# Running circles around symbol manipulation in trigonometry

- Kevin W. Mickey,
*Stanford University, Stanford, CA, USA*
- James L. McClelland,
*Stanford University, Stanford, CA, USA*

## Abstract

Recent evidence suggests that we have an intuitive number sense
and that visuospatial processes may ground simple mathematical reasoning, but
higher level mathematical cognition is often assumed to depend only on the
manipulation of symbolic expressions, governed by a set of rules and logical
axioms. To assess rule vs. visuospatial thinking in a higher level mathematical
domain, we asked undergraduates to solve trigonometry problems and to report
their use of rules, mnemonics, and visuospatial representations including the
unit circle, right triangle, and sine and cosine waves. Use of the unit circle
was reported most commonly, and was associated with better performance, even
after controlling for the extent and recency of trigonometry experience. While
unit circle users took more time, their performance was robust to problems that
rule users tended to fail. Our findings suggest that even higher level
mathematical cognition is more than just the manipulation of symbolic
expressions.

Back to Table of Contents