Integrando a geometria com a álgebra na construção de expressões algébricas

• Ano de defesa: 2007
• Autor(a) principal: Cardia, Luciana Simoneti Ferreira
• Orientador(a): Ag Almouloud, Saddo
• 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: Expressões algébricas; Conceito de área; Conceitos geométricos; Eqüicomposição; Decomposição; Composição; Perímetro; Ensino-aprendizagem; Educacao matematica; Matematica > Estudo e ensino; Geometria algebrica
• Palavras-chave em Inglês: Algebraics expressions; Area concept; Geometrics concepts; Equicomposition; Decomposition; Composition; Perimeter; Teaching-learning
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/11246

The objective of this research is to study phenomena that influence the teaching and learning of the concept of algebraic expressions in Elementary Education (students aged 7-15). It presents a teaching proposal for the conception of Algebraic Expressions; uses the Geometry as a tool of construction and provide a reflection about the learning of this concept through a teaching didactic sequence involving the concept of area as principal tool to construction of mathematic knowledge, as well as, the processes of decomposition and composition of planes figures, equicomposition of figures and area equivalents. The following hypothesis guided the development of the different activities proposed: choose of problem situations involving determinate on of the areas of geometrical figures, in particular the area of rectangle, allowing comparisons these of figures using, area as magnitude. to study area as a magnitude and leading to the construction of generalized algebraic expressions. a proposal for teaching and learning the concept of algebraic expressions, making use of the geometric concepts, like area concept, decomposing and composing processes of plan figures, this allows the student favorable conditions to learning this concept. This research is based mainly on two theories: the Tool-Object Dialectic and the Change of Pictures of Régine Douady (1987) and Registries of Semiotic Representation of Raymond Duval (1993). The adopted methodology follows the principles of the Didactical Engineering. The research involved teachers and students of the 7th grade of Elementary Education