Construções geométricas: uma alternativa para desenvolver conhecimentos acerca da demonstração em uma formação continuada

• Autor(a) principal: Jesus, Gilson Bispo de
• Data de Publicação: 2008
• 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/11316
• topic: Demonstração em geometria; Formação de professores; Construcoes geometricas; Professor de matematica -- Formacao profissional; Geometric constructions; Demonstration in geometry; Teachers training; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The purpose of this study is to analyze a sequence of activities carried out with in service teachers, aiming the construction of the definition of line bisector of a segment and, from this definition, to allow them to demonstrate inherent properties of this mathematical object. Moreover, the study also aimed that the teachers were able to justify it mathematically, based on plane Geometry, some geometric constructions in which this object was the main tool to solve the problem. Our research question was: Can a teaching sequence, carried out with in service teachers, and focus on geometric constructions, contribute for the development of knowledge about demonstration in Geometry? In order to answer this question, we developed a sequence with a group of in-service teachers of Mathematics for Elementary and secondary school. To reach such aim, we base our study on the theoretical approach of Duval (2003) and Brousseau (1986), about Semiotics Representation Registers, and the Didactic Situation Theory respectively. We also used the Duval and Egret (1989) and De Villiers (2001; 2002) ideas about demonstrations. Finally, we still used some authors ideas about teacher s formation. The methodological choice was research-action and Didactic Engineering, which had contributed to achieve the objective of this study. The analysis of the discussions and the behaviors of the teachers during the formation reveled that the activities had caused reciprocal reflections about definitions, properties, theorems, mathematical justifications, demonstrations. Moreover, the sequence allowed these teachers to discover and to construct some plane Geometry concepts, whilst they made geometric constructions. In this sense, we do highlight to the importance of material representation register. We conclude that this formation contributed for the autonomy of these teachers