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Index: modules/gerd/alt2007/graphing.tex
diff u modules/gerd/alt2007/graphing.tex:1.3 modules/gerd/alt2007/graphing.tex:1.4
 modules/gerd/alt2007/graphing.tex:1.3 Tue Mar 6 16:47:16 2007
+++ modules/gerd/alt2007/graphing.tex Wed Mar 7 16:44:10 2007
@@ 33,24 +33,31 @@
\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,meltzer05,clement81}. 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~\cite{elby00}, 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.
+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,meltzer05,clement81}. 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~\cite{elby00}, 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}. The sketching of graphs is an example of a more constructivist approach to teaching these concepts. The students need to make a number of decisions:
+Only too often, instead the 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}.
+Going beyond these types, there may be problems that require selecting from a series of possible graphical answers in a multiple choice setting, inputting an equation and having the software sketch it~\cite{kennedy04}, or plotting a given function or set of data. It was found however that these traditional representationtranslation problem types do not lead to significantly increased conceptual or less procedural solution strategies~\cite{kortemeyer05ana}, i.e., they do not lead students to construct any new knowledge in a manner different from numerical or other multiplechoice problems.
+
+The sketching of graphs is an example of a more constructivist approach to teaching concepts, as well as representationtranslation and visualization skills. The students need to make a number of decisions:
\begin{itemize}
\item Where does the graph start (is the start point known and/or significant)?
\item Where does the graph finish (is the end point known and/or significant)?
\item What is the general shape of the curve (e.g., exponential growth or decay, a hysteresis, sinusoidial, asymptotic)?
\item Are there singularities or significant points along the way?
\end{itemize}
 (list expanded from \cite{kennedy04}). Students need to construct the curve, which is quite different from selecting from a series of possible answers in a multiple choice setting, inputting an equation and having the software sketch it~\cite{kennedy04}, or plotting a given function or set of data. Sketching is an activity that should be manageable with just a few strokes to express a general relationship.
+ (list expanded from \cite{kennedy04}). Students need to construct the curve, not reproduce it or select it from a set of prefab solutions.
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.
+Sketching is an activity that should be manageable with just a few strokes to express a general relationship. 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{Learning Goals}
+Student problems in representation translation between mathematical and ``real world'' scenarios on the one hand, and graphical representations on the other, are well documented in literature. Careful plotting of functions or data does not address the conceptual visualization goals, and selecting between different options does not help students truly construct new knowledge and communicate ideas. Students will learn how to use ``backoftheenvelope" sketches as a tool to communicate real world and mathematical concepts.
\subsection{Technology Goals}
+This project goes beyond offering different options for graphs or drawing graphs based on adjustable parameters to splines. It will develop algorithms that evaluate freehand input of graphs with various randomized constraints or scenarios. The constructed rule set and its tolerances will be adaptive and allow adjustment through feedback loops. Usability and accessibility testing is part of the design process, and scalability concerns will be strongly taken into account in order to develop a widely usable tool, not a laboratorytype proofofconcept. The tools will be developed on top of an existing software infrastructure, but will be kept modular and be made available opensource, so they can be deployed in other contexts.
\subsection{Intellectual Merit}
+The project will develop new understanding regarding the acquisition of visualization skills. Students will be observed as they perform representation translation, using both traditional tools such as multiple choice between different graphical options, and freehand sketching. The results will inform practitioners in assessment design and lead to insights into the cognitive development of students as they are confronted with representation translation tasks.
\subsection{Broader Impact}
+Generating and evaluating simple data visualization in the form of ``backoftheenvelope'' line graphs is an important skill across academic disciplines. While the project will focus on the teaching of physics, the same tools are expected to be useful not only in other natural sciences or mathematics, but also in for example economics and social sciences. The tools will be implemented within a software framework that is already used at 50 secondary and over 40 postsecondary institutions.
\section{Project Overview}
Over the course of this project, we will:
\begin{itemize}
@@ 72,7 +79,7 @@
\caption{Two versions of the same problem in LONCAPA. 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}
Gerd Kortemeyer has been CoPI on the NSFITR grant {\it Investigation of a Model for Online Resource Creation and Sharing in Educational Settings} (\#0085921, \$2,055,000, 09/15/0007/31/06). The project
+Gerd Kortemeyer has been PI on the NSFITR grant {\it Investigation of a Model for Online Resource Creation and Sharing in Educational Settings} (\#0085921, \$2,055,000, 09/15/0007/31/06). The project
developed the crossinstitutional learning content management system Learning{\it{}Online} Network with Computer Assisted Personalized Approach (LONCAPA)\cite{loncapa} and researched methods to assess the educational impact of
content resources and representations within its shared content pool.
@@ 106,7 +113,7 @@
\section{Graph Evaluation}
The LONCAPA 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}.
+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 algorithms than are needed for problems like in Fig.~\ref{induction}.
\subsection{Example Problems}
\subsubsection{OpenEnded Problems}
@@ 115,7 +122,6 @@
\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=3in]{figures/acccorrect1}
@@ 169,7 +175,7 @@
\end{itemize}
Which features to which degree are significant 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 inbetween. 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.
\subsection{Rules}\label{rules}
Rather than constructing the graph using B\'ezier curves and checking if the parameters are within acceptable tolerance~\cite{kennedy04}, we propose to evaluate the graphs using rule sets for the function itself and its derivatives. Figures~\ref{accrule} and \ref{potrule} shows examples of what these rules might look like.
+Rather than constructing the graph using B\'ezier curves and checking if the parameters are within acceptable tolerance~\cite{kennedy04}, we propose to evaluate the graphs using rule sets for the function itself and its derivatives. Figures~\ref{accrule} and \ref{potrule} show examples of what these rules might look like.
\begin{figure}\begin{center}
\begin{tabular}{llllll}\hline
{\bf Type}&{\bf From $x$}&{\bf To $x$}&{\bf From $y$}&{\bf To $y$}&{\bf Rules}\\\hline
@@ 224,6 +230,7 @@
For the clientside functionality, different technologies such as Java applets in connection with CGIsubmissions or servlet communication, or Adobe Flash (for example in connection with red5), will be tested to maximize platform compatibility and bandwidth efficiency.
+The initial coding will be carried out by members of the MSU LONCAPA group and is expected to take approximately nine months. As the tool is refined, additional coding will be necessary.
\section{Usability Testing}
The ease of authoring is crucial for the widespread adoption of the tool, and has been one of the limiting factors to the dissemination of the original Interactive Graphing Tool.~\cite{kennedy04}. The same is true for the student interface: a tool which students cannot use is likely not going to find wide adaption by instructors. In order to ensure that the graphing tool meets user expectations and that the interaction between the system and the user is optimized, usercentered design methodologies should be incorporated into the product development process. Usercentered design means that products are developed such that they are easy, effective, accessible, and enjoyable to use from the {\it userÕs} perspective, supporting the tasks that they are trying to accomplish. We propose that conducting a usability evaluation (with representative end users) and a web accessibility evaluation will significantly enhance the toolÕs usability, thereby resulting in a more successful, usable, enjoyable product.
\subsection{Testing Facility}
@@ 233,7 +240,14 @@
\subsection{Web Accessibility Compliance Inspection}
Accessibility experts will evaluate the graphing tool and identify the improvements needed to ensure legal compliance with Section 508 standards. Coding the tool with accessibility design principles in mind will enhance the user experience of customers who use assistive technology as they interact with the product, thus increasing the ability to reach and satisfy the broadest possible audience. Additionally, including common accessibility features would dramatically improve the user experience for customers using mobile phone browsers, personal digital assistants, and even lowbandwidth connections. We will provide with a detailed report outlining the accessibility standards, whether they have been met, the code examples, and other helpful information.
\section{Initial Content Development}

+Content will initially be developed in areas where there is already existing LONCAPA content that uses representation translation, e.g.,
+\begin{itemize}
+\item Motion in one dimension
+\item Simple harmonic motion
+\item Induction
+\item TimeVarying Currents
+\end{itemize}
+Content will be specifically designed to address the difficulties identified in~\cite{mcdermott,beichner}, and made available networkwide to all participating institutions.
\section{Evaluation of Educational Effectiveness}
\subsection{Assessment of the Tool as Instructional Aid}
@@ 248,15 +262,19 @@
\section{Dissemination}
The tool itself and its documentation will be included in the production version of LONCAPA and thus become part of the regular distribution. The tool will be presented at the annual LONCAPA conferences and included in the training workshops.
+Any content material developed will be made available networkwide to all participating institutions.
+
Research results will be published in the standard journals, including The Physics Teacher for application studies, and the American Journal of Physics or the Physical Review STPER cognitive studies. Presentations will be given at the American Association of Physics Teachers conferences and associated PER conferences.
\section{Project Management}
The primary project responsibility will be with the PI, Gerd Kortemeyer.

The coding of the tool will be supervised with the LONCAPA Technical Director, Guy Albertelli.
+The primary project responsibility will be with the PI, Gerd Kortemeyer. Dr. Kortemeyer will supervise the postdoctoral associate. The coding of the tool will be supervised with the LONCAPA Technical Director, Guy Albertelli. Sarah Swierenga, Director of the Usability \& Accessibility Center at MSU, will be responsible for the direction of the usability and accessibility study.
\section{Project Timeline}
\subsection{Year 1}
+The rule set format as well as the fuzziness algorithms are defined. Prototypes are implemented and tested, followed by the development of the production version.
\subsection{Year 2}
+The usability and accessibility testing will be carried out, as well as an initial formative educational evaluation of the tool in focus group settings. In parallel, content for the tool is developed.
\subsection{Year 3}
+The tool becomes part of the LONCAPA production releases.
+The assessment of its educational effectiveness in carried out in a production setting. Results are analyzed and published, as well as presented at conferences.
\pagebreak
\bibliography{graphing}
\end{document}
\ No newline at end of file
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