Please use this identifier to cite or link to this item: http://hdl.handle.net/11328/535
Title: Matrizes e aplicações no ensino secundário.
Authors: Pinho, Domingos Pires Valente Sevivas
Keywords: Matrizes
Sistemas de Equações Lineares
Aplicações de Matrizes
TMMAT
Issue Date: 2010
Citation: Pinho, D.P.V.S.(2010). Matrizes e Aplicações no Ensino Secundário. Dissertação de Mestrado em Matemática/ Educação.
Abstract: Diversos problemas em matemática recaem na discussão e na resolução de sistemas de equações lineares. As matrizes surgiram em Matemática com o objectivo de facilitar o tratamento de sistemas lineares. O conceito de matriz é usado em muitas áreas da Matemática, estando também presente em áreas tão diversas como Engenharia, Física, Ciências de Computação, Biologia, entre outras. Considerando a importância deste conceito em tantas aplicações práticas, não é de surpreender que tenha sido e continue a ser objecto de intensa investigação, dando corpo a uma literatura muito vasta. Neste trabalho, procuramos mostrar como o uso de matrizes na resolução de sistemas lineares no ensino da Matemática no Ensino Secundário pode ser um instrumento particularmente útil na descrição e estudo de certos fenómenos da natureza. Assim, iremos propor a introdução das matrizes no currículo da Matemática do ensino secundário e o seu uso na resolução de problemas. Começamos por fazer uma breve introdução histórica ao tema Matrizes e Sistemas Lineares, desde o seu aparecimento em tempos remotos até aos nossos dias. Apontamos a contribuição das Matrizes em distintas aplicações. Sugere-se ainda orientações, questões e problemas que um guia didáctico relativo ao tema sobre matrizes, deverá possuir, baseado em documentação bibliográfica. Apresentamos alguns conceitos básicos e resultados fundamentais sobre matrizes sendo parte destes acompanhados de exemplos. Procuramos apresentar estes conceitos e resultados com simplicidade, de uma forma que esperamos que seja útil a todos aqueles que abordam este assunto. Fazemos também uma breve referência à utilização de tecnologia, como material de apoio e sua contribuição no processo ensino aprendizagem, nomeadamente alguns softwares de Matemática e o uso das calculadoras gráficas. Diverse problems in Mathematics fall upon the discussion and resolution of Linear Equation Systems. In Mathematics the matrixes appeared with the aim of dealing with Linear systems in an simpler way. The concept of Matrixes is used in many areas of Mathematics, being also present in such diverse areas as Engineering, Physics, Computer Science, Biology and many others. Considering the importance of this concept in so many practical applications, it is not surprising that it has been and continues being object of intense investigation, contributing to an array of vast literature. In this research work, we have tried to show how the use of matrices in the resolution of linear systems in the teaching of mathematics in the secondary school level may be a particularly helpful instrument in the description and study of certain natural phenomena. Therefore, we are going to suggest the introduction of matrices in the curriculum of Mathematics of the secondary school level and their use in problem solving matters. We begin by doing a brief historical introduction about the theme of Matrices and Linear Systems, since their arrival in remote times till today. We mention the contribution of Matrices in distinct applications. It is also suggested guidelines, questions and problems that a didactic guide about the theme of Matrices should have, based upon bibliographical documentation. We present some basic concepts and fundamental results about Matrices, being part of these accompanied with examples. We make an effort to try to present these concepts and results with simplicity, in a way that we hope to be useful to those who address this matter. We also make a quick reference to the use of technology, as an aid and its contribution to the learning and teaching process, such as: some Mathematical software‘s and the use of graphic calculators.Diverse problems in Mathematics fall upon the discussion and resolution of Linear Equation Systems. In Mathematics the matrixes appeared with the aim of dealing with Linear systems in an simpler way. The concept of Matrixes is used in many areas of Mathematics, being also present in such diverse areas as Engineering, Physics, Computer Science, Biology and many others. Considering the importance of this concept in so many practical applications, it is not surprising that it has been and continues being object of intense investigation, contributing to an array of vast literature. In this research work, we have tried to show how the use of matrices in the resolution of linear systems in the teaching of mathematics in the secondary school level may be a particularly helpful instrument in the description and study of certain natural phenomena. Therefore, we are going to suggest the introduction of matrices in the curriculum of Mathematics of the secondary school level and their use in problem solving matters. We begin by doing a brief historical introduction about the theme of Matrices and Linear Systems, since their arrival in remote times till today. We mention the contribution of Matrices in distinct applications. It is also suggested guidelines, questions and problems that a didactic guide about the theme of Matrices should have, based upon bibliographical documentation. We present some basic concepts and fundamental results about Matrices, being part of these accompanied with examples. We make an effort to try to present these concepts and results with simplicity, in a way that we hope to be useful to those who address this matter. We also make a quick reference to the use of technology, as an aid and its contribution to the learning and teaching process, such as: some Mathematical software‘s and the use of graphic calculators.
URI: http://hdl.handle.net/11328/535
Appears in Collections:REMIT - Dissertações de Mestrado / MSc Dissertations

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