Um relato sobre a introdução às somas de Riemann na educação básica

• Ano de defesa: 2014
• Autor(a) principal: Lopes, Alex Catuzzo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria; Brasil; Matemática; UFSM; Programa de Pós-Graduação em Matemática em Rede Nacional; Centro de Ciências Naturais e Exatas
• Palavras-chave em Português: Ensino; Geometria; Cálculo integral; Área; Teaching; Geometry; Integral calculus; Area; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/22004

The present study describes, by calculation of area of geometric plane gures, an application of the Integral Calculus, intuitively. Usual geometric concepts are applied in high school, considering that the work is applied to a class of third year. At this stage of the studies, students are habituated with speci c concepts such as calculating the area of quadrilaterals and triangles, for example. The work is divided into three chapters. Arguments are presented through literature review in the rst chapter, in order to answer the question, somewhat intriguing: Integral Calculus in high school?. We seek, in these arguments, justify the use of two methods - the Archimedes method (used to determine the area of a circle), and the method of Riemann (used to determine the area of three curvilinear regions, circle, ellipse, the area between the curve described by a polynomial function and the OX axis). In these two methods are implicitly introduced concepts of limits and de nite integral. In chapter two is described the application work. In it are related examples with the transcription of comments, observations and questions of the students. Furthermore, resolutions of evaluative activities by students are presented. In the fourth chapter the author highlights re ections on the applied work, presents some considerations and conclusions about the developed work.