The Influence of Multiple Representations on Secondary Students\u27 Understanding of Trigonometric Functions

Trigonometry is a critical subject in mathematics that both high school and undergraduate students need to learn in order to be prepared for advanced mathematics. Despite the importance of trigonometry in the mathematics curriculum, little is known about best practices for teaching trigonometric functions and what difficulties students face when learning the topic. Using a Grounded Theory approach, this dissertation presents the results of a design study (or teaching experiment) whose purpose was to examine the process by which students constructed the concept of trigonometric functions through multiple representations and how students developed meta-representational competence. The design study involved two stages. In the first stage, initial conditions and elements of the teaching experiment were constructed. In the second stage, proposed conjectures about teaching and learning trigonometric functions were both redefined and redesigned. Qualitative data, including classroom observations and field notes, video recordings of classroom interactions and debriefing sessions, student work (including notebooks and artifacts), student interviews, surveys, and blogs are the focus of analysis. The dissertation presents and analyzes mathematical themes within a framework supporting critical aspects related to learning trigonometric functions through multiple representations and the development of meta-representational competence, that is, the competence to represent trigonometric functions in multiple ways (e.g. ratios, tables, and graphs). Emergent themes connected to the construction and conception of trigonometric functions included students’ conceptions of ratio and proportion, students’ conception of angle, and students’ sense of Cartesian Connectedness. Implications for research and practice include the need to examine how multiple representations stimulate students’ conceptual construction and development of trigonometric functions within the context of inquiry-based instruction