A local instructional theory for the guided reinvention of the group and isomorphism concepts

摘要

In this paper I describe a local instructional theory for supporting the guided reinvention ofthe group and isomorphism concepts. This instructional theory takes the form of a sequenceof key steps as students reinvent these fundamental group theoretic concepts beginningwith an investigation of geometric symmetry. I describe these steps and frame them interms of the theory of Realistic Mathematics Education. Each step of the local instructionaltheory is illustrated using samples of students' written work or discussion excerpts.