O uso das isometrias do Software Cabri-Gèométre como recurso no processo de prova e demonstração

• Autor(a) principal: Vaz, Regina de Lourdes
• Data de Publicação: 2004
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/11152
• topic: Prova; Demonstração; Isometrias; Transformações geométricas; Cabri-Géomètre; Educacao matematica; Matematica -- Estudo e ensino; Cabri-geometre (Programa de computador); Proof; Justification; Isometries; Geometrical transformations; Cabri-Géomètre; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This work aims to investigate an approach to the teaching and learning of proof using the geometrical transformation tools of the software Cabri-Géomètre. Previous research related suggests that neither approaches emphasising predominately inductive aspects nor those privileging the deductive, are sufficient to enable learners to construct robust meaning for the notions involved in constructing valid proofs. With this in mind, the approach developed in this study seeks to engage students in activities that favour spontaneous movement between induction and deduction in a computer-based environment Cabri-Géomètre in which action and its formalisation can occur simultaneously (Healy, 2000). To this end, a teaching experiment was conducted with students of the 7th and 8th grades of a private school in the city of São Paulo. This experiment comprised two phases, design and analysis. During the design phase, three activity sets were developed and piloted. In the analysis phase, theoretical support was drawn from the theory of Piaget and Garcia (1987) concerning the development of geometrical notions, the classification of proofs in Balacheff (1988) and the distinctions figure/drawing and robust/soft in relation to constructions in Cabri-Géomètre. Through the interactions of the students with the research situations, the role of the transformation tools in different aspects of the proof process was explored, from the appropriation of notions of geometrical dependency to the construction of formally-presented proofs. Analysis of the results indicated that the dynamism of the software had an important role in encouraging figures to be seen as general rather than specific cases. It was also found that that students were incorporating some facts, especially those of an intrafigural nature, established in the first activities sets in the proofs written during the final set, although the justifications they elaborated were locally but not globally valid