Um exemplo de transposição didática : o caso das matrizes

Abstract

Long of the history, the Matrices, the Determinant and Systems of Linear Equations, contents of Mathematics in high school had a sequencial order presentation in the books altered certain times. In certain period, for instance, the content was presented the Determinant contents, later a simple definition of Square Matrices and later the Linear Systems. Such presentation that represents one of the possible permutations among the three contents indicates that in certain moment the Matrices weren't a school content. So, the question such how has the Matrices become a school content and when did it happen? Who did begin that process? To answer such questions, the present research has as theoretical base the concept of Didactic Transposition, published by Yves Chevallard. The methodological procedures adopted for that concept was explored better were of the type metanalysis, a documental analysis and content analysis, each one allowing an evaluation of the different interpretations that other authors have about the Didactic Transpositions that was developed from the point of view of this research, the understanding on this concept, that was detached the main characters of the scientific, academic and school places that provided the introduction in the teaching Matrices, that were the professors from the University of São Paulo and teachers from the basic public schools of São Paulo State, all members of the Study Group about the teaching of Mathematics (USP-SP); that it was identified in the analyzed text books the underlying elements to the process of Didactic Transposition of the Matrices, respectively. Based on these studies was possible to understand how the process of doing a school knowledge of the Matrices was built, and also, to find out when that happened, decade of 1960, period of the Introduction of the Modern Mathematics in the basic teaching. The present research had as main goal to answer the mentioned previously questions above, but starting from the analyses was possible to reveal a part of the Matrices history, the history of the Didactic Transposition of the Matrices, of the period in that appears as a knowing school, and also as the Matrices Theory was presented in text books, resulting in a material that interlaced history of the mathematics, of the mathematical education and of the didactic transposition of the Matrices.