Uma seqüência de ensino para a construção de uma tabela trigonométrica

• Ano de defesa: 2005
• Autor(a) principal: Nascimento, Alessandra Zeman do
• Orientador(a): Bongiovanni, Vincenzo
• 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: Trigonometria; Homotetia; Semelhança de triângulos; Instrumentos; Situação didática; Mediação; Pensamento geométrico; Educacao matematica; Matematica > Estudo e ensino; Trigonometria > Tabelas
• Palavras-chave em Inglês: Trigonometry; Homotetia; Similarity of triangles; Instruments; Didactic situation; Mediation; Geometric thought
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/11511

The objective of this study is to construct a trigonometrical table, on the basis of historical surveys of the works of Ptolomeu and other mathematicians of Old Greece, to investigate the appropriation of the meaning of the concepts of the trigonometrical reasons: sine, cosine and tangent, in the rectangular triangle, for students of first year Average education. We look for to answer to the research question: How to teach trigonometry in the rectangular triangle in significant way? E also decurrent questions: Which factors influence the acquisition of such knowledge? How to distanciar the use of Trigonometry in Average Education of mechanization? For in such a way we use the estimated theoreticians of Vygotsky in that if relates to the importance attributed to the social interaction, the language and the simbolizaction in the gradual domain of a conceptual field for the pupils, of the estimated theoreticians of Vergnaud, when dealing with the operations invariants: concept-in-action and theorem-in-action, of its conception, of conceptual field and concept, e also in the model presented for Parzysz for a theoretical picture of the education of geometry, where it detaches four stages of the development of the geometric thought. The results of the experimentation point with respect to an imbalance in Geometry and Algebra. The experimentation showed that despite this, an education of the Trigonometry of the generating rectangular triangle of motivations, including diversified activities, with problems situations, that stimulate thinking, the inquiry and carrying through, contributes so that the pupils construct the meaning of the trigonometrical reasons, besides favoring the argument and modifying some wrong conceptions