  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.
