The possibility of the constitution of the mathematical being in communicative acting

Abstract

In the form of a philosophical reflection, our goal in this article is to make a comparison between two hypothetical situations in a math class, in the face of a supposed math problem proposed to students. The first hypothetical situation is the most common and widespread among us; it presents traces of a traditional class, in which solutions are given predominantly by the teacher, who perhaps disregards the mathematical work of most students. It is a legacy of a pedagogical model that has predominated in the teaching of mathematics for a long time and that still presents some of its traits. The second hypothetical situation represents another possibility, a class centered on communicative action where students interact with each other and, cooperatively, seek a solution to a problem; a situation opposed to the first, where the acts of speech are no longer predominantly those of the teacher, but all the actors in the surroundings of communication are considered; therefore, a meeting distinct from the traditional one where students acquire the possibility of constituting themselves into a mathematical being, for each other, students for other students, students for their teacher. The two situations compared in this text, although in a hypothetical, idealized and exemplary way, reflect different representations of our pedagogical doing and allow a reflection on our established interpersonal relationships. We are in agreement with the second situation, because we understand that the constitution of the mathematical being acquires great possibility if approached to the communicative action