THE TEACHING AND LEARNING OF MATHEMATICS: BETWEEN THE GRAMMATICAL AND THE EMPIRICAL

We analyze some possibilities inherent to mathematics teaching and learning when considering two characteristics of the mathematical propositions: we seek to reflect from Wittgenstein's philosophy of language about how we could think the teach: grammatical and empirical. Based on rules or experience? We carried out a theoretical reflection essay in which there are discussions about the grammatical role of language and mathematics. We consider the mathematical propositions as grammatical propositions, and with empirical uses from the view of the philosopher Wittgenstein. In this sense, we reflect on pedagogical possibilities by looking at the grammatical and empirical contexts. We conclude, based on the analysis performed, that student needs to understand rules of mathematics (grammatical), but also can develop application activities in reality (empirical), which must be seen from the notion of language games.