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diff -u modules/gerd/concept/description.tex:1.2 modules/gerd/concept/description.tex:1.3
--- modules/gerd/concept/description.tex:1.2 Wed Jun 23 15:11:22 2004
+++ modules/gerd/concept/description.tex Sat Jul 3 13:53:33 2004
@@ -21,7 +21,7 @@
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@@ -31,16 +31,57 @@
\else
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-\noindent{\LARGE\sc Physics Education:\\ Does "Conceptual" mean "No Formulas?"}
+\begin{title}
+\title{\LARGE\sc Physics education:\\ Does "conceptual" online formative assessment lead to conceptual understanding?}
+\end{title}
+
\section{Introduction}
\begin{quote}
Mathematics is {\it not} just another language. Mathematics is a language plus reasoning; it is a language plus logic. Mathematics is a tool for reasoning. It is in fact a big collection of the results of some person's careful thought and reasoning. By mathematics it is possible to connect one statement to another.
-\begin{flushright}\sc Richard Feynman\cite{feynmanCharacter}\end{flushright}
+\begin{flushright}\sc Richard Feynman~\cite{feynmanCharacter}\end{flushright}
\end{quote}
+\begin{quote}
+When you guys help us with problems [...] in
+class you really got to start plugging in numbers into the
+equations that you use and solving the problem step by step.
+And then at the end coming up with a concrete answer like 2
+or 4.5654 (not $y_{0x}$ or $x_o$) so when we look at our notes even
+if we don't understand them, with real solutions we can go
+back and figure them out.
+\begin{flushright}\sc Student, MSU phy183~\cite{student}\end{flushright}
+\end{quote}
+
+\subsection{"Thinking like a Physicist"}
+Most physicists would agree that part of "being a physicist" is to "think like a physicist," which manifests itself most strongly in the cognitive and metacognitive skills involved in problem solving~\cite{redish} --- part of the self-image of many physicists is to be expert problem solvers, even outside their own discipline.
+
+As a result, an unfortunately only too common approach to teaching students how to "think like a physicist" is to have
+them solve a lot of problems. It does not take much real-world evidence (such as the student comment above) to refute this reverse conclusion, yet for many teachers, it takes "hard" proof, such as having their students complete the Force-Concept-Inventory~\cite{fci}, to bring about change~\cite{mazur} --- after all, most likely the naive approach actually worked for them.
+
+Expert and novice approaches to problem solving in physics have been studied extensively (e.g.~\cite{chi,larkin}), with one of the most apparent differences being that experts are characterizing problems according to deep structure and physical concepts (e.g., "energy conservation"-problem), while novices tend to characterize them according to surface features (e.g., "sliding-block-on-incline"-problem) or applicable formulas (e.g., "$E=\frac12mv^2+mgh$"-problem"). Redish~\cite{redish} somewhat bleakly describes a novice approach to learning physics as follows:
+\begin{itemize}
+\item Write down every equation or law the teacher puts on the board that is also in the book.
+\item Memorize these, together with the list of formulas at the end of each chapter.
+\item Do enough homework and end-of-the-chapter problems to recognize which formula is to be applied to which problem.
+\item Pass the exam by selecting the correct formula for the problems on the exam.
+\item Erase all information from your brain after the exam to make room for the next set of materials.
+\end{itemize}
+Unfortunately, the above mechanism actually works to pass courses. One cannot really blame learners for shortcircuiting physics "learning" this way, since the cognitive and metacognitive skills which physicists value so much higher than factual knowledge or formulas are hardly ever made explicit in the curriculum, in fact, they are "hidden"\cite{redish}.
+
+\subsection{Transfer between mathematical formulations and physical situations}
+Being able to plug-and-chug has little do with the understanding of mathematics, it is a skill. Students who are lacking this skill are kept from advancing in physics on a very basic level, and remedial instruction is in order. Other students simply have problems operating their pocket calculators.
+
+Moving beyond these initial barriers, students are generally able to correctly substitute variables and execute calculations, but see formulas in a purely operational sense~\cite{torigoe}, while lacking the abilitity to translate between the formulas and the situations~\cite{clement}.
+
+\subsection{Formulas versus "Conceptual"}
+Most frequently, the conflict can be boiled down to the use or abuse of formulas: A trait of expert physicists is that also for them a lot of formulas might have been "erased from the brain," but can be reconstructed from the knowledge of underlying concepts, as well as the cognitive and metacognitive processes needed to make the connections. While experts see mathematics as a means to express complex concepts, novices tend to see them as a mechanism to "plug-and-chug."
+
+If it is then the formulas which are tempting the students to shortcircuit their learning or distract them from it, some physics teachers have turned to almost altogether depriving their students of them. They are developing "conceptual" materials, where {\bf "conceptual" is frequently defined as the absence of formulas}.
+
+A somewhat extreme example is "Conceptual Physics" by Paul Hewitt~\cite{hewitt}, see Fig.~\ref{textbooks} and Table~\ref{alternatetext}, a more moderate example are the famous {\it Feynman Lectures on Physics}~\cite{feynmanLectures}, which have a much lower "formula density" than most textbooks actually in use in undergraduate teaching (Blatt~\cite{blatt} was chosen as a random example representating the style of most any textbook currently used).
\begin{figure}\label{textbooks}
\includegraphics[width=6.5in]{pages}
-\caption{Two textbook pages covering the same topic, {\it Principles of Physics} (Blatt\cite{blatt}) left, {\it Conceptual Physics} (Hewitt\cite{hewitt}) right}
+\caption{Two textbook pages covering the same topic, {\it Principles of Physics} (Blatt~\cite{blatt}) left, {\it Conceptual Physics} (Hewitt~\cite{hewitt}) right}
\end{figure}
\begin{table}\label{alternatetext}
@@ -65,25 +106,26 @@
\caption{Ohm's and Faraday's Law stated in two textbooks, {\it Principles of Physics} (Blatt\cite{blatt}) left, {\it Conceptual Physics} (Hewitt\cite{hewitt}) right}
\end{table}
-\begin{figure}\label{feynmandiag}
-\begin{tabular}{p{4.5in}c}\quad\vspace{-5cm}
+It should be noted that Hewitt also argues that the mathematical language of physics often deters the average nonscience students~\cite{hewitt}, which is contradictory to the observation of students being very satisfied to it for plug-and-chug.
-\begin{eqnarray*}T_{fi}=&\frac{1}{i}&\left\{
-\bar{u}(p_4)(ie\gamma^\mu)u(p_1)\frac{-ig_{\mu\nu}}{(p_4-p_1)^2}\bar{u}(p_3)(ie\gamma^{\nu})u(p_2)\right.\\
-&-&\left.\ \
-\bar{u}(p_3)(ie\gamma^\mu)u(p_1)\frac{-ig_{\mu\nu}}{(p_3-p_1)^2}\bar{u}(p_4)(ie\gamma^{\nu})u(p_2)\right\}
-\end{eqnarray*}&
-\includegraphics[width=1.6in]{photonexch}
-\end{tabular}
-\caption{Mathematical and diagramatic form of the Transition Matrix for electron-electron scattering}
-\end{figure}
% references
\newpage
\pagestyle{plain}
\begin{thebibliography}{99}
-\bibitem{feynmanCharacter} Richard Feynman, {\it The Character of Physical Law}, The MIT Press, ISBN 0 262 56003 8
-\bibitem{blatt} Frank J. Blatt, {\it Principles of Physics}, Allyn and Bacon, ISBN 0 205 11784 8
+\bibitem{feynmanCharacter} Richard Feynman, {\it The Character of Physical Law}, The MIT Press, ISBN 0 262 56003 8 (1967)
+\bibitem{student} Student online discussion contribution, "Introductory Physics for Scientists and Engineers," phy183, Michigan State University (2004)
+\bibitem{redish} Edward F. (Joe) Redish, {\it Teaching Physics}, Wiley, ISBN 0-471-39378-9 (2003)
+\bibitem{fci} D. Hestenes, M. Wells, and G. Swackhamer, {\it Force Concept Inventory}, Phys. Teach. {\bf 30}, 141-158 (1992)
+\bibitem{mazur} Eric Mazur, {\it Peer Instruction}, Prentice Hall, ISBN 0-13-565441-b (1997)
+\bibitem{chi} Michelene T. H. Chi, Paul J. Feltovich, Robert Glaser, {\it Categorization and Representation of Physics Problems by Experts and Novices}, Cognitive Science, Vol 5, p121-152 (1981)
+\bibitem{larkin} J. Larkin, J. McDermott, D. P. Simon, and H. A. Simon, {\it Expert and novice performance in solving physics problems}, Science {\bf 208} 1335-1342 (1980)
+\bibitem{torigoe} Eugene Torigoe, {\it Student Difficulties with Equations in Physics}, ISAAPT Spring Meeting, Urbana, IL, (April 2004)\bibitem{clement} J. Clement, J. Lochhead, and G. S. Monk, {\it Translation difficulties in learning mathematics}, Amer. Math. Mon. {\bf 88}, 286 (1981)
\bibitem{hewitt} Paul G. Hewitt, {\it Conceptual Physics}, Little, Brown, ISBN 0 673 39541 3
+\bibitem{feynmanLectures} Richard Feynman, Robert B. Leighton, and Matthew L. Sands, {\it The Feynman Lectures on Physics}, Addison-Wesley, ISBN 0-201-5100(3,4,5)-(0,9,0) (1963-65)
+\bibitem{blatt} Frank J. Blatt, {\it Principles of Physics}, Allyn and Bacon, ISBN 0 205 11784 8
+
+
+
\end{thebibliography}
\end{document}
\end
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