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/modules/gerd/discussions/paper discussions.tex
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Per reviewer: compare to other methods, comment on discussion
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Index: modules/gerd/discussions/paper/discussions.tex
diff -u modules/gerd/discussions/paper/discussions.tex:1.25 modules/gerd/discussions/paper/discussions.tex:1.26
--- modules/gerd/discussions/paper/discussions.tex:1.25 Sat Dec 10 17:16:23 2005
+++ modules/gerd/discussions/paper/discussions.tex Sat Dec 10 21:24:52 2005
@@ -266,22 +266,23 @@
\item[Type and feature sums] - number of all related contributions belonging to a certain type, subtype, or feature.
\end{description}
While a certain discussion contribution can only be in one class, for example ``Emotional/Physics-Related/Question,'' the same contribution can be in more than one
-superclass, for example both ``Chat'' and ``Physics-Related.''
+superclass, for example both ``Chat'' and ``Physics-Related.'' Figure~\ref{fig:discussionexample} shows an example of a homework problem and its associated discussion, as well as the appropriate discussion entry classification.
The majority of the discussion contributions were of type surface-level or procedural, followed by emotional
contributions.
The vast majority of discussion contributions had the feature of being solution-oriented,
yet a considerable number dealt with the physics
of the problems.
-
+\begin{figure*}
+\begin{quote}
A bug that has a mass $m_b=4g$ walks from the center to the edge of a disk that is freely turning at 32 rpm. The disk has a mass of $m_d=11g$. If the radius of the disk is $R=29cm$, what is the new rate of spinning in rpm?
-
-Student A (anonymous); female; 4.0:
+\end{quote}
+Student A (anonymous); female; 4.0 {\it (Emotional/Negative/Physics; Chat)}:
\begin{verbatim}
What is that bug doing on a disk? Boo to physics.
\end{verbatim}
-Student B (named); male; 3.5:
+Student B (named); male; 3.5 {\it (Procedural/Answer/Physics)}:
\begin{verbatim}
OHH YEAH
@@ -303,13 +304,13 @@
and solve for T
\end{verbatim}
-Student C (named); female; 3.0:
+Student C (named); female; 3.0 {\it (Surface/Question/Solution)}:
\begin{verbatim}
What is T exactly? And do I have to do anything to it to
get the final RPM?
\end{verbatim}
-Student B (named); male; 3.5:
+Student B (named); male; 3.5 {\it (Procedural/Answer/Solution)}:
\begin{verbatim}
ok so T is the period... and apparently it works for some
and not others.... try to cancel out some of the things
@@ -317,7 +318,7 @@
better equation that has less numbers in it
\end{verbatim}
-Student D (anonymous); female; 3.5: {\bf what did I do wrong?}
+Student D (anonymous); female; 3.5 {\it (Procedural/Question/Solution)}: {\bf what did I do wrong?}
\begin{verbatim}
This is what I did. initial inertia x initial angular velocity = final
inertia x final angular velocity. I=mr^2, angular velocity = w... so
@@ -328,27 +329,27 @@
be 23.3 rpm. This was wrong...what did I do incorrectly?
\end{verbatim}
-Student E (anonymous); male; 4.0: {\bf Re: what did I do wrong?}
+Student E (anonymous); male; 4.0 {\it (Procedural/Answer/Solution)}: {\bf Re: what did I do wrong?}
\begin{verbatim}
im not totally sure since i too got it wrong, but i know
your units are not in SI so that may be part of the problem.
\end{verbatim}
-Student E (anonymous); male; 4.0: {\bf whats the bug?}
+Student E (anonymous); male; 4.0 {\it (Surface/Question/Physics)}: {\bf whats the bug?}
\begin{verbatim}
a particle, a disk, initially part of the big disk, what? a
"bug" doesn't explain what we should consider it, inertia-
wise.
\end{verbatim}
-Student E (anonymous); male; 4.0: {\bf Re: whats the bug?}
+Student E (anonymous); male; 4.0 {\it (Procedural/Answer/Physics)}: {\bf Re: whats the bug?}
\begin{verbatim}
nevermind i got it. initially, the bug has no inertia since
distance from center=0. but at the end when bug is at the
edge of disk, just use I(bug)=mr^2.
\end{verbatim}
-Student F (anonymous); female; 2.5:
+Student F (anonymous); female; 2.5 {\it (Procedural/Question/Solution)}:
\begin{verbatim}
Ok- So I used to formula I initial = mr^2+ (1/2)cm^2 the
bug is in the center so there is no inertia. For the I
@@ -357,7 +358,7 @@
Can someone explain what I am doing wrong?
\end{verbatim}
-Student A (anonymous); female; 4.0: {\bf finally}
+Student A (anonymous); female; 4.0 {\it (Procedural/Answer/Solution)}: {\bf finally}
\begin{verbatim}
so i finally got this somehow...
We know that the Iw initial = Iw final.
@@ -373,20 +374,20 @@
still love gerd.
\end{verbatim}
-Student G (anonymous); female; 2.5: {\bf Re: finally}
+Student G (anonymous); female; 2.5 {\it (Surface/Question/Solution)}: {\bf Re: finally}
\begin{verbatim}
I'm still confused, which r do you put 0 in for? either
spot I either get 0 or the rpm i started wtih and neither
are right... something isn't right, can someone help me
\end{verbatim}
-Student H (named); male; 3.5: {\bf :sigh:}
+Student H (named); male; 3.5 {\it (Emotional/Negative/Solution)}: {\bf :sigh:}
\begin{verbatim}
Wow. So, many, little things, can go wrong in calculating
this. Be careful.
\end{verbatim}
-Student I (anonymous); female; 3.0: {\bf question?}
+Student I (anonymous); female; 3.0 {\it (Surface/Question/Solution)}: {\bf question?}
\begin{verbatim}
Everything seems to make sense up to where people say to
put in the radius of the bug.. what would it be? For I
@@ -396,24 +397,26 @@
again i get the same w as before and thats not correct???
\end{verbatim}
-Student J (anonymous); female; 2.5: {\bf Re: question?}
+Student J (anonymous); female; 2.5 {\it (Surface/Question/Solution)}: {\bf Re: question?}
\begin{verbatim}
That's the same thing that is messing me up. How is the
answer any different from the initial if the radius of the
bug is zero?
\end{verbatim}
-Student J (anonymous); female; 2.5: {\bf Re: Re: question?}
+Student J (anonymous); female; 2.5 {\it (Emotional/Negative/Solution)}: {\bf Re: Re: question?}
\begin{verbatim}
HELP PLEASE!!!!!
Nothing is working!
\end{verbatim}
-Student K (anonymous); female; 2.5 {\bf Re: Re: Re: question?}
+Student K (anonymous); female; 2.5 {\it (Procedural/Answer/Solution)}: {\bf Re: Re: Re: question?}
\begin{verbatim}
for the radius of the bug it is the same as the other
radius of the disk.
\end{verbatim}
+\caption{\label{fig:discussionexample}Example of a standard homework discussion and associated discussion}
+\end{figure*}
\section{Results of Analysis by Student}
\subsection{Participation}
@@ -423,7 +426,7 @@
\end{figure*}
\begin{table}
-\caption{Same as Table~\ref{table:disccat} for the first semester calculus-based class only. The table includes a small number of contributions by students who eventually dropped the course, while the analysis by student only considered students who completed the course.\label{table:disccatfirst}}
+\caption{Same as Table~\ref{table:disccat} for the first semester calculus-based class only. The table includes a small number of contributions by students who eventually dropped the course, which were included in the analysis by question type, but not in the analysis by student characteristics.\label{table:disccatfirst}}
\begin{ruledtabular}
\begin{tabular}{lcccccccc|l}
&\multicolumn{2}{c}{Emotional}
@@ -580,17 +583,44 @@
\end{itemize}
Especially the last observation is discouraging, since as the students in the calculus-based course progressed further into their study of physics, the degree to which they were discussing concepts
decreased. This might partly be due to the different subject matter (electricity and magnetism versus mechanics), but also due to the lack of reward for conceptual considerations in solving standard
-homework problems~\cite{lin}.
+homework problems~\cite{lin}.
\subsection{Qualitative Observations}
Reading the online discussions associated with the homework provides valuable insights to the instructor, which are hard to quantify.
When assigning homework, instructors usually have an instructional goal in mind, for example, they would like the students to grapple with a certain concept or work through a specific strategy of problem
-solving. Until the ``reality check,'' the fact that a specific problem only serves this purpose when being approached with an expert mindset is under-appreciated. An even deeper misconception is the
+solving. Until the ``reality check,'' the fact that a specific problem only serves this purpose when being approached with an expert mindset is under-appreciated.
+
+
+An even deeper misconception is the
assumption that solving the problem correctly is a reliable indicator of the concept or problem solving strategy being successfully communicated. What the (expert) instructor had in mind, and what the
(novice) learner actually does, can be worlds apart~\cite{lin,chi}. Students are going through reasoning processes and steps that are hardly imaginable to the instructor, and more often than not do several times more work
than necessary. The situation that they get a problem right for the wrong reasons is rare, but the instances that they get the problem correct with the same (minimal) amount of steps that an expert
would are equally rare --- in the end, the concept that was meant to be communicated is lost.
+As an example, consider the example Figure~\ref{fig:discussionexample}: there is no external torque, and the problem was meant as a simple example of angular momentum conservation. Since the disk has several centimeters radius, a bug can safely be approximated as a point mass. It is $(\frac{1}{2}m_dr^2+m_b0^2)\omega_0=(\frac{1}{2}m_dr^2+m_br^2)\omega$, and therefore $\omega=\omega_0m_d/(m_d+2m_b)$. As long as the disk is much larger than the bug, the result is independent of its radius, and no unit conversions are needed. Several things jump out to the expert reader of the discussion:
+\begin{itemize}
+\item No student mentions the fact that there is no external torque.
+\item No student gives the final solution.
+\item The idea that a bug could be approximated as a ``point mass'' compared to the size of the disk is never mentioned, even though Student E raises the issue.
+\item Regarding the calculation of the moment of inertia, there is confusion between the radius of an extended symmetrical object and the radius of the orbit of a point mass (thus, presumably, the question ``what is the radius of the bug?'').
+\item Students are plugging in numbers early and do not eliminate the radius of the disk from their calculations (with the possible exception of Student B who hints that ``cancel out some of the things
+that are found on both sides of the equation to get a
+better equation that has less numbers in it.'').
+\item Students do not appear to realize that unit conversions are in fact not needed.
+\item No student simply posts the final symbolic solution, which is true for virtually all analyzed discussions.
+\item Students went through considerable effort to solve this rather straightforward problem and do not realize that the solution is much simpler to achieve. Here, numerical online homework clearly falls short of handgraded homework, since the students are only graded on the correct final solution, not on their solution strategy.
+\end{itemize}
+Particularly the last point is distressing, since it instills a false sense of mastery among the students and confirms them in their undesirable techniques, which is an observation already pointed out by Pascarella~\cite{pascarella} in an earlier study of online homework systems.
+The discussion in Figure~\ref{fig:discussionexample} is typical, in spite of the fact that in lecture, problem solving strategies had been discussed, and examples had been given how the derivation of a final result in symbolic form can lead to faster and more reliable results. When discussing examples during lectures, the instructor attempted to model good problem solving strategies.
+
Many of these shortcomings may be correctable through early detection, and closely following the online student discussions prior to lecture, particularly around the assigned reading problems, may be a valid extension of the Just-in-Time Teaching~\cite{jitt} technique.
+\subsection{Comparison to other research approaches}
+To gain insight into student problem solving behavior, there are a number of appropriate research techniques. The presented technique of analyzing threaded online discussions has parallels to the following methods:
+\begin{description}
+\item[Interview techniques]
+\item[Observations of ``Thinking out loud'']
+\item[Analysis of group discussion recordings]
+\end{description}
+
\section{Conclusions}
Online student discussions are a rich source of insight into student problem solving behavior. It was verified that indeed conceptual and physics-related discussion contributions are characteristics of students who are successful in the course, while the prominance of solution-oriented
discussion contributions is strongly negatively correlated with success in the course.
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