Problem Solving as a Path to Comprehension Mathematical Software and Structured Symbolism

• Published in: Mathematics in computer science Vol. 14; no. 3; pp. 607 - 621
• Main Authors: Kim, Seyeon, Pollanen, Marco, Reynolds, Michael G., Burr, Wesley S.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.09.2020
• Subjects: Computer Science; Mathematics; Mathematics and Statistics; Mathematical software interfaces; 97C70; Symbolism; Eye-tracking; Problem identification; Mathematical notation; 97A10; 97C30
• ISSN: 1661-8270; 1661-8289
• DOI: 10.1007/s11786-020-00457-1

The ability to read, write and manipulate complex mathematical expressions is assumed in most user interfaces for programs designed for authoring, collaboration and reasoning in mathematics. However, little is actually known about how people cognitively process and integrate information when solving complex mathematical problems. In this paper eye-tracking was used to examine how people read and integrate information from mathematical symbols and complex formula, with eye fixations being used as a measure of their current focus of attention. We studied two groups of subjects: mathematically “Expert” and “Non-Expert”. Each participant in the study was presented with a series of stimuli in the form of mathematical problems and their eyes were tracked as they worked through the problems mentally. We discuss the performance differences between Experts and Non-Experts, and between subjects who completed problems Correctly and Incorrectly. From these examinations, we were able to demonstrate differences in both the comprehension and problem-solving approach of the two groups, with the results suggesting that what information is selected, and how, is responsible for a particularly large portion of success in solving such problems. This study has implications in mathematical software usability and accessibility, in particular for educational software, as comprehension of mathematical notation and formalism is often inherent in the implementation of structured mathematical software interfaces.