Identification of Errors in Mathematical Symbolism and Notation: Implications for Software Design

Mathematical user interfaces for authoring, collaboration, problem-solving and reasoning invariably rely on the ability to read, write and manipulate complex mathematical expressions. However, very little research has been done on how people read mathematical expressions, let alone how they are understood by the mind. One technique which researchers use to gain insight into how people read and comprehend symbols and complex phenomena are studies using eye-tracking hardware: focus on, and tracking of, pupils in order to determine the reader’s attention and fixation. In this paper we will explore the results of a study on two classes of students: mathematically “expert” (mathematical sciences students) and non-expert (Faculty of Science majors from outside the mathematical sciences). Each participant was presented with a series of mathematical problems (stimuli) and their eyes and attention/focus tracked as they worked through the problems mentally. We will discuss the differences in the two classes, both with respect to the correctness of responses to the problems and the structure of the scanning and identification of important components within the problem. This study has applications in mathematical software usability, accessibility, and design of interfaces, as comprehension of mathematical notation and formalism is assumed in the implementation of the modified symbolism inherent in structured mathematical software interfaces.