O Movimento da Matemática Moderna: Repercussão na abordagem no Brasil do conceito de função nos livros didáticos das décadas de 1950 a 1970.

Abstract

This research work aims to examine the approach of the concept of mathematical function as presented by four collections of textbooks, pointing out how the Modern Mathematics Movement impacted on their methodological structures. Initially, we present an outline of the history of the emergence of the concept of function over time, from remote past to the present day, and how this subject was introduced in secondary school education in Brazil. Subsequently, we turn our attention to analyzing the context in which the Modern Mathematics Movement took place in Brazil and abroad. Based on this knowledge, we give an overview of how the concept of function was addressed in pre-modern mathematics and modern mathematics periods; we then proceed to analyze the textbooks. This analysis was firstly performed from an external viewpoint, emphasizing bibliographical aspects and then from an internal standpoint, taking into account their methodological aspects. As a natural step forward we examine some research works published from 1990 to 2001 dealing with difficulties faced by students when learning the concept of mathematical function, and taking these observations as a basis we present a critique of traditional and modern curricula of school mathematics. Finally, we point out some suggestions to be used by mathematics teachers in teaching functions.