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The Unit Circle and Unit Conversions

Abstract

"While the unit circle is a central concept of trigonometry, students' and teachers' understandings of trigonometric functions typically lack connections to the unit circle. In the present work, we discuss a teaching experiment involving two pre-service secondary teachers that sought to characterize and produce shifts in their unit circle notions. Initially, both students experienced difficulty when given a circle that did not have a stated radius of one. The students relied on memorized procedures, including "unit-cancellation," to relate the unit circle to given circles. In an attempt to foster more robust connections between novel circle contexts and the unit circle, we implemented tasks designed to foster thinking about a circle's radius as a unit of measure. We report on the students' progress during these tasks."