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Index: modules/gerd/alt2007/graphing.tex
diff -u modules/gerd/alt2007/graphing.tex:1.11 modules/gerd/alt2007/graphing.tex:1.12
--- modules/gerd/alt2007/graphing.tex:1.11	Wed Apr  4 21:34:15 2007
+++ modules/gerd/alt2007/graphing.tex	Sat Apr  7 09:44:24 2007
@@ -135,7 +135,7 @@
 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 will provide the platform on which the tools will be developed and evaluated, and will be the initial dissemination platform for problems authored over the course of this project.
 \subsubsection{Investigating and Questioning our World through Science and Technology}\label{iqwst}
-David Fortus is a co-PI on the NSF grant {\it Investigating and Questioning our World through Science and Technology} (ESI-0439352, \$712,034 for MSU subcontract, 10/01/04-09/30/10). The project is developing a coordinated and comprehensive middle school science curriculum that emphasizes several scientific practices, one with is DGOA - data gathering, organization, and analysis.
+David Fortus is a co-PI on the NSF grant {\it Investigating and Questioning our World through Science and Technology} (ESI-0439352, \$712,034 for MSU subcontract, 10/01/04-09/30/10). The project is developing a coordinated and comprehensive middle school science curriculum that emphasizes several scientific practices, one of which is DGOA -- data gathering, organization, and analysis.
 \subsection{Relevant Results from Other Related Projects}
 In 1997, the Interactive Graphing Tool was developed at the University of Melbourne in support of chemistry instruction~\cite{kennedy98}. Over the years, the project went through a number of technology iterations, and was eventually re-implemented online as the Interactive Graphing Object (IGO) and on PDAs as the mobile Interactive Graphing Object (mIGO)~\cite{kennedy04}.
 
@@ -177,7 +177,7 @@
 \begin{figure}
 \includegraphics[width=3in]{figures/correct1}
 \includegraphics[width=3in]{figures/correct2}
-\caption{Examples for acceptable solutions (blue, solid) 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, dashed). The electric field is given by $\vec E=-\nabla V$.\label{potentialcorrect}}
+\caption{Examples for acceptable solutions (blue, solid) for the example problem described in section~\ref{potproblem}. The system provides a graph of a potential versus location (black, dashed) along an axis that has two charges placed on it. 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.
 
@@ -192,7 +192,7 @@
 \begin{itemize}
 \item linear versus nonlinear\vspace*{-2mm}
 \item asymptotic behavior at infinity or at particular points\vspace*{-2mm}
-\item approximate positions of maxima and minima\vspace*{-2mm}
+\item approximate positions of maxima, minima, and points of inflexion (as appropriate)\vspace*{-2mm}
 \item approximate positions of axis intercepts\vspace*{-2mm}
 \item curvature (convex/concave)
 \end{itemize}
@@ -226,7 +226,7 @@
 \end{tabular}\end{center}
 \caption{Example of a possible rule set for the electric potential problem of section~\ref{potproblem}. The variables \$pos1 and \$pos2 denote the positions of the charges and are determined by the randomization of the problem. The variable \$zerofield denotes the axis intercept and is calculated by the problem.\label{potrule}}
 \end{figure}
-Instead of applying tolerances to parameters, the system now needs to allow for degrees of ``fuzziness'' in the application of the rules: sketches are not plots, and students who correctly sketch the significant features of the graph need to receive credit. One of the values of the tool is that it starts from the students' thinking and not from the instructors'.  The students draw what they think; they don't choose from options the instructors selected.  It will be very important to have a large enough fuzziness so that the students are not  too restricted by the instructors' categories. To ensure this, student input from the sketching client needs to be processed server-side and appropriate fuzzy algorithms need to be developed to apply the rules. Figure~\ref{processing} shows a possible sequence of processing steps. The server receives raw data of the student sketch, in this example, the current in an RLC-circuit (blue) and the enveloping exponential decay functions (red and green). In the next step, several of these artifacts are removed by applying a smoothing algorithm to the data. In a subsequent step, the data is fit by a function. As it turns out, in this freehand drawing, while being a correct sketch, the frequency increases slightly with time, so if in the last step, the differential equation itself is used to verify the function, sufficient fuzziness needs to be applied to accept the sketch.
+Instead of applying tolerances to parameters, the system now needs to allow for degrees of ``fuzziness'' in the application of the rules: sketches are not plots, and students who correctly sketch the significant features of the graph need to receive credit. One of the values of the tool is that it starts from the students' thinking and not from the instructors'.  The students draw what they think; they don't choose from options the instructors selected.  It will be very important to have a large enough fuzziness so that the students are not  too restricted by the instructors' categories. To ensure this, student input from the sketching client needs to be processed server-side and appropriate fuzzy algorithms need to be developed to apply the rules. Figure~\ref{processing} shows a possible sequence of processing steps. The server receives raw data of the student sketch, in this example, the current in an RLC-circuit (blue) and the enveloping exponential decay functions (red and green). In the next step, several of these artifacts are removed by applying a smoothing algorithm to the data. In a subsequent step, the data are fit by a function. As it turns out, in this freehand drawing, while being a correct sketch, the frequency increases slightly with time, so if in the last step, the differential equation itself is used to verify the function, sufficient fuzziness needs to be applied to accept the sketch.
 \begin{figure}
 \begin{tabular}{p{1.9in}l}
 \vspace*{-1.8in}
@@ -246,8 +246,8 @@
 \end{tabular}
 \caption{Server-side processing of sketches\label{processing}}
 \end{figure}
-\subsection{Rules for Conditional Feedback to the Learner}\label{adaptive}
-The LON-CAPA problem engine allows for conditional feedback to the learner, based on the learner's input. Anywhere in a problem, the author cannot only specify the expected correct answer, but also expected incorrect answers, and display adaptive feedback or follow-up questions. In the graphing tool, the author will thus be able to also specify rules that correspond to anticipated or observed misconceptions by the learners.
+\subsection{Feedback to the Learner}\label{adaptive}
+The LON-CAPA problem engine allows for conditional feedback to the learner, based on the learner's input. Anywhere in a problem, the author cannot only specify the expected correct answer, but also expected incorrect answers, and display adaptive feedback or follow-up questions. In the graphing tool, the author will thus be able to also specify rules that correspond to anticipated or observed misconceptions by the learners. In cases where an instructor permits multiple attempts at sketching a particular phenomenon correctly, the capability of LON-CAPA to display submission history (to both the student and instructor) will permit the student to critically evaluate previously submitted (incorrect) sketches and the rules-based feedback given to each attempt, before sketching a new solution.  In addition, once submissions are closed, LON-CAPA's embedded GNUplot functionality allows for dynamic generation of an annotated graph of the ``correct" answer, as defined by the author, which can be displayed to the student for the specific randomized version of a problem the student received. 
 \subsection{Authoring}
 Authoring an appropriate rule set is likely a task that would be perceived by the average instructor as too complex. We will thus implement two sets of tools to facilitate authoring:
 \begin{itemize}
@@ -274,13 +274,7 @@
 Usability specialists will conduct two usability evaluations: Faculty user group, consisting of 10 representative faculty members, and a Student user group comprised of 10 representative college students. The goal of the user experience testing is to assess the degree to which the product matches the way that they expect to interact with the graphing tool based on their background and experience. This study would involve conducting one-on-one user experience sessions lasting 1-1/2 hours each. Additionally, the session will consist of users performing 5-6 task scenarios that concentrate on the core functionality of the product. For the Faculty group, the tasks will include general problem editing, specifying which characteristics of the graphs are important, using the tool to test problems, and working with student results. The tasks for the Student group will concentrate on inputting their graphs, making corrections to graphs, and the quality of the feedback by the system. Key usability goals would include effectiveness, which refers to how well a system does what it is supposed to do (measures: percentage of tasks completed successfully; number and types of errors); efficiency, or the way a system supports users in carrying out their tasks (measure: time to perform a particular task successfully); and satisfaction which relates to the subjective responses users have to the system (measures: user satisfaction ratings; verbal and written feedback). This usability evaluation will save time and reduce development costs by anticipating user expectations and reactions before the product design or redesign is finalized. \subsection{Web Accessibility Compliance Inspection}\label{accessibility}
 Accessibility experts will evaluate the graphing tool and identify the improvements needed to ensure legal compliance with Section 508 standards~\cite{section508}. 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 low-bandwidth connections. 
 \section{Initial Content Development}\label{content}
-Content will initially be developed in areas where there is already existing LON-CAPA content that uses representation translation, e.g.,
-\begin{itemize}
-\item Motion in one dimension\vspace*{-2mm}
-\item Simple harmonic motion\vspace*{-2mm}
-\item Induction\vspace*{-2mm}
-\item Time-Varying Currents
-\end{itemize}
+Content will initially be developed in areas where there is already existing LON-CAPA content that uses representation translation, e.g., Motion in one dimension, Trajectory Motion, Simple harmonic motion, Induction, and Time-Varying Currents.
 Content will be specifically designed to address the difficulties identified in~\cite{mcdermott,beichner}, and made available network-wide to all participating institutions.
 
 In addition, a small number of training problems will be authored to familiarize the students with the tool. In these problems, the solution will be given, for example, students will be asked to sketch a parabola or copy a given sketch. This practice has been successful with other problem types, e.g., symbolic formula input, scientific notation, and the input of physical units, since it allows students to practice mastery of the tool before embarking into more complex tasks, where they may not be able to distinguish between mastery of the tool and mastery of the physics.
@@ -309,7 +303,7 @@
 
 Any content material developed will be made available network-wide 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 ST-PER cognitive studies. Presentations will be given at the American Association of Physics Teachers conferences and associated PER conferences.
+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 ST-PER for 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. Dr.~Fortus will coordinate the educational research component, and together with Dr.~Kortemeyer  supervise the postdoctoral associate in physics education research, who will assist in both the content development and the study of the educational effectiveness. Dr.~Kortemeyer and the postdoctoral associate will develop the problems in consultation with Dr.~Denton. Drs.~Kortemeyer and Denton will use the problems in their courses at MSU and NDSU, which will be the venues for the evaluation of the tool. Stuart Raeburn will be the lead programmer for the tool development. All coding efforts will be coordinated with the LON-CAPA 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}

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