Running circles around symbol manipulation in trigonometry

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.


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