A abordagem dada à taxa de variação no livro didático do ensino médio e a sua relação com o conceito da derivada no livro didático do ensino superior

• Ano de defesa: 2017
• Autor(a) principal: Lobo, Rogério dos Santos
• 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: Faculdade de Ciências Exatas e Tecnologia
• País: Brasil
• Palavras-chave em Português: Derivada; Taxa de variação; Livro didático
• Palavras-chave em Inglês: Derivative; Rate of change; Textbook; Mathematics - Textbook
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/20671

Reflected on how a subject that uses the fundamental idea of Change is the source of various problems in regard to the initial concept of the Derivative. We elaborated the following research questions: What explanations of the concepts of Change and Rate of Change are given in Secondary School and Higher Education Textbooks? How are these explanations organised in Secondary School and Higher Education Textbooks? What meaning of Derivative can be constructed from Higher Education Textbooks? Moreover, in order to answer these questions, we seek the following general objective "to investigate the meanings of Change, Rate of Change and Derivative that can be constructed from the Secondary School and Higher Education Textbooks." The advancement of this objective is based on the achievement of the following specific objectives: To study the approaches given to the concepts of Change and Rate of Change in Secondary School Textbooks, more specifically in the Analytical Geometry - Study of the Tangent Line chapter; To Analyse the links between entries Semiotic Representation entries and the criteria for Epistemic Suitability for understanding the Rate of Change as applications of the Angular Coefficient, Calculation of Speeds, Average Economic Functions (Average Revenue, Average Profit, Average Cost), Direct Reasoning and the Rate of Relative Change (Percentage); To Analyse the links between Semiotic Representation entries and the criteria for Epistemic Suitability for understanding the Derivative and emphasising it as Rate of Change, alongside the applications of the Angular Coefficient, Calculation of Speeds, Marginal Economic Functions (Marginal Revenue, Marginal Profit and Marginal Cost), Direct Reasoning and Relative Change Rate (Percentage). For these analyses, we construct tables that use our theoretical-methodological references: Bardin's Content Analysis, Duval's Registers of Semiotic Representation Theory, the Holistic Meaning of the Derivative, and the criteria for Epistemic Impartiality. In the final considerations, we answer our research questions. The analyses of the Secondary School textbooks enabled us to draw a conclusion, among others, that the authors of these books explore the fundamental ideas of Change and Rate of Change mainly as an application of the Angular Coefficient and that meaning is constructed in alignment with only one of our various indicators. In the introduction to the Derivative, this concept is dealt with, among other approaches, as an application of the Angular Coefficient and the construction of meanings does not use any of our indicators