Estudo das concepções e competências dos professores: a passagem da aritmética à introdução da representação algébrica nas séries iniciais do ensino fundamental

• Ano de defesa: 2009
• Autor(a) principal: Yamanaka, Otávio Yoshio
• Orientador(a): Magina, Sandra Maria Pinto
• 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: Generalização agébrica; Raciocínio aritmético; Relações funcionais; Campos conceituais; Algebra > Estudo e ensino; Aritmetica > Estudo e ensino; Campos algebricos
• Palavras-chave em Inglês: Algebraic generalization; Arithmetical reasoning; Functional relations; Conceptual fields
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/11418

The purpose of this study was to investigate the way the teacher conceives a transition between the developed arithmetical concepts to an introduction of algebraic representation in the first grades of Elementary School and also which are the actions that he or she will unleash in order for this transition or passage to happen. So, the teacher s conceptions were researched as for the problem elaboration of additive and multiplicative structures, as well as competences related to the solving of certain problem and its algebraic representation as basis in a simple linear equation. For such, the theoretical foundation used was the Conceptual Fields Theory from Gerard Vernaud, focusing specifically on the Additive and Multiplicative Conceptual Fields, and also the ideas from Ponte (1992) and Tall & Vinner (1981). The research methodological approach is qualitative, making use of statistical instruments to show the data analyzed. As for the purpose it is descriptive with diagnostic outlining, having as a diagnosing tool an inquiry. For the data survey, two kinds of inquiries, being one for the teachers working in the first grades of Elementary School and other for students of the teaching credential course in Pedagogy. These inquiries correspond to three different parts, being, (1) Profile, (2) Conceptions and (3) Competences. The analysis of the obtained result was done quantitative and qualitatively and following the same order in which the tools were composed. The results showed that the teachers conceive problems related to additive structures to groups of Composition and Transformation of two measures. For the multiplicative structures the problems were elaborated basically of quaternary structures. In relation to the competences, the subjects are more familiar and have more familiarity when dealing with arithmetical representations, having a complex competence in relation to the algebraic focus that might be classified as an elementary competence