Cálculo diferencial : uma proposta de abordagem no ensino médio

• Ano de defesa: 2019
• Autor(a) principal: Souza, Jonas Ferreira de
• Orientador(a): Mateus, Marta Elid Amorim
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Programa de Pós-Graduação: Mestrado Profissional em Matemática
• Palavras-chave em Português: Matemática; Cálculo diferencial; Física; Ensino médio; Gráficos; Software Geogebra
• Palavras-chave em Inglês: High school; Mathematics; Differential calculation; Physics; Graphics
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://ri.ufs.br/jspui/handle/riufs/12763

This work is aimed for high school teachers, and is intended to present methodologies to approach Differential Calculus with one variable within the three grades of high school, taking into account that, with this knowledge, students will be able to interpret the behavior of algebraic and transcendent functions, which are Mathematical topics and other subjects in most part of this study cycle, as well as assisting students in a solid preparation aiming at facing the initial subjects of some university courses, mainly in the area of exact sciences, which have been presenting negative results on the student grades in subjects such as Differential and Integral Calculus I and Physics I. In order to bring Calculus ideas closer to real situations and relate Mathematics with other disciplines, in this paper, we argue that in the first year of high school, an approach should be made initially to the derivative study focused on the Physical discipline, in the definition of the rate of change instantaneous, in content of Scalar Kinematics, with this subject teachers’ help, and that these initial ideas are harnessed to the study of the Polynomial Function of the 2nd degree, in the Mathematical discipline, equation of the tangent line, the graphical behavior and the problems of maximum and minimum values related to this function. In the second year, Physics will continue as an active participant in the rate of change study with the help of derivative, and mathematics will have in Newton's binomial the opportunity of approach some derivation rules. In the third year, physics will maintain its role, as in previous series, while Mathematics will present to the students who want to devote more discipline to more formal content, with the aid of notions of limits and continuity, addressing since the definition derivative until the study of the rules of derivation, with the appropriate justifications, in addition to a broader treatment of graphing and problem solving optimization, using GeoGebra software as a support tool.