A visualização na aprendizagem dos valores máximos e mínimos locais da função de duas variáveis reais

• Ano de defesa: 2014
• Autor(a) principal: Ingar, Katia Vigo
• Orientador(a): Silva, Maria José Ferreira da
• 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: Visualização; Cálculo de duas variáveis; Situações didáticas; Máximos e mínimos; CAS Mathematica
• Palavras-chave em Inglês: Visualization; Calculus of two variables; Didactic situations; Maximum and minimum
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/11013

This work aimed to analyze the process of visualization during the learning of notions of maximum and minimum local values in functions of two real variables by students of engineering. The methodology of the study is the Artigue Didactic Engineering. The theoretical reference was based on the theory of Semiotic Register by Duval, particularly in the perceptive, discursive, operational and sequential apprehension of a graphic register represented in the CAS Mathematica and in the articulation between the graphic and algebraic registers. Our theoretical referential was also based on the Theory of Didactic Situation by Brousseau, for we got started with situations which have as their main frame the position of the professor-researcher who faces a group of students in a milieu formed by a computer laboratory, questionings and feedback. The a posteriori analysis of didactic situations helped us see that the students presented difficulties converting the register from natural language to algebraic but, anyway, they coordinated three registers of semiotics representation: natural language, algebraic and graphic. In the graphic register presented in the CAS Mathematica, through operational apprehension and by means of optical, positional and mereologic modifications, the students identified the visual variables inherent to the graphic register. To the students it was not easy to articulate the visual variables with the meaningful values of the algebraic register presented in the definitions and theorems of maximum and minimum values of functions of two real variables. Validating results was not simple for them either. Therefore, the study of visualization through the theory of Semiotic Register by Duval proved itself to be the way to the apprehension of maximum and minimum local values of functions of two real variables