Resolução de problemas no cenário da matemática discreta
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Data
2013-03-06
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Universidade Estadual Paulista (Unesp)
Resumo
Esta pesquisa tem como objetivos tratar matematicamente um problema gerado pelo uso das peças do Dominó, identificando a matemática que pode ser construída para a sustentação teórica desse problema, e oferecer recomendações aos professores do Ensino Básico, visando ao trabalho em sala de aula, envolvendo problemas matemáticos a partir das peças do Dominó, fazendo uso da Metodologia de Ensino- Aprendizagem-Avaliação de Matemática através da Resolução de Problemas. Adotamos para o desenvolvimento desta pesquisa a Metodologia de Thomas A. Romberg. Definido o Fenômeno de Interesse - o envolvimento da Matemática e da Resolução de Problemas, consideradas no contexto do uso das peças do Dominó - foi criado o Modelo Preliminar em três e ampliadas versões. O apoio em ideias de outros pesquisadores, sobre a fundamentação teórica da pesquisa: a Matemática Discreta e a Resolução de Problemas, nos conduziu às seguintes questões: Como a Matemática Discreta pode ser trabalhada através da resolução do Problema da Fernanda? De que forma a Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas pode contribuir para o trabalho em sala de aula, na construção de conceitos, de conteúdos e de procedimentos matemáticos em diferentes séries da Educação Básica? Para responder a essas inquietações, criamos dois projetos frente aos quais a pesquisadora assumiu duas posturas diferentes: a primeira voltada à Matemática e a segunda voltada à Educação Matemática. No cenário da Matemática Discreta, conjugados esses dois projetos, seus desenvolvimentos operacionais trouxeram tanto resultados matemáticos novos como recomendações para o uso da metodologia adotada, oferecendo caminhos para o trabalho do professor em sala de aula, com importantes resultados para sua prática docente
The objective of the present research is to treat mathematically a problem that was generated by the use of Domino tiles, identifying the Math that can be built for the theoretical foundation of that problem, and to provide guidelines to Elementary school teachers aiming at classroom work, involving Math problems from Domino tiles and making use of Methodology of Math Teaching-Learning-Evaluation through Problem Solving. For the development of the present research we adopted the Methodology of Thomas A. Romberg. Once the interest phenomenon was defined, the involvement of Mathematics and problem solving considered in the context of using Domino tiles, the Preliminary Model in three expanded versions was created. The support on other researchers’ ideas about the research theoretical foundation: Discrete Mathematics and problem solving, led us to the following questions: How can Discrete Mathematics be worked through Fernanda’s problem resolution? In what way can the Methodology of Teaching-Learning-Evaluation through Problem Solving contribute to classroom work in the construction of Math concepts, contents and procedures in different grades of Elementary school? To answer those questions we created two projects in which the researcher developed two different approaches: the first one regarding Mathematics and the second one regarding Mathematics Education. In the Discrete Mathematics scenario, once those two projects were combined, their operational developments brought new mathematical results as well as guidelines for the use of the adopted methodology, offering the teachers ways to work in classroom, with important results for their teaching practice
The objective of the present research is to treat mathematically a problem that was generated by the use of Domino tiles, identifying the Math that can be built for the theoretical foundation of that problem, and to provide guidelines to Elementary school teachers aiming at classroom work, involving Math problems from Domino tiles and making use of Methodology of Math Teaching-Learning-Evaluation through Problem Solving. For the development of the present research we adopted the Methodology of Thomas A. Romberg. Once the interest phenomenon was defined, the involvement of Mathematics and problem solving considered in the context of using Domino tiles, the Preliminary Model in three expanded versions was created. The support on other researchers’ ideas about the research theoretical foundation: Discrete Mathematics and problem solving, led us to the following questions: How can Discrete Mathematics be worked through Fernanda’s problem resolution? In what way can the Methodology of Teaching-Learning-Evaluation through Problem Solving contribute to classroom work in the construction of Math concepts, contents and procedures in different grades of Elementary school? To answer those questions we created two projects in which the researcher developed two different approaches: the first one regarding Mathematics and the second one regarding Mathematics Education. In the Discrete Mathematics scenario, once those two projects were combined, their operational developments brought new mathematical results as well as guidelines for the use of the adopted methodology, offering the teachers ways to work in classroom, with important results for their teaching practice
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Palavras-chave
Matemática - Estudo e ensino, Ensino, Aprendizagem, Educação, Avaliação educacional, Mathematics - Study and teaching
Como citar
MENINO, Fernanda dos Santos. Resolução de problemas no cenário da matemática discreta. 2013. 289 f. Tese (doutorado) - Universidade Estadual Paulista, Instituto de Geociências e Ciências Exatas, 2013.