Experimentação, tecnologias digitais e o Teorema de Pappus-Guldin: Uma proposta pedagógica para o ensino de sólidos de revolução
Carregando...
Data
2023-06
Autores
Orientador
Strohschoen, Andreia Aparecida Guimarães
Banca
Gonzatti, Sônia Elisa Marchi
Dullius, Maria Madalena
Rocha, Messenas Miranda
Título do periódico
ISSN
Título do Volume
Editor
Resumo
Esta dissertação tem como objetivo apresentar os resultados do estudo intitulado "Experimentação, Tecnologias Digitais e o Teorema de Pappus-Guldin: Uma Proposta Pedagógica para o Ensino de Sólidos de Revolução", realizado no Programa de Pós-Graduação em Ensino de Ciências Exatas da Universidade do Vale do Taquari - Univates. O estudo teve como objetivo geral investigar as potencialidades de uma sequência didática orientada pela experimentação, utilizando materiais concretos manipuláveis e tecnologias digitais, no ensino de sólidos de revolução. Foi aplicado a uma turma de técnico integrado de química do terceiro ano do ensino médio, com duração de sete encontros. No primeiro encontro, foram identificados os conhecimentos dos alunos sobre poliedros. Nos seis encontros seguintes, os alunos foram submetidos a uma sequência didática que incluía a apresentação dos sólidos de revolução por meio de uma máquina elétrica giratória, experimentação com o uso de sólidos em acrílico para determinar o volume de alguns sólidos de revolução e fazer comparações entre os volumes de cilindros e cones com a mesma altura e base, apresentação do teorema de Pappus-Guldin, determinação do centro de gravidade de polígonos por meio de experimentos com material concreto e cálculo analítico, criação de sólidos de revolução no GeoGebra e determinação de seus volumes utilizando o teorema de Pappus-Guldin. Foi realizada uma análise descritiva dos dados para examinar os resultados desta pesquisa qualitativa. Os resultados indicaram que as atividades experimentais com o uso de materiais manipuláveis proporcionaram uma experiência tangível e prática no estudo dos sólidos geométricos, permitindo aos alunos investigarem os cálculos realizados e comprová-los por meio de experimentação. O uso do GeoGebra proporcionou uma experiência visual e interativa dos sólidos de revolução, permitindo aos alunos explorarem diferentes perspectivas, realizar análises mais aprofundadas e investigar as propriedades dos sólidos de forma dinâmica. Dessa forma, os registros escritos, por meio de questionários e observações, forneceram evidências claras do progresso alcançado, demonstrando a aquisição de conhecimentos e a aplicação dos conceitos estudados. Com o resultado deste estudo, foi desenvolvido um produto educacional intitulado "Explorando o Teorema de Pappus-Guldin: Atividades Experimentais para o Cálculo do Volume de Sólidos de Revolução".
This dissertation aims to present the results of the study entitled "Experimentation, Digital Technologies, and the Pappus-Guldin Theorem: A Pedagogical Proposal for the Teaching of Solids of Revolution," conducted in the Postgraduate Program in Teaching Exact Sciences at the University of Vale do Taquari - Univates. The study had the overall objective of investigating the potential of a didactic sequence guided by experimentation, using manipulable concrete materials and digital technologies, in the teaching of solids of revolution. It was applied to a class of third-year integrated chemistry technicians in high school, lasting for seven sessions. In the first session, the students' knowledge of polyhedra was identified. In the following six sessions, the students were subjected to a didactic sequence that included the presentation of solids of revolution through a rotating electric machine, experimentation using acrylic solids to determine the volume of some solids of revolution and make comparisons between the volumes of cylinders and cones with the same height and base, presentation of the Pappus-Guldin theorem, determination of the center of gravity of polygons through experiments with concrete material and analytical calculation, creation of solids of revolution in GeoGebra, and determination of their volumes using the Pappus-Guldin theorem. A descriptive analysis of the data was performed to examine the results of this qualitative research. The results indicated that the experimental activities using manipulable materials provided a tangible and practical experience in the study of geometric solids, allowing students to investigate the calculations performed and verify them through experimentation. The use of GeoGebra provided a visual and interactive experience of solids of revolution, enabling students to explore different perspectives, conduct more in-depth analyses, and investigate the properties of solids dynamically. Thus, the written records, through questionnaires and observations, provided clear evidence of the progress achieved, demonstrating the acquisition of knowledge and the application of the studied concepts. Based on the results of this study, an educational product titled "Exploring the Pappus-Guldin Theorem: Experimental Activities for Calculating the Volume of Solids of Revolution" was developed.
This dissertation aims to present the results of the study entitled "Experimentation, Digital Technologies, and the Pappus-Guldin Theorem: A Pedagogical Proposal for the Teaching of Solids of Revolution," conducted in the Postgraduate Program in Teaching Exact Sciences at the University of Vale do Taquari - Univates. The study had the overall objective of investigating the potential of a didactic sequence guided by experimentation, using manipulable concrete materials and digital technologies, in the teaching of solids of revolution. It was applied to a class of third-year integrated chemistry technicians in high school, lasting for seven sessions. In the first session, the students' knowledge of polyhedra was identified. In the following six sessions, the students were subjected to a didactic sequence that included the presentation of solids of revolution through a rotating electric machine, experimentation using acrylic solids to determine the volume of some solids of revolution and make comparisons between the volumes of cylinders and cones with the same height and base, presentation of the Pappus-Guldin theorem, determination of the center of gravity of polygons through experiments with concrete material and analytical calculation, creation of solids of revolution in GeoGebra, and determination of their volumes using the Pappus-Guldin theorem. A descriptive analysis of the data was performed to examine the results of this qualitative research. The results indicated that the experimental activities using manipulable materials provided a tangible and practical experience in the study of geometric solids, allowing students to investigate the calculations performed and verify them through experimentation. The use of GeoGebra provided a visual and interactive experience of solids of revolution, enabling students to explore different perspectives, conduct more in-depth analyses, and investigate the properties of solids dynamically. Thus, the written records, through questionnaires and observations, provided clear evidence of the progress achieved, demonstrating the acquisition of knowledge and the application of the studied concepts. Based on the results of this study, an educational product titled "Exploring the Pappus-Guldin Theorem: Experimental Activities for Calculating the Volume of Solids of Revolution" was developed.
Descrição
Palavras-chave
Sólidos de revolução; Experimentação; Teorema de Pappus-Guldin; GeoGebra; Solids of revolution; Experimentation; Pappus-Guldin theorem; GeoGebra
Citação
NEITZEL, Gustavo Stênio Magnago. Experimentação, tecnologias digitais e o Teorema de Pappus-Guldin: Uma proposta pedagógica para o ensino de sólidos de revolução. 2023. Dissertação (Mestrado) – Curso de Ensino de Ciências Exatas, Universidade do Vale do Taquari - Univates, Lajeado, 28 jun. 2023. Disponível em: http://hdl.handle.net/10737/3905.