O conceito de ângulo: experiências e reflexões sobre o conhecimento matemático de (futuros) professores do 1º ciclo

Abstract

Mathematical concepts perform a crucial role in the construction of mathematics, being the basis of the mathematical building. Historically, mathematical concepts are not spontaneous and their meaning is altered and refined several times. They aren’t also produced by a single person since the process of creating notations, terms or symbols involves the agreement between the, so called, “users” of such concepts. Nevertheless, once formed, mathematical concepts are acquirable: they are taught and learned.

In this article, we rebuild theories related to mathematical concepts, especially geometrical ones and explore the role performed both by the definitions of the concepts and by their representations. Considering the concept of angle as our object of study, we analyse the answers given by 216 (future) primary school teachers to two questions (part of a larger questionnaire) concerning the mathematical knowledge involved within that concept.

We shall end with some reflections where, based on the results of the study, we question, on the one hand, the meaning that these professionals got from the explanations they were given about “elementary” math concepts during their training and experience and, on the other hand, we question the degree of effective literacy of these (future) teachers, highlighting our concern related to the rigour of their teaching.