The school mathematical activity as an introduction of paradigms in language

Abstract

From a Wittgensteinian perspective, this article assumes that the use we make of our mathematical statements is of a different nature from the hypotheses of the natural sciences, which have a predominantly referential use. While these have an explanatory and descriptive purpose, the objects of mathematics and their relations expressed through axioms and theorems play a normative role. In contrast to a referential conception of mathematical knowledge, my goal is to show the importance of this distinction for the mathematical activity in the school context, from the most elementary level of introduction of paradigms in preparatory language games, to the most complex level of their demonstrations, which in turn produce new paradigms. I conclude that certain interpretations of mathematical statements coming from a referential conception of mathematical language can lead to dogmatic images, causing several misunderstandings in their pedagogical practices, particularly when they are anchored in mentalist or empiricist theories of meaning.