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Index: modules/gerd/alt2007/graphing.tex
diff -u modules/gerd/alt2007/graphing.tex:1.7 modules/gerd/alt2007/graphing.tex:1.8
--- modules/gerd/alt2007/graphing.tex:1.7 Thu Mar 29 15:38:50 2007
+++ modules/gerd/alt2007/graphing.tex Sat Mar 31 09:54:54 2007
@@ -51,25 +51,22 @@
{\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 curve. But how often do we intentionally teach our students about this important representation format?
+The ability to work with graphs is a basic skill of any scientist. Sketching is a skill that allows one to express general relationships with just a few strokes. 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 curve. 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 origins 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}.
-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 representation-translation 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 multiple-choice problems.
+Students need practice in both generating and interpreting graphs, but appropriate formative assessment frequently is lacking 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. Too often, instead the problems given in physics courses focus on numerical calculations, e.g., ``A car accelerates from rest at $2 m/s^2$ 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, problems may 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 has been found, however, that such traditional representation-translation 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 multiple-choice problems.
-The sketching of graphs is an example of a more constructivist approach to teaching physics concepts, as well as representation-translation and visualization skills. The students need to make a number of decisions:
+The sketching of graphs is an example of a more constructivist approach to teaching conceptual and visualization skills, requiring students 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 Where does the graph start and finish (are the start and end points 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, not reproduce it or select it from a set of prefabricated solutions.
+ (list expanded from \cite{kennedy04}). In short, students need to {\it construct} the curve, not reproduce it or select it from a set of prefabricated solutions.
-Sketching is a skill that allows one to express general relationships with just a few strokes. In this project we will develop an online assessment tool for graph sketching, which will provide randomized scenarios and 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.
+The main objective of this project is to develop an online assessment tool for graph sketching, which will provide randomized scenarios and 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. To minimize overhead, the tool will be developed on top of an existing course and learning content management system. However, both the algorithms and the code will be made freely available, so they can be incorporated into other systems.
\subsection{Learning Goals}
A sketched graph can be thought of as a pictorial description of a phenomenon. It emphasizes the major features of the phenomenon while ignoring details that may be distracting or better represented in other ways. Sketched graphs are regularly used by scientists and engineers in informal discourse, as means for describing and supporting claims. In the Benchmarks for Science Literacy~\cite{aaas93}, Project 2061 makes an explicit recommendation regarding the importance of using graphs in making arguments (12D/H7). Graphs are best used to present data, describe ideas, and support claims that involve trends, comparisons, and general behavior. The ability to sketch a graph and use it in an argument involves not only an understanding of the holistic characteristics of graphs, such as general shape, number and general location of intersections with axes, and asymptotes, but also the general behavior of the phenomenon being graphed. As such, opportunities to sketch graphs and receive formative feedback on them should foster students' conceptual understanding of the phenomena being graphed.
@@ -101,7 +98,7 @@
\item make algorithms and tools available open-source and freely\vspace*{-2mm}
\item disseminate results\vspace*{-2mm}
\end{itemize}
-Several of these steps will be carried out iteratively over the duration of the project while refining both tool and content
+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 Related Projects}
\subsection{Relevant Results from Prior NSF Support to the PIs}
\subsubsection{LON-CAPA}\label{loncapa}
@@ -118,11 +115,11 @@
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'' meaning 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).
-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.
-
-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
+Over the years, LON-CAPA has been 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,
@@ -133,21 +130,19 @@
\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.
+LON-CAPA has 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}, and serves approximately 35,000 students every semester.
+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.
+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.
-\section{Relevant Results from Other Related Projects}
+\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}.
The IGO is more constrained than the proposed tool, in that it models all graphs through B\'ezier curves, and allows the users to then tweak the location and angles of the starting and end points, as well as a number of midpoints. These additional controls have been introduced into the learner interface over the initial freehand graphing as a result of usability concerns~\cite{kennedy04}. The display to the learners includes these coordinates and angles, and the evaluation of the graph is based on agreement of these values and those provided by the educator through the authoring interface.
\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 algorithms than are needed for problems like in Fig.~\ref{induction}.
+The LON-CAPA system currently allows dynamically generated 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 problem that can evaluate student input of graphs requires far more sophisticated algorithms than does a problem such as that in Fig.~\ref{induction}.
\subsection{Example Problems}
\subsubsection{Open-Ended Problems}
@@ -156,7 +151,7 @@
\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.
+Fig.~\ref{acccorrect} shows possible 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}
\includegraphics[width=3in]{figures/acccorrect2}
@@ -164,7 +159,7 @@
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.
+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 specifying the criteria for these anticipated wrong solutions.
\begin{figure}
\includegraphics[width=3in]{figures/accincorrect1}
\includegraphics[width=3in]{figures/accincorrect2}
@@ -177,7 +172,7 @@
\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.
+Fig.~\ref{potentialcorrect} shows possible acceptable solutions. Note that the scale is irrelevant in this case, but the electric field must diverge at the positions of the charges, go to zero at infinite distances, and tend to zero where the potential plateaus.
\begin{figure}
\includegraphics[width=3in]{figures/correct1}
@@ -336,7 +331,8 @@
\item[David Fortus] is a senior scientist at the Weizmann Institute of Science in Israel and an assistant professor of science education at Michigan State University. He is a co-PI on the IQWST project
(section~\ref{iqwst}), has won research awards from the National Association for Research on Science Teaching (NARST) and from the American Psychological Association (APA), and has worked as a project manager in the hi-tech industry.
\item[Stuart Raeburn] is currently a postdoctoral staff member in the Division of Science and Mathematics Education (DSME) at Michigan State University, where he is a member of the LON-CAPA development team. In the past decade at Michigan State University (prior to joining DSME) he was a visiting faculty in the Department of Geological Sciences, where he taught a variety of geology courses, from introductory to graduate level, and he was also a developer and administrator for a number of course management systems in the centrally-supported Faculty Facility for Creative Computing.
-\item[Sarah J. Swierenga] is the director of the MSU Usability \& Accessibility Center (UAC, section~\ref{uac}) and Professor by Courtesy in the Department of Telecommunication, Information Studies, and Media. She is responsible for developing and disseminating innovations in theory building, research methodologies, and technologies to enhance usability and accessibility in Web and information technology contexts. She has worked with users in commercial, military, and academic environments. Swierenga received a Ph.D. in human factors psychology with a concentration in human-computer interaction from the University of South Dakota, and a B.A. in psychology from Calvin College. She is also a Certified Professional Ergonomist (C.P.E.).
+\item[Sarah Swierenga] is the director of the MSU Usability \& Accessibility Center (UAC, section~\ref{uac}) and Professor by Courtesy in the Department of Telecommunication, Information Studies, and Media. She is responsible for developing and disseminating innovations in theory building, research methodologies, and technologies to enhance usability and accessibility in Web and information technology contexts. She has worked with users in commercial, military, and academic environments. Swierenga received a Ph.D. in human factors psychology with a concentration in human-computer interaction from the University of South Dakota, and a B.A. in psychology from Calvin College. She is also a Certified Professional Ergonomist (C.P.E.).
+\item[Alan Denton] is an associate professor of Physics at North Dakota State University. He facilitated NDSU's implementation of LON-CAPA, which now is the local course-management, homework-assignment, and testing system for all introductory Physics courses (serving 600 students per semester). Over the past 10 years, he has taught a spectrum of physics courses from undergraduate to advanced graduate, using LON-CAPA from introductory mechanics to senior-level quantum mechanics. His keen interest in physics pedagogy was sparked by attending an APS/AAPT-sponsored Physics and Astronomy New Faculty workshop. His research interests are in theoretical and computational condensed matter physics, with emphasis on modeling of colloids, polymers, and other soft materials.
\end{description}
\pagebreak
\bibliography{graphing}
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