Uma proposta de ensino para o estudo da geometria hiperbólica em ambiente de geometria dinâmica

• Ano de defesa: 2009
• Autor(a) principal: Rocha, Marília Valério
• Orientador(a): Ag Almouloud, Saddo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Pontifícia Universidade Católica de São Paulo
• Programa de Pós-Graduação: Programa de Estudos Pós-Graduados em Educação Matemática
• Departamento: Educação
• País: BR
• Palavras-chave em Português: Geometria euclidiana; Engenharia didática; Cinderella (Software); Euclides, Elementos de; Geometria hiperbolica; Professores de matematica > Formacao profissional
• Palavras-chave em Inglês: Hyperbolic geometry; Euclidian geometry; Didactical engineering
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/11370

This dissertation had as its main objective to propose an environment computational to the learning of Hyperbolic Geometry in the training of teachers of mathematics. Based on the Theory of Didactical Situation developed by Guy Brousseau (1986) and studies with the Comprehension of Demonstrations from Raymond Duval (1993), a didactic sequence has been prepared on the subject. The present work is oriented by the question to what extent the dinamic geometry could interfere in the build of hyperbolic geometry s concepts, in the axiomatic study by the professor of mathematics and how this new knowledge could contribute to your formation? This research is founded on some assumptions of Didactic Engieneering, described for Artigue (1988). The relevance of this research is justified by the Nacional Curriculum Guidelines for the courses off Bachelor s Degree in Mathematics, and shortage of teaching-material for the study of this content. Aimed at responding the question of research and gather information that enable the improvement of this didactic proposal, a pilot project was implemented with students of the Professional Master s Degree in Mathematics Education given by PUC-SP University. The results showed that the use of dinamic geometry in the formation of concepts of Hiperbolic Geometry, in the inicial axiomatic proposal, is a resource that contribute to understing these concepts