Some implications of Wittgenstein’s idea of use for learning mathematics through mathematical modelling

This article reports a study which aim was to identify and characterise ways of understanding mathematics learning through mathematical modelling in a school environment from a Wittgensteinian perspective. Mathematical modelling in a school context can be understood as an approach involving real problem situations in school mathematical content. The subject to be discussed is based philosophically on the idea of meaning as the use we attribute to words, a concept developed by the philosopher Ludwig Wittgenstein. Based on this understanding, we analyse the theoretical definitions that Anna Sfard, following Wittgenstein, posits regarding mathematics learning in schools. We conducted a qualitative study in which we analysed the discourse of a group of students and a teacher produced during the implementation of mathematical modelling. The analysis of this discourse, based on the ideas of both Ludwing Wittgenstein and Anna Sfard, allowed us to point out that mathematics learning through mathematical modelling is characterised by the identification of similarities between the uses for which words are mobilised in the school environment and the uses of words suggested by problem situations addressed in mathematics modelling. We have also identified how the teacher guides students regarding the legitimate uses of words in mathematics classes