Análise combinatória e proposta curricular paulista: um estudo dos problemas de contagem

• Ano de defesa: 2011
• Autor(a) principal: Campos, Carlos Eduardo de
• Orientador(a): Igliori, Sonia Barbosa Camargo
• 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: Análise combinatória; Modelo combinatório implícito; Ensino médio; Problemas de contagem; Proposta Curricular do Estado de São Paulo
• Palavras-chave em Inglês: Combinatorial analysis; Implicit combinatorial model; Secondary school; Counting problems; The Curriculum of the State of São Paulo
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/10901

This dissertation is focused on the teaching and learning of the Combinatorial Analysis, specifically mentioning, Counting Problems. The report is about a documentary research, as a result of the analysis of the coursebook, thus the methodological procedures are the most appropriate to this kind of investigation. The aim of this research is to evaluate the types of Counting Problems, which are included in the student s book, Secondary school second grade third term from the Department of Education of the state of São Paulo, in the view of the combinatorial research, taking into account that is the presupposition of the Curriculum of the state of São Paulo, the resolution of the problems in a teaching approach for the combinatorial concepts. The studied problems are the simple ones, in other words, those which could be solved by using only one combinatorial operation. The yardsticks of the content analysis accomplished in the book are the task variables used by Batanero, Navarro-Pelayo, implicit combinatorial model, combinatorial operation, the nature of the elements to be combined and the values of the parameter m and n. They are supported by the theory of the conceptual fields developed by Vergnaud, in which those concepts couldn t be learnt with the approach of a single type of problem. Our investigation led us to the conclusion that, even working with an important list of issues, many of them involved similar situations. It is because not all the considered variables were found in this list