laviola_SBIM06 - EUROGRAPHICS Workshop on Sketch-Based...

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EUROGRAPHICS Workshop on Sketch-Based Interfaces and Modeling (2006) Thomas Stahovich and Mario Costa Sousa (Editors) An Initial Evaluation of a Pen-Based Tool for Creating Dynamic Mathematical Illustrations Joseph J. LaViola Jr. Brown University, Department of Computer Science, USA Email: [email protected] Abstract MathPad 2 is a pen-based application prototype for creating mathematical sketches. Using a modeless gestural in- terface, it lets users make dynamic illustrations by associating handwritten mathematics with free-form drawings and provides a set of tools for graphing and evaluating mathematical expressions and solving equations. In this paper, we present the results of an initial evaluation of the MathPad 2 prototype, examining the user interface’s intuitiveness and the application’s perceived usefulness. Our evaluations are based on both performance and questionnaire results including first attempt gesture performance, interface recall tests, and surveys of user inter- face satisfaction and perceived usefulness. The results of our evaluation suggest that, although some test subjects had difficulty with our mathematical expression recognizer, they found the interface, in general, intuitive and easy to remember. More importantly, these results suggest the prototype has the potential to assist beginning physics and mathematics students in problem solving and understanding scientific concepts. Categories and Subject Descriptors (according to ACM CCS) : H.5.2 [Information Interfaces and Presentation]: User Interfaces — Interaction Styles, Evaluation/Methodology 1. Introduction MathPad 2 (see Figure 1) is a pen-based, Tablet PC applica- tion prototype for creating dynamic illustrations used for exploring mathematics and physics concepts [LZ04]. The fundamental technology behind MathPad 2 is mathematical sketching, a pen-based gestural interaction paradigm for mathematics problem solving that derives from the familiar pencil-and-paper process of drawing supporting diagrams to facilitate the formulation of mathematical expressions; how- ever, with mathematical sketching, users can also leverage their physical intuition by watching their hand-drawn dia- grams animate in response to continuous or discrete param- eter changes in their written formulas [LaV05]. Diagram ani- mation is driven by associations that are inferred, either auto- matically or with gestural guidance, from handwritten math- ematical expressions, diagram labels, and drawing elements. The essential goal in developing the MathPad 2 user inter- face was that it be as similar and fluid as pencil and paper, since mathematics and physics problems are often solved using this medium. Thus, we did not want to use any ad- ditional hardware (e.g., a modifier key or stylus button) or software (e.g., buttons) modes. Instead, we wanted all inter- action to be derived from using digital ink. We developed a gestural user interface for invoking different operations in MathPad 2 because we wanted users able to work as fluidly as possible with the mathematics and drawings they create. We
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