Uma introdução ao estudo de derivadas no ensino médio

Abstract

This work is a didactic proposal for introductory teaching of derivative, linked to the functions of teaching first and second grades. For this, we sought to examine the feasibility of introducing Calculus education this school phase in view of the difficulties inherent in this discipline and extensive high school curriculum.From a literature review, described a brief history of the appearance of the Calculus as mathematical knowledge, pointing out the main problems that triggered such a study, and the calculation of teaching in high school in Brazil highlighting the reasons why the withdrawal of Calculus topics of math programs. Also a survey was conducted on the campus database IFCE of Limoeiro do Norte to investigate how higher education contains the Calcukus discipline in their programs and what are the rates of the approval indexes / reproof in these subjects in semesters 2014.1 and 2015.1. Based on the alarming results of that research, which vary from 33% to 90% disapproval, we propose to draw up a teaching sequence on derivatives of functions of the 1st and 2nd grades in context and interdisciplinary manner, with an emphasis on problem solving and applications , aiming to provide a material that can be tested in the classroom and it will be useful to improve the Calculus teaching in higher education. It is observed that the Calculus has always been an important tool for scientific and technological development and that currently plays a key role in various areas of knowledge. Therefore, the need to insert topics of Calculus in high school is undeniable in view of the continuing education of these students and the facilitating role that the Calculus plays in other mathematical content and other areas of knowledge. In addition, it is noted that it is entirely feasible to insert the concept of derived soon in the 1st year of high school, provided the mathematical rigor and excessive formalities are not overly exploited but which, instead, are highlighted in geometric interpretation and applications. Thus, it is imperative that more research be done in this area by providing support for high school teachers introduce intuitive notions of properly Calculus to your audience