PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
The Unit Circle and Unit Conversions
Page: 2-121
The unit circle is a central concept of trigonometry. Yet, students and teachers are often tied to using right triangles to reason about trigonometric functions with only superficial connections to the unit circle. In an attempt to identify ways to better support student learning in trigonometry, we conducted a teaching experiment investigating two pre-service secondary teachers’ notions of the unit circle. Initially, both students had difficulty relating circle contexts to the unit circle. The students’ actions suggested that their calculations stemmed from memorized procedures, as opposed to reasoning about quantitative relationships. In an attempt to foster connections between novel circle contexts and the unit circle, we implemented tasks that developed the unit circle as the result of conceptualizing a circle’s radius as a unit of measure. We report on the students’ progress during these tasks and the subsequent improvements in their ability to apply trigonometric functions to circle contexts.