Students' understanding of mathematical objects in the context of transformational geometry: Implications for constructing and understanding proofs [An article from: Journal of Mathematical Behavior]

This digital document is a journal article from Journal of Mathematical Behavior, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
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.