Aprendizagem da derivada: uma perspectiva de análise pelos fluxos de pensamento

• Ano de defesa: 2016
• Autor(a) principal: Leme, Jayme do Carmo Macedo
• Orientador(a): Igliori, Sonia Barbosa Camargo
• Tipo de documento: Tese
• 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: Faculdade de Ciências Exatas e Tecnologia
• País: Brasil
• Palavras-chave em Português: Aprendizagem da derivada; Três Mundos da Matemática; Fluxos de pensamento
• Palavras-chave em Inglês: Learning of derivative; Three Worlds of Mathematics; Thought flows
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/19156

This thesis has as main theme the learning of the derivative. The research was motivated by the questioning: What are the different thoughts related to the learning process of a concept? Thus, the theory of the Three Worlds of Mathematics proposed by David Tall was used as basis, what brought elements that allow us to understand how humans learn to think mathematically. From this framework, was developed nine thought flows involved in learning a mathematical concept. A study of the derivative is also held to compose the material analyzed in this research and, from the perspective of thought flows, specific flows that allow us to observe learning elements of derivative were highlighted, as in the embodied world, which presents sensitive and noticeable aspects, when it is treated as the tangent line slope, place of righteousness instant variation curve or rate. In the symbolic world, it’s possible to observe routines and tacit processes to this concept, which are run in order to create their own symbols; and in the formal world, it was observed the axiomatic structure that a derivative can be designed. This thesis follows the exploratory theoretical proposal, because it is a research that relies only on documents to build its own concepts and arguments, using the accuracy and logical consistency to produce a base material for further research. Another result observed, which resulted in a breakthrough among the theories discussed, refers to noticeable feature of the derivative, belonging to the embodied world as this unlinked is procedural characteristics, providing thus provide a reference basis for further investigations in the process teaching and learning derivative