the equation number in an appendix: -$$-E=mc^2. -$$ - -\subsection{\label{app:subsec}A subsection in an appendix} - -You can use a subsection or subsubsection in an appendix. Note the -numbering: we are now in Appendix \ref{app:subsec}. - -Note the equation numbers in this appendix, produced with the -subequations environment: -\begin{subequations} -\begin{eqnarray} -E&=&mc, \label{appa} -\\ -E&=&mc^2, \label{appb} -\\ -E&\agt& mc^3. \label{appc} -\end{eqnarray} -\end{subequations} -They turn out to be Eqs.~(\ref{appa}), (\ref{appb}), and (\ref{appc}). -\newpage %Just because of unusual number of tables stacked at end -\bibliography{apssamp}% Produces the bibliography via BibTeX. +An unexpected result were the low correlations between the MPEX cluster scores and the student discussion behavior. One would have expected strong correlations between for example the score on the Concepts Cluster and the prominence of conceptual discussion contributions ($r=0.14 (0.18)$), or the comfort level with the usage of mathematics as a language and the corresponding lack of purely mathematical contributions (non significant or$r=-0.14\$ when including only students with more than five contributions overall).
+
+The relative weakness of many of the expected correlations with the MPEX might indicate that maybe -- in spite of the efforts of the author -- the students did not take the MPEX very seriously or did not carefully read the statements. An argument for this possible explanation is that the overall scores of the students on the MPEX were low (Independence 42\%; Coherence 46\%; Concepts 48\%; Reality Link 55\%; Math Link 40\%; Effort 47\%). Also, students relatively frequently chose the answer "3" ("Neutral") on the MPEX Likert scale, which is by definition never correct --- answering that way could indicate true indifference, confusion regarding the statement, or simply "don't care." By the same token, students appear to be taking the FCI more seriously, probably because it more closely relates to the other (grade-relevant) assessments they encounter in the course.
+\section{Conclusions}
+In this introductory calculus-based course, correlations between different performance and attitude indicators were found to be lower than expected. The FCI is most strongly correlated with grade performance and the final exam grade, while in turn the prominence of solution-oriented and physics-related discussion contributions are most strongly correlated with the FCI.
+
+Correlations with the MPEX were generally low, where the Coherence Cluster appears to be the strongest single indicator of success in the course. The individual statements "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"  (Coherence Cluster) and "The most crucial thing in solving a physics problem is finding the right equation to use"  (Concept Cluster) stand out as the most indicative ones.
+\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.
+\end{acknowledgments}
+\bibliography{correlations}% Produces the bibliography via BibTeX.

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