Uma investigação sobre a aprendizagem do teorema fundamental do cálculo

• Ano de defesa: 2007
• Autor(a) principal: Anacleto, Grácia Maria Catelli
• Orientador(a): Silva, Benedito Antonio da
• 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: Teorema fundamental do cálculo (TFC); Ferramenta objeto; Calculo; Matematica > estudo e ensino
• Palavras-chave em Inglês: Fundamental theorem of calculus (FTC); Tool-object
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/11280

This study aims to investigate the knowledge mobilized by students who have already studied the Fundamental Theorem of Calculus (FTC) regarding the concepts of differentiation and integration and its relationship. The FTC is one of the most important topic in any Calculus course according to Segadas (1998). The intention of the study is to evaluate if the mobilization of these concepts occurred in the proper manner for specific questions resolution where necessarily they have to be applied. The research was based on Douady s (1987) theoretical beliefs of the tool-object dialectic and change of frameworks. As support the study was carried through Segadas (1998) research on the understanding of the FTC by students at the end of the course of Calculus. A pilot-questionnaire was applied to students of a Computer Science course in a private University of São Paulo city. In this first inquiry we perceive the participant students had not received the FTC related content in the deep required for our research in this course. Thus we have decide restructure the questionnaire and apply it to a different group of students in the Mathematics Bachelors course where the FTC content was teach deeper due to greater teaching load in the same university. The research found the majority of the students have found difficulties to solve problems where the simple visualization of graphs would solve it without developing extensive algorithms. This findings shows the students obstacles to understand the FTC are related to an incomplete mobilization of differentiation, integration and continuity concepts since to solve the given questions they have only partially used these knowledge. Such fact is probably associated the students habits who do not tend to focus their attention to the conceptual aspects of the theorem but only memorizing the procedures algorithm without reflecting on its applicability. The theoretical fundamentals used revealed an efficient tool in the analysis of the protocols who led us to these conclusions