Os signos peirceanos e os registros de representação semiótica: qual semiótica para a matemática e seu ensino?

• Ano de defesa: 2013
• Autor(a) principal: Silva, Cintia Rosa da
• Orientador(a): Ag Almouloud, Saddo
• Tipo de documento: Tese
• 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: Registro de representação semiótica; Semiótica peirceana; Geometria Analítica
• Palavras-chave em Inglês: Semiotic representation registers; Peircean semiotics; Analytic geometry
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/10982

This research dealt with a reflection on the theories of semiotic representation registers by Raymond Duval and Charles Sanders Peirce Semiotics. The study answers the following question: which Peircean signs are used to analyze the registers of semiotic representation and what is the semiotics for mathematics and its teaching? To seek answers to our question, we conducted, through a literature review, analysis of the analogies we found between them. The main analogies that guided the study were: a) the formation of semiotic representation can be a qualisign, an icon, or a rheme b) the treatment may be a sinsigno, an index, or a dicent sign and c) the conversion can be a legisign, a symbol, or an argument. In addition, we summarize these analogies in a table containing the main terms of Duval and Peirce theories, which resulted in a semiotic model to analyze the teaching and learning of mathematics. Having said that, we apply this model in the study of mathematical objects, plane, straight line, vector, and points of spatial analytic geometry. With the result of the analysis of the objects, we find that Peircean semiotics can help identify potential problems and solutions that we can find in the teaching and learning of analytic geometry. We note that the Peircean signs that allow such identification and solution are legisign and symbol. Also, we realize that the argument can be the sign that propels individuals make the decision to solve problems and accomplish tasks. We suggest that the tenth Piercean class, (symbolic legisign) argument, may be responsible for the success in the teaching and learning of mathematics. We also infer that the model of Peirce classes for the teaching and learning of mathematics can help in finding the inferences of the actions taken in those cases. By analogy, we assume that the conversion is an activity of great importance in teaching and learning of mathematics and the theories of Duval and Peirce are valid to explain the mathematics and its teaching, even though the theory of semiotic representation registers treats mathematical objects and their representations as a whole, and the theory of Peirce takes its parts as different signs. Therefore, from the didactic point of view, our analysis was important regarding the study of the teaching and learning of mathematics, more specifically of analytic geometry, as we can see, in advance, in which sign of this mathematical object individuals will have difficulties