Madhav Kaushish | Searcharxiv

arXiv2021

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

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.

math.HO↗

arXiv2021

Assumption Digging in Euclidean Geometry

Theory Building has been largely ignored in Mathematics Education, especially at the Middle and High School Levels. This thesis focuses on Assumption Digging, a type of Theory Building similar to what Hilbert undertook in his Grundlagen with Euclidean Geometry. The Euclidean Geometry course in schools is a potentially productive for Assumption Digging since, as has been noted, many courses in Euclidean Geometry contain extraneous postulates and unclear definitions. This focus of this thesis is a teaching experiment with 7th-10th grade students in two schools in Western India, which is an Assumption Digging exercise in Euclidean Geometry. The goal of this thesis is to ascertain the various ways students engage in Assumption Digging, and the role played by the instructor in the Assumption Digging sessions. While most of the student engagement with Assumption Digging was at the level of justifying claims which the instructors questioned, there were a few instances of students questioning arguments and claims made by the instructors. The role the instructors played was crucial in two ways. Firstly, deciding what path the session took and, secondly, engaging with student arguments and skepticism.

math.HO↗