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.