Estudo dos sólidos de revolução com ênfase nos corpos redondos: concepções e práxis de uma sequência didática à luz da teoria de Guy Brosseau

• Ano de defesa: 2022
• Autor(a) principal: Pinheiro, Ana Lúcia Vaghetti
• 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: Sólidos de revolução; Corpos redondos; Teoria das situações didáticas; Princípio de Cavalieri; Teorema de Pappus; Áreas e volumes; Revolution solids; Round bodies; Theory of didactic situations; Cavalieri's principle; Pappus' theorem; Areas and volumes; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/24401

In this research we present conceptions and praxis of a didactic sequence about the solid object of study of revolution with an emphasis on round bodies. In order to do so, we seek in Guy's Theory of Didactic Situations Brousseau as a character of scientific instrument the apparatus for methodological structuring of such a proposal and we architect a didactic sequence configured in didactic and didactic situations, taking into account the skills and competencies proposed in the National Curricular Common Base for the object of reference knowledge aiming at the appropriation of significant knowledge that may trigger in the subjects involved a posture of autonomy and protagonism in the face of this new knowledge, in order to corroborate its performance in the face of challenges of knowledge and in its subsequent studies. In this way, we seek to investigate which contributions the Theory of Didactic Situations can provide about the study of this object of knowledge and are aimed at a praxis that consolidates this knowledge in a significant way. The qualitative research took place in two classes of the third year of high school in a State Institute of Education located in the municipality of Júlio de Castilhos, RS. The context of the research took place in the hybrid teaching modality, using as a mediator the Google Classroom application of the Google Suite for Education Platform. In this context we propose the resolution of problem situations concerning the calculation of surface areas and volumes of solids of revolution using Cavalieri's principle and Pappus' theorems from concepts studied in high school. The proposed didactic situations involved the use of manipulable materials such as acrylic solids and solids of revolution simulator and experimental activity for centroid determination of flat figures, as well as the construction of physical and virtual models using SketchUp software representative of silos, a very common type of construction in the municipality locus of the research and its borders, whose architecture is privileged by the presence of round bodies. The survey results indicated that the development of the didactic sequence favored intellectual autonomy and significant learning about of the object of knowledge in question, as well as revealing that the Theory of Didactic Situations provided important subsidies for didactic organization and analysis of the knowledge consolidation process involving the study of solids of revolution.