Articulação entre Álgebra Linear e Geometria - Um Estudo sobre as Transformações Lineares na Perspectiva dos Registros de Representação Semiótica

• Autor(a) principal: Karrer, Monica
• Data de Publicação: 2006
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/11068
• topic: Transformações Lineares; Registros de Representação Semiótica; Trajetórias de Aprendizagem; Cabri-Géomètre; Livros Didáticos; Educacao matematica; Matematica -- Estudo e ensino; Algebra linear; Geometria; Linear Transformations; Semiotic Representation Registers; Learning Trajectories; Cabri-Géomètre; Textbooks; CNPQ::CIENCIAS HUMANAS::EDUCACAO::ENSINO-APRENDIZAGEM::TECNOLOGIA EDUCACIONAL

This study addressed questions related to the teaching and learning of Linear Algebra in Higher Education. More precisely, it involved the design of activities which concerned the mathematical object linear transformations and which engaged learners in exploring the conversion of registers in a dynamic geometry environment. The aim was to investigate the learning trajectories of university students and the impact of the didactical choices which characterized the teaching approach. The study was organized into two phases. In the first, preliminary studies along with theoretical considerations led to the formulation of hypotheses and to the identification of the conceptual tools to be used in the analysis of the learning trajectories. Using as a theoretical framework Duval s theory of semiotic representation registers (1995, 2000, 2003), during this phase the registers and conversions present in sections on linear transformations in both Linear Algebra and Computational Graphics textbooks were analyzed. In addition, eighty-six students of Computer Science completed a questionnaire about linear transformation. These studies highlighted difficulties in relation to the exploration of different semiotic registers on the part of the students, particularly as concerned matrixial and graphical registers. In the second phase, which employed the methodology of Design Experiments (COBB et al., 2003), activities were developed to explore the diverse representation of planar linear transformations using Cabri-Géomètre and paper&pencil environments. Six students of Computational Engineering at a private university in the city of São Paulo participated in the experiment. The results indicated evolutions in the subjects understandings of the conditions for determinating linear transformations and of the particularities of their graphs, as well as a more comprehensive mastery of diverse representations and conversions. Analysis of students trajectories also revealed how students strategies were mediated by characteristics of the tasks and the computational environment.