Date of Award

Spring 2017

Project Type


Program or Major

Mathematics Education

Degree Name

Doctor of Philosophy

First Advisor

Sharon McCrone

Second Advisor

Karen Graham

Third Advisor

Orly Buchbinder


Trigonometry is an essential part of mathematics education (NCTM, 2000; NGA, 2010). Trigonometry is prevalent in studies of pure mathematics as well as physical applications. Trigonometric identities and transformations are particularly important. However, students and even teachers have struggled to articulate and justify trigonometric concepts (Moore, 2013; Tuna, 2013). Students have also struggled with identities and transformations in non-trigonometric contexts (Borba & Confrey, 1996; Tsai & Chang, 2009). This paper will describe a research project which articulates the critical stages through which students must pass to understand trigonometric identities and transformations. These critical stages were first hypothesized based on a review of the literature. Then undergraduate precalculus students were recruited to participate in a series of task-based interviews in order to examine the process by which students come to understand and justify trigonometric identities and transformations. The critical stages were revised based on the results of these interviews. Following the interviews, hypothesized lesson plans for the subjects were revised and implemented. The implementation of the lesson plans did not collect enough information to draw any conclusions, but the critical stages underscore the importance of students being able to move fluidly among representations.