A conceptual model of mathematical reasoning for school mathematics

The development of students’ mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR, this research project aimed to qualify it from a theoretical perspective, with an elaboration that would not only indicate its ways of being thought about and espoused but also serve as a tool for reflection and thereby contribute to the further evolution of the cultures of the teaching and research communities in mathematics education. To achieve such an elaboration, a literature search based on anasynthesis (Legendre, 2005) was undertaken. From the analysis of the mathematics education research literature on MR and taking a commognitive perspective (Sfard, 2008), the synthesis that was carried out led to conceptualizing a model of mathematical reasoning. This model, which is herein described, is constituted of two main aspects: a structural aspect and a process aspect, both of which are needed to capture the central characteristics of MR.