Teachers’ Geometric Reasoning with Invariant Features of Change in a Dynamic Environment

• In Event: Exploring Various Teaching and Learning Methods of Mathematics Topics

Abstract

In this study, I investigated how teachers used invariant features of change as part of their reasoning in a dynamic geometry environment. Drawing on the Discernment of Invariance Theory, I analyzed the connections that teachers made between invariant features of change, the ways these invariants informed their reasoning, and the key elements in how they used these invariants. The findings show that invariant features of change can facilitate pattern recognition, support the unpacking and generalization of mathematical theorems, and provide basis for their justification and explanation. A central finding highlights a transitional phase that appears to be a pivotal cognitive progression in shifting from concrete observation to abstract generalization. Implications for future research, professional development, and teacher education are discussed.

Author

• Gal Gili Nagar, University of Massachusetts - Dartmouth