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

•A local instructional theory for the reinvention of isomorphism is presented.•A local instructional theory for the reinvention of the group concept is presented.•The emergent models heuristic is explored in the context of abstract algebra.

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