ESPAÇO DE TRABALHO GEOMÉTRICO: CONTRIBUIÇÕES PARA O ENSINO E A APRENDIZAGEM EM TÓPICOS DE SUPERFÍCIES PARAMETRIZADAS

Resumo

This work belongs to the research line of Teaching and Learning in Science and Mathematics and aimed to analyze the contributions of a Geometric Workspace (ETG), involving the Theory of Semiotic Representation Records (TRRS) teaching and learning in parameterized surface topics. The ETG proposes elements for the construction of a workspace to address, reflect and interpret a geometric problem in a way that allows learning articulating two levels: the cognitive and the epistemological. The research methodology is qualitative. The research subjects are academics of the Postgraduate Course in Science Teaching and Mathematics of a confessional and community university of Santa Maria/RS. To obtain the data, a sequence of activities was applied structured in four modules: solids and surfaces (representations), parameterization of the plane, parameterization of the surface of the straight circular cylinder and parameterization of the spherical surface. The modules were developed in five meetings, lasting approximately 2h and 30 min each. The TRRS of Duval associated to the ETG of Kuzniak was used as teaching methodology. Data collection took place from the following instruments: observation of productions; audio and screen recordings of GeoGebra; screen print; researcher’s notes in her field diary; sequence of activities; records written by academics; and figural records made in GeoGebra. We sought to analyze the resolution procedures by students in relation to the different types of transformations (treatments and conversions) of semiotic representations anchored in the triple analysis suggested by Duval and adapted to the created ETG. It was concluded the research, showing, among other contributions of this ETG involving the TRRS, that this favored the development of geometric knowledge for the understanding and resolution of problems in surface topics parameterized, from visualization to the construction of concepts and properties. Still, it shows evidence that encouraged students to reflect, making them remember concepts, create connections, assign meaning to the object addressed, interpret and try to reorganize their thoughts and knowledge. In addition, by exploring the content from simple contexts of reality, starting from a motivational story with the use of concrete materials and GeoGebra as didactic resources, the teaching and learning of parameterized surface topics was potentiated. In addition, it helped in the development of geometric thinking, spanning different disciplines of mathematics, providing a general overview of the content covered. The mobilization of different records helped in the activation of Gêneses for the acquisition and understanding of the contents worked and in the articulation of the plans by Gêneses, either in the semiotic, instrumental or discursive genesis, blocking points that were worked during the application. It was noticed that the personal ETG of each activity made more sense when integrated in a larger context, where the ETG encompasses the three proposed phases, the previous concepts, the exploration and the formulation of concepts. For future work and research, it is recommended to explore other aspects of surfaces. Thus, it is expected that this thesis will also contribute to future research in the field of Teaching and Learning in Science and Mathematics.

Dados da obra

Tipo

Tese (doutorado)

Instituição

UFN

Programa

Programa de Pós-Graduação em Ensino de Ciências e Matemática

Ano

2024

Defesa

28/03/2024

Idioma

pt

Palavras-chave

Ensino de Ciências e Matemática; Semiotic Representation Records. Mathematics Education. Teaching Methods. Geometric Learning. Parameterization.; Registros de Representação Semiótica. Educação Matemática. Métodos de Ensino. Aprendizagem Geométrica. Parametrização.

Temas

Didática da Matemática, Geometria, Tecnologias Digitais

Handle

http://www.tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/1291

Acesso

Texto completo na fonte

Fontes

BDTD/IBICT

Na Biblioteca desde

01/10/2026 · verificada em 03/10/2026