O conteúdo de funções na escola : rastros dos movimentos de reforma nos livros didáticos de matemática do ensino fundamental

Abstract

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 Matemática Elementar, authored by Euclides Roxo , Matemática, by Cecil Thiré and Mello e Souza, Curso de Matemática, by Cecil Thiré and Mello e Souza, co-authored by Euclides Roxo, Matemática Ginasial, by Euclides Roxo, Cecil Thiré and Mello e Souza, and Matemática: 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.