Teorema de Pappus: conceitos e aplicações no ensino médio
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Data
2018-07-11
Autores
Bueno, Marcos Paulo Rodrigues
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Este trabalho tem como objetivo apresentar uma proposta de abordagem dos conceitos de área de superfícies e volume de sólidos que podem ser obtidos pela rotação de uma curva, ou figura, no Ensino Médio. As práticas correntes mostram que a apresentação desses conceitos no Ensino Médio se dá, em geral, pelo uso de fórmulas. Com a intenção de colaborar com novas propostas e possibilidades de trabalho com esses conceitos no Ensino Médio, nesse trabalho foi realizada a proposta de uso das aplicações dos teoremas de Pappus a partir de conceitos conhecidos dos alunos desse segmento de ensino, sem a necessidade do uso de recursos matemáticos mais sofisticados necessários nas demonstrações dos Teoremas, ambientados no Cálculo Integral. A partir disso, foram elaboradas e aplicadas atividades com alunos da 3ª série do Ensino Médio em uma escola na cidade de Bauru. A percepção do pesquisador, frente às atividades realizadas pelos alunos e o diálogo estabelecido com eles, evidenciou boa receptividade em relação ao método utilizado e a aparente compreensão do conteúdo de modo satisfatório.
The aim of this work is to present a proposal to approach the concepts of surface area and volume of solids that can be obtained by the rotation of a curve, or figure, in High School. The current practices show that the presentation of these concepts in High School is usually by the use of formulas. With the intention of collaborating with new proposals and possibilities to work with these concepts in High School, in this work, the proposal was to use the applications of Pappus theorems from concepts known to the students of this segment of education, without the need of more sophisticated mathematical resources involving the demonstrations of theorems, such as integral calculus. From this, activities were carried out and applied to students of the 3rd grade of High School in a school in the city of Bauru. The researcher's perception of the activities carried out by the students and the dialogue established with them showed a good acceptance to the method used and the apparent understanding of the content in a satisfactory way.
The aim of this work is to present a proposal to approach the concepts of surface area and volume of solids that can be obtained by the rotation of a curve, or figure, in High School. The current practices show that the presentation of these concepts in High School is usually by the use of formulas. With the intention of collaborating with new proposals and possibilities to work with these concepts in High School, in this work, the proposal was to use the applications of Pappus theorems from concepts known to the students of this segment of education, without the need of more sophisticated mathematical resources involving the demonstrations of theorems, such as integral calculus. From this, activities were carried out and applied to students of the 3rd grade of High School in a school in the city of Bauru. The researcher's perception of the activities carried out by the students and the dialogue established with them showed a good acceptance to the method used and the apparent understanding of the content in a satisfactory way.
Descrição
Palavras-chave
Teoremas de Pappus, Área de superfícies, Volume, Cálculo integral, Pappus theorems, Surface area, Integral calculus