Theory Building in Geometry Education: Designing and implementing a course for 12-15 year old students

Abstract: If we want mathematics education to be valuable to everybody, including those who do not pursue mathematics-related careers, we need to use mathematics as a training ground for certain ways of thinking. This dissertation focuses on one aspect of mathematical thinking, namely theory building. It has three parts - unpacking what constitutes theory building, the development of a course aimed at theory building, and a qualitative description of an implementation of that course with 12 to 15-year-old students in two schools in Pune, India. The description aims to understand some of how students engaged with the course and the role of the instructor in the implementation of the course. The data used in this description includes video recordings of the sessions, teacher reflections at the end of each session, and student reflections and feedback. The ultimate goal of the description is to suggest considerations we should keep in mind when designing and implementing theory-building courses. The focus of the dissertation is within mathematics, and more specifically, within geometry. However, this is hopefully just a first step towards a transdisciplinary framework aimed at developing thinking abilities useful to everybody in their personal, public, and professional lives.