Função quadrática: aplicações de situações didáticas em sala de aula e laboratório de ensino de matemática

Abstract

The present work presents an investigation about the study of some topics of quadratic functions during applications of didactic situations in the classroom and in the Mathematics Teaching Laboratory. It seeks to answer the question: what are the contributions of a didactic sequence, according to Brousseau's Theory of Didactic Situations, for student learning about the content of quadratic functions? It is characterized as a qualitative research, of an exploratory nature, developed in a group of the 1st year of technical education of the Business Administration course, at the Instituto Pleno Rio Anil, in São Luís. It takes Artigue's Didactic Engineering and Brousseau's Theory of Didactic Situations as theoretical contributions. The methodological path follows: 1) analyze the development of the study of functions, in particular, the quadratic function through historical-epistemological aspects and textbooks in Brazil; 2) to identify possible barriers and trends for the teaching of Mathematics in basic education in Brazil in the 21st century; 3) record the students' behavior with the application of didactic situations during the search for solutions; and, 4) recognize the main contributions (and obstacles) experienced by students during the development of didactic situations. It appears that the study of the quadratic function through didactic situations articulated by Brousseau's Theory of Didactic Situations contributes to interactive, efficient and meaningful learning by students, who, when challenged, think critically and apply mathematical concepts in practical situations.