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Unformatted text preview: MathPad 2 : A System for the Creation and Exploration of Mathematical Sketches Joseph J. LaViola Jr. Robert C. Zeleznik Brown University * Abstract We present mathematical sketching , a novel, penbased, modeless gestural interaction paradigm for mathematics problem solving. Mathematical sketching derives from the familiar pencilandpaper process of drawing supporting diagrams to facilitate the formula tion of mathematical expressions; however, with a mathematical sketch, users can also leverage their physical intuition by watch ing their handdrawn diagrams animate in response to continuous or discrete parameter changes in their written formulas. Diagram animation is driven by implicit associations that are inferred, either automatically or with gestural guidance, from mathematical expres sions, diagram labels, and drawing elements. The modeless nature of mathematical sketching enables users to switch freely between modifying diagrams or expressions and viewing animations. Math ematical sketching can also support computational tools for graph ing, manipulating and solving equations; initial feedback from a small user group of our mathematical sketching prototype applica tion, MathPad 2 , suggests that it has the potential to be a powerful tool for mathematical problem solving and visualization. CR Categories: H.5.2 [Information Interfaces and Presentation]: User Interfaces—Interaction Styles G.4 [Mathematics of Comput ing]: Mathematical Software—User Interfaces; Keywords: penbased interfaces, mathematical sketching, ges tures 1 Introduction Diagrams and illustrations are often used to help explain math ematical concepts. They are commonplace in math and physics textbooks and provide a form of physical intuition about abstract principles [Hecht 2000; Varberg and Purcell 1992; Young 1992]. Similarly, students often draw pencilandpaper diagrams for math problems to help in visualizing relationships among variables, con stants, and functions. With the drawing as a guide, they can write the appropriate math to solve the problem. However, such static diagrams generally assist only in the initial formulation of mathe matical expressions, not in the “debugging” or analysis of those ex pressions. This can be a severe limitation, even for simple problems with natural mappings to the temporal dimension, or for problems with complex spatial relationships. By animating sketched diagrams from changes in associated math ematical expressions, users can evaluate different formulations with * Email: { jjl,bcz } @cs.brown.edu Figure 1: A mathematical sketch used to explore damped harmonic oscillation. It shows a spring and mass drawing and the necessary equations for animating the sketch. The label inside the mass asso ciates the mathematics with the drawing....
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This note was uploaded on 06/12/2011 for the course CAP 6105 taught by Professor Lavoila during the Spring '09 term at University of Central Florida.
 Spring '09
 LaVoila

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