A continuous training, through didactic engineering, of polyvalent teachers with a focus on knowledge and pedagogical practices related to the concept of natural number

Abstract

This article is a clipping of a doctoral thesis whose objective was to investigate, through a continuous training of multipurpose teachers who teach mathematics, their knowledge about the concept of natural number and their pedagogical practices to teach such content. The theoretical orientation to establish the concept of natural number in this formation was based on the Piagetian theory, focusing on the study of the complementarity of the cardinal and ordinal aspects of the natural number. The methodology was the Didactic Engineering presented by Artigue, in the 2nd generation conception of Perrin-Glorian. The research subjects were 8 teachers from the initial years of elementary school of a public school in Belo Horizonte/MG. The problem situations of the didactic sequence, one of the components of the methodology, were elaborated from the experiences of Piaget and Szeminska and took as reference elements of Brousseau's Didactic Situations Theory. Didactic Engineering developed in phases: the analysis of mathematical knowledge and pedagogical practices of teachers; the delimitation of the variables for the elaboration of the didactic sequence; classroom experimentation of the sequence; the confrontation between a priori and a posteriori analyses. It was evidenced that pedagogical materials elaborated with theoretical support and focusing on the cardinal and ordinal aspects of the natural number, provide better understanding for students and expand the knowledge of teachers for their practice. It is added, as a result, that the didactic engineering methodology favored data analysis and was configured as an appropriate methodology for the continued training of multipurpose teachers.