Uma terapia filosófica da Modelagem Matemática na Educação Matemática

Abstract

Based on Ludwig Wittgenstein's therapeutic philosophy, the aim is to clarify conceptual confusions that exist in possible images related to what is described about Mathematical Modelling in Mathematics Education as found in dissertations and theses developed in Brazil. The research approach is qualitative, and it is classified as exploratory and bibliographic, when the uses of the linguistic expressions, mathematical modelling and mathematical model are explored in an empirical material constituted by forty-seven Brazilian dissertations and theses from the period 1976 to 2022. The interpretation of the use of these linguistic expressions occurred in the construction of three images: 1) in Modelling, the student discovers mathematics inserted in some extralinguistic reality; 2) the mathematical model is an underlying representation of empirical reality; 3) in Modelling, mathematical knowledge would originate in mental constructions. Inspired by Wittgenstein's therapy, possible clarifications of the conceptual confusions imbricated in these images were initiated. Concerning the first image, two conceptual confusions were verified, indicating that in Modelling the nature of mathematical statements is taken as equal in nature to the statements of the empirical sciences, and the conclusions of the students (rediscoveries or personal discoveries) in Modelling are of empirical nature. As a possible clarification, it is argued that mathematical statements are of a normative nature that enable the understanding of the empirical world. In this sense, the student will be able to do Modelling from the moment he knows the rules of mathematics and of Modelling itself and is able to act guided by these rules. As for the second image, the confusion is that there would be an isomorphism between the mathematical model and the empirical reality. To clarify, it is argued that, from a Wittgensteinian perspective, the mathematical model can be conceived as representation (Darstellung), such as a paradigm, a linguistic object that organizes and gives meaning to empirical experience. As for the third image, the conceptual confusion is that the mathematical knowledge constructed in the Modelling is mental representations (Vorstellungen) of mathematical concepts. It is made explicit that there can be a kind of construction of mathematical knowledge initiated by the various uses of mathematical rules presented to the student. Paying attention to the use of the linguistic expressions mathematical modelling and mathematical model in the empirical material of this research, it is pointed out that in Modelling there is an exclusive use of the referential conception of language related to the empiricist and intuitionist meanings of Mathematics.