LaViola-Jr-2004 - MathPad2 A System for the Creation and...

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Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 1515 Broadway, New York, NY 10036 USA, fax +1 (212) 869-0481, or [email protected] 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, pen-based, modeless gestural interaction paradigm for mathematics problem solving. Mathematical sketching derives from the familiar pencil-and-paper 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 hand-drawn 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: pen-based 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 pencil-and-paper 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
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