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Coherence, Quantitative Reasoning, and the Trigonometry of Students

Abstract

"Over the past five years I have sought to better understand student thinking and learning in the context of topics central to trigonometry, including angle measure, the unit circle, trigonometric functions, periodicity, and the polar coordinate system. While each study has provided unique insights into students' learning of trigonometry, a common theme connects the studies' findings: quantitative reasoning plays a central role in students' trigonometric understandings. In this chapter, I first describe a coherent system of understandings for trigonometry that is grounded in quantitative reasoning. Against this backdrop, I compare students' quantitative reasoning in the context of trigonometry in order to illustrate the role of quantitative reasoning in the learning of a particular mathematical topic."