Students’ understanding of mathematical objects in the context of transformational geometry: Implications for constructing and understanding proofs

This research explored students’ views of geometric objects through the implementation of a curriculum module that allowed them to explore the relationships between transformational geometry and linear algebra. The majority of the students were middle and secondary mathematics education majors enrolled in a one-semester geometry course that is aimed at prospective teachers. A preponderance of the evidence suggests that the participating students, for the most part, viewed isometries operationally and viewed geometric objects (triangle, etc.) as “perceived.” Results also suggest that these two views influenced the students’ abilities to understand and to construct geometric proofs in transformational geometry.