Uma análise da abordagem da fórmula poliedral de Euler em livros didáticos de matemática

Abstract

This research has the main objective to analyze the approach of content Formula Polyedral of Euler for Brazilian mathematics textbooks, intended for middle-level education, published in the period before, during and after to the Movement of Modern Mathematics (MMM). For this, we adopted the qualitative research in that we conducted a study historical, bibliographical, documentary and interpretive to understand the didactic transposition of the content Formula Polyhedral of Euler in textbooks published at various times since, over time, this knowledge has acquired different varieties of the "knowing wise" until to be, nowadays, presented simply as a curiosity about the study of polyhedra. By these changes, we adopted as reference analysis theoretical to the textbooks the Theory of Didactic Transposition and the Anthropological Theory of Didactics, from the french mathematician educator Yves Chevallard, by providing elements for the study of mathematics organization and didatic organization the content Formula Polyhedral of Euler in textbooks. From the analysis results, we noted that until the period of the MMM, the Formula Polyhedral of Euler was approached very close to the "knowing wise”. However, the textbooks of the period MMM differ from the textbooks of the period previous, because them adopt the language mathematic championed by this movement. Already textbooks after the MMM do not present the Formula Polyhedral of Euler close to the “knowing wise”, they just seek through figural representations in text and/or exercises that the students themselves identify the formula and/or accept as true after presentation of some figural representations of convex polyhedra in the textbook. We noted that over the period investigated the presentation the content Formula Polyhedral of Euler differ in the books, characterized by the historical moment of each period.