Resolução de problemas: enfoque metodológico e teórico

• Autor(a) principal: Souza, Helena Tavares de
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/21648
• topic: Educação Matemática; Resolução de problemas; Registro de representação semiótica; Mathematics Education; Problem solving; Registers of semiotic representation; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This work aims at dealing with Problem Solving methodology in Mathematics education following two theoretical bases, Polya and Duval, analyzing convergences, divergences and complementarities. We sought to extract some stages of resolution from this analysis in order to contribute with the comprehension and interpretation of problem-situations in Mathematics; we also describe specific contributions from each approach and indicate complementarities from the Registers of Semiotic Representation to the Problem Solving methodology. In order to achieve such objectives, our investigations were designed to respond to the research question: Which are the contributions from the Registers of Semiotic Representation according to Duval to the Problem Solving methodology in Polya perspective, among other authors, to the comprehension and interpretation of problem-situations in Mathematics? The research was developed under a bibliographic and qualitative approach with the use of the Grounded Theory methodology. This theory presents categories in pictures, memorandums and theoretical compositions of the analyses. The results point to the fact that the theory of Registers of Semiotic Representation according to Duval applied to the Problem Solving methodology indicated by Polya, among other authors, favors the cognitive development of the subjects to the comprehension of concepts and the formation of a mathematical thinking. This development is magnified as this theory promotes that it is only through these semiotic representations that the activity about mathematical objects are made possible. And, under this perspective, this theory disassembles the common sense that students do not know how to solve problems as they are not familiar with the mother tongue. Duval indicates that this knowledge should go further than the mother tongue, and that the student needs to be aware of how to go by the concepts representation registers that come in the heading of a mathematical problem