LIMITE DE FUNÇÃO EM UM PONTO: UMA ANÁLISE DAS DEFINIÇÕES PROPOSTAS EM ALGUNS LIVROS DIDÁTICOS

Abstract

This monograph aims to analyze how some textbooks introduce the concept of limit of function at a point, by studying the definitions used by these authors. This research was developed, on the one hand, by some concerns that arose in my experience in Calculus I, in which I had difficulty understanding these definitions. On the other hand, we noticed that this is a common problem in students of this subject pointed out by several researches. Students have a lot of difficulty in understanding these definitions and, moreover, they cannot relate the formal definition to what is presented in the intuitive definition. For this study we selected the three most frequently used textbooks in the Calculus I in the courses of Licentiate Degree in Mathematics and Bachelor Degree in Mathematics offered by the Universidade Federal de Mato Grosso do Sul (UFMS), in six cities of the state. From this, we identified and analyzed the situations used for the presentations of the definitions, by means of the theory of conceptual fields, trying to identify the concepts and representations used in the definitions and the relation existing among them. We saw in our studies that the textbooks present different situations in which the definitions require students to know several concepts. This is an important aspect for the teacher to consider, he/she needs to be attentive, because depending on the situation chosen to present these definitions, students may have to deal with concepts that do not favor relating the notions involved in the intuitive definition to what is presented in the formal definition.