Challenges and Opportunities for Mathematics Software in Expert Problem Solving

Abstract

Computer Algebra Systems and matrix-based mathematics packages provide sophisticated functionality to assist with mathematical problem solving. However, despite their widespread adoption, little work in the human-computer interaction community has examined the extent to which these computational tools support expert problem solving. In this article, we report findings from a qualitative study comparing and contrasting the work practices and software use of practicing researchers in mathematics and engineering who share the goal of developing and defending new mathematical formulations. Our findings indicate that although computational tools are used by both groups to support their work, current mathematics software plays a relatively minor, somewhat untrusted role in the process. Our data suggest that five primary factors limit the applicability of current mathematics software to expert work practices: (a) a lack of transparency in how current software derives its computed results; (b) the lack of clearly defined operational boundaries indicating whether the system can meaningfully operate on the user's input (whether expressions or data); (c) the need for free-form two-dimensional input to support annotations, diagrams, and in-place manipulation of objects of interest; (d) the potential for transcription problems when switching between physical and computational Andrea Bunt is a computer scientist with an interest in cognitive tools, software complexity, and intelligent interactive systems; she is an Assistant Professor in the Department of Computer Science at the University of Manitoba. Michael Terry is a computer scientist who uses webcentric data sets to model how people think about and use publicly available interactive systems; he is an Associate Professor in the David R. Cheriton School of Computer Science at the University of Waterloo. Edward Lank is a computer scientist with an interest in models of low-level movement in interfaces, pen-based interfaces, and sketch recognition; he is an Associate Professor in the David R. Cheriton School of Computer Science at the University of Waterloo. 222

Students’ Comparison of Their Trigonometric Answers with the Answers of a Computer Algebra System

“…CAS users could compare their (or others') answers with the answers of a CAS for various reasons. For example, a mathematical researcher could use a CAS to confirm hand-derived solutions (see [1]). Some mathematicians use a CAS in order to check the solutions of students (see [2]).…”