This article presents a case study of a seven-year-old girl named Amanda who participated in an eighteen-week teaching experiment I conducted in order to model the development of her intuitive and informal topological ideas. I designed a new dynamic geometry environment that I used in each of the episodes of the teaching experiment to elicit these conceptions and further support their development. As the study progressed, I found that Amanda developed significant and authentic forms of geometric reasoning. It is these newly identified forms of reasoning, which I refer to as "qualitative geometry," that have implications for the teaching and learning of geometry and for research into students' mathematical reasoning.
|Number of pages||22|
|Journal||Journal of Mathematical Behavior|
|State||Published - 1 Dec 2014|
- Geometric reasoning
- Student thinking
- Teaching experiment
- Topological reasoning