[LON-CAPA-cvs] cvs: modules /gerd/alt2007 acc.ppt acccorrect1.pdf acccorrect2.pdf accincorrect1.pdf accincorrect2.pdf coil1.pdf coil2.pdf correct1.pdf correct1.ppt correct2.pdf correct2.ppt graphing.bib graphing.tex incorrect1.pdf incorrect1.ppt incorrect2.pdf incorrect2.ppt potentialgraph.ppt potentialgraph.tiff

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  Added files:                 
    /modules/gerd/alt2007	acc.ppt acccorrect1.pdf acccorrect2.pdf 
                         	accincorrect1.pdf accincorrect2.pdf coil1.pdf 
                         	coil2.pdf correct1.pdf correct1.ppt 
                         	correct2.pdf correct2.ppt graphing.bib 
                         	graphing.tex incorrect1.pdf incorrect1.ppt 
                         	incorrect2.pdf incorrect2.ppt 
                         	potentialgraph.ppt potentialgraph.tiff 
  Log:
  ALT 2007
  
  
--www1171320532
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Index: modules/gerd/alt2007/acc.ppt
+++ modules/gerd/alt2007/acc.ppt
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Index: modules/gerd/alt2007/correct1.ppt
+++ modules/gerd/alt2007/correct1.ppt
ࡱ






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Index: modules/gerd/alt2007/correct2.ppt
+++ modules/gerd/alt2007/correct2.ppt
ࡱ







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Index: modules/gerd/alt2007/graphing.bib
+++ modules/gerd/alt2007/graphing.bib
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  howpublished="\url{http://www.lon-capa.org/institutions.html}"
}

@MISC{loncapashared,
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   author = "Francesca Ferrara",
   year = "2004",
   booktitle = "Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education",
   volume="2",
   pages="375-382",
   title = {"Why doesn't it start from the origin?": Hearing the Cognitive Voice of Signs}
}
   
Index: modules/gerd/alt2007/graphing.tex
+++ modules/gerd/alt2007/graphing.tex
\documentclass[11pt]{article}
\newif\ifpdf
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	\pdffalse % we are not running PDFLaTeX
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\newcommand{\url}[1]{{\tt #1}}
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\begin{document}

	\ifpdf
	\DeclareGraphicsExtensions{.pdf, .jpg, .tif}
	\else
	\DeclareGraphicsExtensions{.eps, .jpg}
	\fi
\begin{center}
{\Large\sc Online Assessment of Back-of-the-Envelope Graph Sketches in Introductory Physics}
\end{center}
\section{Introduction}
The ability to work with graphs is a basic skill of any scientist. When scientists are discussing concepts and phenomena, they quickly resort to sketches of one variable versus another, sometimes just three lines on a paper: two axes and a graph. But how often do we intentionally teach our students about this important representation format?

Even with the relatively simple concept of position, velocity, and acceleration, students have unexpected difficulties translating between graphical representations and both the mathematical representation and the ``real world.''~\cite{mcdermott,beichner}. These difficulties can sometimes have subtle reasons that lead to cognitive disconnects: for example,  using a graph showing the position of a bouncing ball versus time, Ferrara~\cite{ferrara} found that even the sign, i.e., measuring the distance from the ground versus from the launch points, can make a large difference. Students might misinterpret a graph as a pictorial representation of a situation, mix up what is on the axes, or become confused when approximating the slope of a graph that does not start at the origin~\cite{beichner}. Students need practice both interpreting and generating these graphs, but appropriate formative assessment frequently does not happen in the typically large enrollment introductory courses due to scalability problems: there are simply not enough teaching assistants to give the students appropriate feedback on these complex tasks.

Only too often, problems given in physics courses focus on numerical calculations, e.g., ``A car accelerates from rest with $2 m/s^2$ for 10 seconds, what is the distance covered?'' -- students can ``solve'' these problems without any understanding of the underlying concepts~\cite{lin,heuvelen}. More sophisticated problems may ask students to match graphs with physical situations, but do not involve generating the graphs.

Sketching a graph is also different from plotting a function or data, something which students already might have practice in: it is an activity that should be manageable with just a few strokes.

Within this project, we will develop an online assessment tool for graph sketching, which can provide randomized scenarios and provide immediate feedback to graph sketches entered online with a mouse or trackpad. We will evaluate usability for both faculty and students, as well as impact on student problem solving strategies and conceptual learning.

The tool will be developed on top of an existing course and learning content management system in order to minimize overhead. However, both the algorithms and the code will be made freely available, so they can be incorporated into other systems.
\subsection{Intellectual Merit}
\subsection{Broader Impact}
\section{Project Overview}
Over the course of this project, we will:
\begin{itemize}
\item develop the tools to evaluate graph sketches submitted online
\item refine the authoring aspects in a faculty usability study
\item refine the learner interface in a student usability study
\item develop an initial set of problems in relevant introductory physics areas
\item analyze student problem solving strategies for these problems versus traditional numerical and graph identification/matching problems
\item evaluate the educational effectiveness of these problems versus traditional numerical and graph identification/matching problems
\item make algorithms and tools available open-source and freely
\item disseminate results
\end{itemize}
Several of these steps will be carried out iteratively over the duration of the project while refining both tool and content
\section{Relevant Results from Prior NSF Support}
\subsection{The LON-CAPA System}
Gerd Kortemeyer has been Co-PI on the NSF-ITR grant {\it Investigation of a Model for Online Resource Creation and Sharing in Educational Settings} (\#0085921, \$2,055,000, 09/15/00-07/31/06). The project
developed the cross-institutional learning content management system Learning{\it{}Online} Network with Computer Assisted Personalized Approach (LON-CAPA)\cite{loncapa} and researched methods to assess the educational impact of
content resources and representations within its shared content pool.

LON-CAPA is open-source (GNU General Public License) freeware, there are no licensing costs associated. 
Both aspects are important for the success of this project: the open-source nature of the system allows researchers to modify and adapt the system in order to address research needs, and the freeware character allows 
easier dissemination of results, in particular adaptation and implementation at other universities.

The system started in 1992 as a tool to deliver personalized homework to students. ``Personalized'' means that each student sees a different version of the same 
computer-generated problem: different numbers, choices, graphs, images, simulation parameters, etc\cite{kashyd01}, see Fig.~\ref{induction} for an example.
\begin{figure}
\includegraphics[width=3.5in]{figures/coil1}
\includegraphics[width=3.5in]{figures/coil2}
\caption{Two versions of the same problem in LON-CAPA. Different students would see different currents as a function of time in coil 1, and need to identify the corresponding induced voltage in coil 2. In this scenario, it is simply $V_2(t)=M\frac{dI_1(t)}{dt}$, with $V_2(t)$ being the induced voltage in coil 2, $I_1(t)$ being the current in the first coil, and and $M$ being the mutual inductance factor between the coils. The second and third part of the question are multiple choice and numerical response (with physical units), respectively.\label{induction}}
\end{figure}
Over the years, the system was expanded with content management and standard course management features, such as communications, gradebook, etc., similar to those in commercial course management systems, such as 
BlackBoard, WebCT, or ANGEL. In addition to standard features, the LON-CAPA delivery and course management layer is designed around STEM education, for example: 
\begin{itemize}
\item support for mathematical typesetting throughout (\LaTeX\ inside of XML) (formulas are rendered on-the-fly, 
and can be algorithmically modified through the use of variables inside formulas)
\item integrated GNUplot support (graphs can be rendered on-the-fly, 
and allowing additional layered labeling of graphs and images)
\item support for multi-dimensional symbolic math answers, using sampling or the integrated Maxima symbolic algebra system
\item and full support of physical units.
\end{itemize}

LON-CAPA developed into a content sharing network of more than 40 institutions of higher education including community colleges and four-year institutions, as well as 50 middle and high schools~\cite{loncapainst}. In addition, LON-CAPA houses commercial textbook content from seven major publishing companies, and a commercial service company was established around the product at the end of 2004. 
The shared content pool currently contains over 250,000 learning resources~\cite{loncapashared}, including more than 80,000 randomizing homework problems. Disciplines include astronomy, biology, business, chemistry, civil engineering, computer science, family and child ecology, geology, human food and nutrition, human medicine, mathematics, medical technology, physics, and psychology.
LON-CAPA is used by approximately 35,000 students every semester.

LON-CAPA will provide the platform on which the tools will be developed and evaluated. It also provides the initial dissemination platform for problems authored over the course of this project.


\section{Graph Evaluation}
The LON-CAPA system currently allows to dynamically generate randomized graphs both in the problem text and in the answers. For example, in Fig.~\ref{induction}, different students get different graphs for the current in coil 1 over time, and need to identify the resulting induced voltage in coil 2. 

The activity of identifying the correct graph however is very different from sketching the right graph. A system that can evaluate student input of graphs needs far more sophisticated than is needed for problems like in Fig.~\ref{induction}.

\subsection{Example Problems}
\subsubsection{Open-Ended Problems}
\label{accproblem}
A typical open-ended problem would be
\begin{quote}
Draw a graph of acceleration versus time for a car that first stands at a red light, drives off when the light turns green, and then coasts with a constant velocity. Take ``forward'' to be positive.
\end{quote}

Fig.~\ref{acccorrect} shows different acceptable solutions. Note that any solution that would show a positive acceleration for a limited time would be correct. Also note that due to the lack of precision in graphical input with a mouse, the left edge of the curve in the right panel actually slightly bends backward -- the software should accept these minor flaws.
\begin{figure}
\includegraphics[width=3.5in]{figures/acccorrect1}
\includegraphics[width=3.5in]{figures/acccorrect2}
\caption{Example of solutions that would be acceptable to the problem described in
section~\ref{accproblem}.
\label{acccorrect}}
\end{figure}
The panels in Fig.~\ref{accincorrect} are not acceptable. The left panel appears to be the velocity, while the right panel would be position. Using the adaptable hint feature of LON-CAPA, the system should allow to specify the criteria for these anticipated wrong solutions.
\begin{figure}
\includegraphics[width=3.5in]{figures/accincorrect1}
\includegraphics[width=3.5in]{figures/accincorrect2}
\caption{Example of solutions that would not be acceptable to the problem described in
subsection~\ref{accproblem}.\label{accincorrect}}
\end{figure}
Different randomizations of this problem might have the car braking in front of a red light, or accelerate while overtaking another car.
\subsubsection{Constrained Problems}\label{potproblem}
A more constrained problem would be the following:
\begin{quote}
The graph shows the electric potential along an axis connecting two charges. Draw the component of the electric field along this axis.
\end{quote}
Fig.~\ref{potentialcorrect} shows different acceptable solutions. Note that the scale is irrelevant in this case, but the graphs need to go to infinity and minus infinity at the positions of the charges, respectively, go to zero at infinite distances, and be zero at the point where the potential is flat. 

\begin{figure}
\includegraphics[width=3.5in]{figures/correct1}
\includegraphics[width=3.5in]{figures/correct2}
\caption{Examples of acceptable solutions (blue) for the example problem described in section~\ref{potproblem}. The system provides a graph of a potential versus location along an axis that has two charges placed on it (black). The electric field is given by $\vec E=-\nabla V$.\label{potentialcorrect}}
\end{figure}
The graphs in Fig.~\ref{potentialincorrect} are not correct because of a sign error and the assumption that the field is zero where the potential is zero, respectively.

\begin{figure}
\includegraphics[width=3.5in]{figures/incorrect1}
\includegraphics[width=3.5in]{figures/incorrect2}
\caption{Examples of incorrect solutions for the example problem in section~\ref{potproblem}.\label{potentialincorrect}}
\end{figure}
Different randomizations of this problem will have other charge distributions or relative strengths, which will result in different system-provided graphs for the potential.
\subsection{Salient versus spurious features}
When the system evaluates a student-provided graph, it is important to distinguish salient from spurious graph features. Examples for salient features might include:
\begin{itemize}
\item linear versus non-linear
\item asymptotic behavior at infinity or possibly certain points
\item approximate position of maxima or minima
\item approximate position of crossing axes
\end{itemize}
Spurious features might include:
\begin{itemize}
\item scale
\item artifacts from inputting the graph using a mouse
\item exact position of crossing axes, minima and maxima
\end{itemize}
Which features to which degree are salient depends on the problem posed. For example, for the acceleration problem in section~\ref{accproblem} the exact shape of the graph is irrelevant, as long as the graph starts with zero and ends with zero, and is positive for a finite time in-between. In the potential versus field problem~\ref{potproblem} on the other hand, the asymptotic behavior at certain positions and the position of crossing axes is important. 
\section{Tool Development}
\section{Usability Testing}
\subsection{Authoring Interface}
\subsection{Learner Interface}
\section{Initial Content Development}
\section{Analysis of Problem Solving Behavior}
In order to evaluate the influence of this problem type on student problem solving, the associated online discussions will be analyzed. These are a rich source of information~\cite{kortemeyer05ana,kortemeyer07correl}, and it was found that different problem types lead to different student discussion behavior.
\section{Evaluation of Educational Effectiveness}
As an instrument to evaluate the effectiveness of the online homework, we will deploy the Test of Understanding Graphs in Kinematics (TUG-K)~\cite{beichner} in consecutive semesters, both before and after introducing the problems. We will also compare scores on the Force Concept Inventory (FCI)~\cite{fci}, for which already several years of pre- and post-test scores exist for the course initially under investigation.
\section{Dissemination}
\section{Project Management}
\section{Project Timeline}
\bibliography{graphing}
\end{document} 
Index: modules/gerd/alt2007/incorrect1.ppt
+++ modules/gerd/alt2007/incorrect1.ppt
ࡱ








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Index: modules/gerd/alt2007/incorrect2.ppt
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Index: modules/gerd/alt2007/potentialgraph.ppt
+++ modules/gerd/alt2007/potentialgraph.ppt
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