Propriedades da Geometria Plana exploradas por alunos do Ensino Fundamental com o uso do GeoGebra Discovery

• Ano de defesa: 2024
• Autor(a) principal: Russo, Alexandre Matias
• Orientador(a): Abar, Celina Aparecida Almeida Pereira
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Pontifícia Universidade Católica de São Paulo
• Programa de Pós-Graduação: Programa de Pós-Graduação em Educação Matemática
• Departamento: Faculdade de Ciências Exatas e Tecnologia
• País: Brasil
• Palavras-chave em Português: Demonstração e prova; Geometria plana; GeoGebra Discovery; Teoria de Van Hiele; Ensino Fundamental
• Palavras-chave em Inglês: Demonstration and proof; Plane geometry; GeoGebra Discovery; Van Hiele’s theory; Elementary School
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.pucsp.br/jspui/handle/handle/41193

The present research aims to analyze whether the commands and tools of GeoGebra Discovery contribute to the teaching and learning process of the properties of Plane Geometry, by students in the final years of Elementary School. The study covers a brief history of demonstrations and proofs, carried out by mathematicians and scholars from past generations, and some investigations carried out using Geometry software, with dynamic representations, within the scope of Mathematics Education. Proof algorithms called Automated Reasoning Tool (ART) are being implemented in GeoGebra, which make it possible to confirm or refute a mathematical truth or discover properties not initially explained. To achieve the research objective, activities and proposals are developed for students, longing for them to be able to explore, build, Interact, and use ART tools. The analyses of the activities carried out, using GeoGebra Discovery, are founded on the development of thinking in Geometry by the couple Dina van Hiele-Geldof and Pierre Marie van Hiele. As methodological support, Design Research is used, as it allows cycles of analysis during the development of the investigation, and because it promotes the active participation of the student during their learning process. The research participants were students in the 8th and 9th years of Elementary School, in 2021 and 2022, respectively, from a private school in the city of São Paulo. In 2021, nine meetings took place, online and in person, simultaneously, due to the Covid-19 pandemic, and, in 2022, the tenth and final meeting, in person, in the school's IT Laboratory. During the meetings, students developed exploratory activities around the properties of Plane Geometry, through constructions, raising conjectures, interaction, dialogues, verification, validation or not, and discoveries. The analyses carried out during the development of the research indicate that the ART tools from GeoGebra Discovery contribute to students reaching different levels of development of thinking in Plane Geometry, according to van Hiele's theory. The students started at Level 0 – Recognition (visualization) and, during the development of the activities, showed signs of mastery of the properties proposed for the study of Plane Geometry, going through the others until Level 3 – Deduction, in which GeoGebra Discovery confirmed the conjectures presented by the students in the context of deductive reasoning