  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.
