Introduzindo os conceitos de limite, derivada e integral no ensino médio.

Abstract

This paper aims to study how to introduce the concepts of limit, derivative and integral in high school. From this perspective, this research aims to present a contribution on how to introduce each of these fundamental concepts of Calculus in this phase of schooling. Given what is recommended by the Common National Curricular Base - High School Stage for the teaching of Mathematics, the study of Calculus in High School proves to be a convenient tool for the formation of young people. To achieve this goal, we state the definition of each of these concepts, as studied in the Differential and Integral Calculus courses. Then, we present suggestions of approaches, contained in dissertations of the Professional Master in National Network Mathematics - PROFMAT, of how to introduce basic notions of these concepts in High School. Subsequently, we present contributions to the introduction of each concept in this segment. The contributions presented were based on approaches that only require knowledge that are already familiar to high school students and that seek to reach every student at this school level, except for the contribution of how to introduce the concept of integral. Because it is a slightly more sophisticated approach, it turned to students with a recognized degree of experience and maturity with mathematical argumentation. Finally, we deepen the discussion of area calculation by showing that it is not possible to calculate the area of ​​every subset of the plane, given our intuitive notion of the area of ​​a region.