The Intuitive and the Logical in the Mathematical Knowledge: analysis of a pedagogical proposal from a viewpoint of new philosophical approaches and in the educational context of mathematics

Abstract

In this paper we consider the Meneghetti & Bicudo’s proposal (2003) about the constitution of the mathematical knowledge and analyze it with respect to the following two focuses: under the conceptions of the mathematical knowledge after the mathematical fundamentalist crises and in the educational context of mathematics. The investigation of the first focus is done analyzing news claims to the mathematical philosophy. The investigation of the second focus is done firstly by a theoretical reflection and, soon after that, by focalizing the implementation of the proposal in the process of development of the didactic materials to teaching and learning of Mathematics. Finally, we present the main results of the application of one of those materials. Keywords: Mathematical Knowledge. Intuitive Aspect. Logical Aspect. Philosophy of Mathematics. Mathematics Education. Pedagogical Proposal.