Promoting Understanding of the Role of Assumptions in Mathematics

Abstract

‘Assumptions’ play a crucial role in mathematical activity, yet there is limited research on how to help students and prospective teachers understand this concept. In this talk, I will discuss two interventions, developed in multi-year design experiments, to address this gap: one for secondary students and another for prospective elementary teachers. Both interventions used the notion of ‘productive ambiguity’ in the context of deliberately ambiguous tasks where the role of assumptions surfaced naturally and was utilized purposefully. The intervention with prospective teachers also created opportunities for them to enhance their mathematical knowledge for teaching about assumptions.