A dialogue between two theoretical perspectives on languages and resource use in mathematics teaching and learning

In this paper, we turn to the notion of networking theories with the aim of contrasting two theoretical mathematics education perspectives inspired by Vygotsky’s work, namely, the Theory of Objectification and the Documentational Approach to Didactics. We are interested in comparing/contrasting these theories in accordance with the following three main questions: (a) the role that the theories ascribe to language and resources; (b) the conceptions that the theories bring forward concerning the teacher, and (c) the understandings they offer of the mathematics classroom. In the first part of the paper, some basic concepts of each perspective are presented. The second part includes some episodes from a lesson on the teaching and learning of algebra in a Grade 1 class (6–7-year-old students). The episodes serve as background to carry out, in the third part of the paper, a dialogue between proponents of the theoretical perspectives around the identified main questions. The dialogue shows some theoretical complementarities and differences and reveals, in particular, different conceptions of the teacher and the limits and possibilities that language affords in teaching–learning mathematics.