(Re)significar a demonstracao nos curriculos da educacao basica e da formacao de professores de matematica

Abstract

The present study aims to search for an understanding about the need and accessibility of implementing proofs and demonstrations in school mathematics curricula (from elementary through secondary education grades), and to investigate the implications of such an innovation for initial teacher education curricula. In terms of Methodology, the study adopts a qualitativa approach. Since the purpose was to obtain results based upon a synthesis of several sources, documentary and bibliographic research was carried out and interviews were conducted with Mathematics Education researchers and with school teachers, whose teaching practice included some sort of work involving proofs. For its theoretical underpinning, the study drew from research conducted on this subject along with studies concerning curricula and teacher education development. Among the body of research into proof in mathematics, varies studies were identified, although not within the Brazilian contextoIn general, these studies were not based on a consistent theory, tended not to be articulated with each other and neither did they seek to articulate different teaching levels. In the analysis of the empirical data, a consensus was noticed among the interviewed group: "proof' is perceived as content and a quite rich pedagogical resource to Mathematics classes for elementary and secondary school mathematics, since a broad sense of the word is admitted. It was not deemed appropriate to approach its teaching through simple reproduction, by the teacher ar by the student, of the proofs presented in the books but, instead, by "doing Mathematics" in the classroom, thus involving experimentations, conjectures, arguments. However, for to happen, this principie needs to be enshrined in teacher education courses. Among the school teachers, some tension was observed in relation to the analysis af proofs produced by the students: on the one hand, there was praise for initiative and creativity and, on the other, concerns that the resulting productions could not be assessed positively as they could not be considered proofs, from the mathematical point of view. The interleaving of the analyses from the different data sources enabled the canstruction of a set of proposals for the (re)consideration of proof in school mathematicsand in teacher development programmes.