Assumption Digging in Euclidean Geometry

Abstract

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.