A local instructional theory for the guided reinvention of the quotient group concept

• A local instructional theory for the reinvention of quotient groups is presented.
• The emergent models heuristic is explored in the context of group theory.
• The proofs and refutations heuristic is explored in the context of group theory.

In this paper we describe a local instructional theory for supporting the guided reinvention of the quotient group concept. This local instructional theory takes the form of a sequence of key steps in the process of reinventing the quotient group concept. We 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 example instructional tasks and either samples of students’ written work or excerpts of discussions.