Conceitos fundamentais de álgebra linear: uma abordagem integrando geometria dinâmica

• Autor(a) principal: França, Michele Viana Debus de
• Data de Publicação: 2007
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/11281
• topic: Álgebra linear; Geometria dinâmica; Registros de representação semiótica; Educacao matematica; Matematica -- Estudo e ensino; Mathematics education; Linear algebra; Dynamic geometry; Semiotic representation registers; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This study treats questions related to the learning of Linear Algebra concepts in in the superior education. The research involved the design of activities on the concepts of vector coordinates, linear dependency, base and linear transformation on the plane, articulating different records in a Dynamic Geometry environment. It was intended to investigate in what measure a geometric treatment and the articulation among representation registers (algebraic, graphical and geometric), assisted by the Cabri-Géomètre environment, influence in the conceptions of students who have already attended the discipline of Linear Algebra. The theoretical bases of this study are the Duval s theory of Semiotics Representation Registers (1995, 2000, 2005) and the Vergnaud s theory of the Conceptual Fields (1990, 1997, 1998). Based on the teaching experiment methodology (Steffe & Thompson, 2000), exploration activities of different representations for the concepts already mentioned were conceived. Eighteen third grade Mathematic students from a Private University from the city of São Paulo participated in the experiment. Although the students tried to reproduce a symbolic algebraic register, they did not show sense domain, what was not foreseen in the design of activities. Even so, based on the results, we can identify the individual s evolution on the understanding of the concepts, as well as a wider domain of the graphical, algebraic and geometric representations, carrying through conversions in both directions, to make them collate with false invariants, which they possessed, and compelling them to question and to explain notions. The Dynamic Geometry environment provided positive effects in the students resolution strategies, providing means of experimental validation of the theorem-in-action and leading them to explicitate and rediscuss the involved notions, from the different aspects evoked in the representations