The Unit Circle as a Grounded Conceptual Structure in Precalculus Trigonometry

Learning trigonometry poses a challenge to many high school students, impeding their access to careers in science, technology, engineering, and mathematics. We argue that a particular visuospatial model called the unit circle acts as an integrated conceptual structure that supports solving problems encountered during learning and transfers to a broader range of problems in the same domain. We have found that individuals who reported visualizing trigonometric expressions on the unit circle framework performed better than those who did not report using this visualization. Further, a brief lesson in use of the unit circle produced postlesson benefits relative to no lesson or a rule-based lesson, but only for participants who exhibited some partial understanding of the relevant concepts in a pretest. The difficulties encountered by students without sufficient prior knowledge of the unit circle underscores the challenge we face in helping them build grounded conceptual structures that support acquiring mathematical abilities.

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