Introdução ao conceito de integral de funções polinomiais em um curso de Engenharia de Produção por meio de tarefas fundamentais em princípios da Modelagem Matemática

• Ano de defesa: 2013
• Autor(a) principal: Silva, Carlos Antônio da
• Orientador(a): Silva, Benedito Antonio da
• Tipo de documento: Dissertação
• 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: Conceito integral; Princípios de modelagem matemática; Aprendizagem significativa; Criticidade
• Palavras-chave em Inglês: Integral concept; Principles of mathematical modeling; Meaningful learning; Criticality
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://tede2.pucsp.br/handle/handle/10960

This thesis has as research object to analyze the difficulties and the meanings for students of a course in Production Engineering, through a sequence of tasks using calculation of area measurements based on principles of mathematical modeling, as a resource facilitator in introducing the concept of integral polynomial functions. For the developing of such a sequence we started from geometric figures supposedly known to students in order to lead them to the definition of integral. The research had two directions: theoretical and empirical. The first was developed by documentary studies that provided historical information on engineering courses, especially the Production Engineering. Recent results of research in mathematics education show the potential use of Principles of Mathematical Modeling in teaching. The empirical research was based on these principles as an approach to teaching Calculus and was developed in two phases consisting of activity, each of which divided into two stages, one for solving tasks and another for the socialization of results. In the first phase were developed four activities that involved the exploitation of calculating measures of areas of figures to introduce the concept of integral. In the second, students performed eight activities about the involved ideas in the concept of integral, and modeling was explored in the last three. At this stage a differentiator was the performance of the first phase participants who returned now as observers in order to verify what actually was learned after a semester of implementation of tasks, watching younger colleagues perform similar activities to theirs. With this type of qualitative research - action research, we sought to provide students the meaning of the integral elements and explore the criticality and analytical instruments that were the researcher's own observations, reports and resolutions of the students, recordings of conversations in different moments and the comments of participants in the first phase. The procedures analysis reveals that it´s possible to insert Principles of Mathematical Modeling in activities to be developed in the classroom and that fit the curriculum, especially satisfying the criterion of time devoted to subjects. The results also show a consistency in terms of learning, so that when students, after six months, review such content, searching real problems and presenting solutions relevant applications inside and outside the industry, and also when the group of students who participated in the first stage demonstrated evidence of learning while playing, in the second stage, the role of observers, argued that had really learned integral and that the application in engineering is of extreme relevance. We believe that such research can be performed from the basic concepts of physics, thus reinforcing the importance of research as producers of materials that can implement the work in the classroom and change the course of the teaching of Calculus