O conte?do de fun??es na escola : rastros dos movimentos de reforma nos livros did?ticos de matem?tica do ensino fundamental

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This doctoral thesis in Education presents a study that involves the history of mathematics education in Brazil and specifically the content of functions in secondary school. The objective of this thesis is to identify the elements relating to the content of functions in the Brazilian secondary school which added with the advent of curricular reforms in the teaching of mathematics and appear currently as traces in textbooks of elementary school (final years). The Reform movements explored in the thesis are: the Campos Reform, in 1931, the Capanema Reform, in 1942, and the Modern Mathematics Movement (MMM), in the 1950s and 1960s. The study has as object of analysis collections of textbooks published at the heart of these reform movements, especially the best-selling collections and/or the collections that best represented the established programs for teaching mathematics by virtue of the reforms, which are: Curso de Matem?tica Elementar, authored by Euclides Roxo, Matem?tica, by Cecil Thir? and Mello e Souza, Curso de Matem?tica, by Cecil Thir? and Mello e Souza, co-authored by Euclides Roxo, Matem?tica Ginasial, by Euclides Roxo, Cecil Thir? and Mello e Souza, and Matem?tica: Curso Moderno, authored by Osvaldo Sangiorgi. Ten collections of mathematics textbooks selected by the National Program for Textbooks (NPT) for the year 2014 are also analysed. Through the analysis of these collections in the light of ideas about the teaching of mathematics of each time, it can be concluded that the content of functions in elementary school (final years), currently presented in textbooks, consists of a superposition of elements related to reform movements that have established, in addition to a specific space to the content of functions in the curriculum of the course, the method used in their presentation, their notation, conceptualization and definition.
Esta tese de Doutorado em Educa??o apresenta um estudo que envolve a hist?ria do ensino de matem?tica no Brasil e, especificamente, o conte?do de fun??es na escola. O objetivo desta tese ? o de identificar os elementos referentes ao conte?do de fun??es no ensino secund?rio brasileiro que se somaram com o advento das reformas curriculares para o ensino de matem?tica e que se apresentam, atualmente, como rastros nos livros did?ticos de ensino fundamental (s?ries finais). Os movimentos de reforma explorados na tese s?o: a Reforma Campos, em 1931, a Reforma Capanema, em 1942, e o Movimento da Matem?tica Moderna (MMM), nas d?cadas de 1950 e 1960. O estudo traz como objeto de an?lise cole??es de livros did?ticos editadas no cerne desses movimentos de reforma, em especial as cole??es que tiveram maior vendagem e/ou as cole??es que melhor representaram os programas estabelecidos para o ensino de matem?tica em virtude das reformas, s?o elas: Curso de Matem?tica Elementar, de autoria de Euclides Roxo; Matem?tica, de Cecil Thir? e Mello e Souza; Curso de Matem?tica, de Cecil Thir? e Mello e Souza, com coautoria de Euclides Roxo; Matem?tica Ginasial, de Euclides Roxo, Cecil Thir? e Mello e Souza e Matem?tica: Curso Moderno, do autor Osvaldo Sangiorgi. S?o analisadas tamb?m as dez cole??es de livros did?ticos de matem?tica selecionadas pelo Programa Nacional do Livro Did?tico (PNLD) para o ano de 2014. Atrav?s da an?lise dessas cole??es, ? luz do ide?rio sobre o ensino de matem?tica de cada ?poca, ? poss?vel concluir que o conte?do de fun??es no ensino fundamental (s?ries finais), atualmente apresentado nos livros did?ticos, ? constitu?do por uma sobreposi??o de elementos referentes aos movimentos de reforma que estabeleceram, al?m de um espa?o espec?fico ao conte?do de fun??es no curr?culo da disciplina, a metodologia empregada na sua apresenta??o, a sua nota??o, conceitua??o e defini??o.