ABSTRACT
A key aspect of what makes mathematics powerful is the wide applicability of mathematical tools and results across a multitude of seemingly dissimilar examples and situations. In this chapter, we probe what it might mean to teach for generality in the context of “traditional” instruction, where learner working is often framed in terms of imitating taught procedures, and also what staging points towards teaching for generality might consist of in these contexts. To do this, we draw on two frameworks developed in the course of our research and development work across primary and secondary schools in South Africa: the Mediating Primary Mathematics (MPM) framework, and the Mathematical Discourse in Instruction (MDI) framework. We discuss the different ways of analysing how instruction can expand the example spaces that students are provided opportunities to work with across these two frameworks, and the rationales underlying the similarities and differences in the two formulations.
