Equações diofantinas lineares: possibilidades didáticas usando a resolução de problemas

Detalhes bibliográficos
Ano de defesa: 2015
Autor(a) principal: Campos, Adilson de
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Santa Maria
BR
Matemática
UFSM
Programa de Pós-Graduação em Matemática em Rede Nacional
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://repositorio.ufsm.br/handle/1/10945
Resumo: This work presents an educational experiment carried out in a 9th grade class of elementary school, in order to assess the didactic and pedagogical possibilities involving the Linear Diophantine Equations theme, with the contextual support of Problem Solving. This application intends to expand the students' conceptions in arithmetic and algebra courses, also providing a concrete possibility of applicability of the greatest common divisor of two integers, a very neglected theme throughout the elementary school. In a level of elementary school, one of the main vehicles that allows you to work the initiative, creativity and exploring spirit is through Problem Solving. A Mathematics Teacher has a great opportunity to challenge the curiosity of the students by presenting them problems that are compatible with their knowledge and guiding them through incentive questions and this teacher can also try to input on them a taste for discovery and independent thinking. Thus, a very reasonable way is to prepare the student to deal with new situations, whatever they may be. The paper is organized in three chapters. In the first chapter entitled "Problem Solving in mathematics teaching" a theoretical foundation on the Teaching of Problem Solving is searched based on the Hungarian-American author George Polya and Luiz Roberto Dante and, it also presents some aspects from the learning theory proposed by Vygotsky. In the second chapter entitled "arithmetic concepts" the themes treated are: Greatest Common Divisor (gcd), Euclidean algorithm, Bèzout theorem and Linear Diophantine Equations. In the third and final chapter entitled "pedagogical experimentation" as mentioned above, the experimentation in a class of ninth grade of an elementary school. This experiment is based on the Didactic Engineering methodology, comprising the following stages: theme and scope of action; previous analyzes associated with the dimensions: epistemological, didactic and cognitive; prior analysis; experimentation; aftermost analysis and validation of Didactic Engineering.