Simplificação de frações aritméticas e algébricas: um diagnóstico comparativo dos procedimentos

• Ano de defesa: 2002
• Autor(a) principal: Notari, Alexandre Marques
• Orientador(a): Franchi, Anna
• 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: Fracoes aritmeticas e algebricas; Equivalencia de fracoes; Procedimentos de simplificacao; Erros; Educacao matematica; Matematica > Estudo e ensino; Matematica: Educacao Matematica
• Palavras-chave em Inglês: Arithmetical and algebraic fractions; Equivalence of fractions; Procedures of simplification; Errors
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/11227

This research has as objective to get a systematic diagnosis of the main errors and difficulties revealed for pupils of Basic Ensino and Average Ensino in the simplification of arithmetical and algebraic fractions. They had been selected, for the inquiry, one 8ª series of Basic Ensino and one 1ª series of Average Ensino of two public schools of the Region West, of the city of São Paulo. We assume as referencial theoretician the happened ones of research where Algebra, in these levels of education, must search its beddings in the laws of the Arithmetic. However, it does not reduce it to a generalization of these laws, a time that algebraic the conceptual system incorporates elements and Inter-relations with proper characteristics. The data had been gotten by means of period of training in a classroom of each one of the mentioned series, application of a test and interviews. The main conclusions point with respect to one high number of errors in the simplification of algebraic fractions that disclose a incompreensão of the formal rules that regulate these transformations. Between these, a predominance of errors due to a generalization of rules of a situation for another one occurs, without an analysis of the conditions that validate this generalization. They disclose in the treatment of the arithmetical expressions a predominance of automatically carried through computational procedures, without a reflection on the nature of the task proposal; they indicate, still, an absence of integration between the arithmetical and algebraic conceptual domínios