Topology, Technology, and Children's Ideas
Seminar given by Dr. Steven Greenstein, Assistant Professor, Department of Mathematical Sciences, CSAM.
Children’s school experiences in geometry are entirely Euclidean. But they also have topological, or at least non-metric, ideas. In this talk I will describe the forms of mathematical reasoning that I identified in my investigations of children’s intuitive and informal topological ideas. It is these forms of non-metric reasoning that I refer to as "Qualitative Geometry." I will also introduce a new version of the dynamic geometry environment I designed to elicit and further support the development of these ideas and discuss the theoretical and conceptual approach I used to design it.