PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matematica
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Navegando PROFMAT - Programa de Pós-graduação em Matemática em Rede Nacional - Sociedade Brasileira de Matematica por Assunto "Algebra"
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Item Uma proposta de oficina sobre códigos para a contextualização do estudo de aritmética e matrizes no ensino médio(Universidade Federal de Goiás, 2015-08-07) Alves, Bruno Coelho; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Souza, Flávio Raimundo de; Lima, Lidiane dos Santos MonteiroThis work aims to present the content of Error-Correcting Codes to teachers, in a way to use this content in their classes. A code representing a particular word or symbol by another word or symbol. This study handle with the error correcting codes, especially that said linears. Thus, the concept of code is disclosed along two examples. The Linear Algebra and Algebra requirements are exposed, handling the concept of nite elds, the de nition of linear space and linear transformation. The error correcting codes, from alphabets de ned in nite elds, allow sending messages, even in noisy channels, they can be interpreted with a lower probability of error. This process is done in linear codes through linear transformations. Hamming codes and Reed-Solomon codes are exemples of linear codes which are showed in this work. After presented the theoretical basis of content, it is proposed a workshop that has as target students from the nal years of High School. This workshop explore some common feature codes, such as the use of check digits and the interpretation of texts by digital machines by zeros and ones. It is hoped that this work can assist the release of some current research topics among teachers and encourage the use of new methodologies for teaching content that is considered di cult and useless to several students of High School.Item Uso de jogos e materiais concretos no ensino e expressões algébricas e equações do 1º e 2º grau no ensino fundamental(Universidade Federal de Goiás, 2017-03-27) Rocha, Hélio Roberto da; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Leandro, Bianka Carneiro; Lima, Thaynara Arielly deDue to the poor performance of students from all over Brazil in the mathematic subject, currently there’s a great concern regarding mathematics teaching. Researches indicate that Brazil has the second largest number of students with low performance in basic mathematics, in a list of 64 countries (second report of the Organization and Economic Co-operation for Development - OECD, Paris - 02/10/2016). In relation to that, this work indicates a proposal to teach algebra in the 7th and 9th grades of Elementary School, more specifically Algebraic Expressions,1st degree Equations, 2nd degree Equations and a brief study on 3rd degree Equations, using games and concrete materials. This paper is based on studies of some theorists who wrote about the subject. Based on these studies, a theoretical basis of the contents of the theme was made, along with suggestions of several activities proposed using games and concrete materials. It’s hoped that this work will support other mathematic teachers in their daily work. We know that it’s not always possible to use this methodology due to various problems that occur in schools, but I hope that at some point it can be used.Item Inserções de metodologias diferenciadas no ensino de divisibilidade na educação básica(Universidade Federal de Goiás, 2021-03-18) Santos, Claudio dos; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Lima, Thaynara Arielly de; Rodrigues, Eunice Candida PereiraAs a teacher in the final grades of elementary school, I have observed that among the four basic operations, the division is the one that presents the greatest degree of difficulty for students. With the motivation to reduce this difficulty, the present work approaches the modular congruence as a way to take the student to see the Euclidean division in a different aspect. Considering that since the early years the student has had contact with concepts of modular arithmetic, in this work it is suggested a differentiated approach to the divisibility process. The study addresses algebra topics at an advanced level, so that the teacher can improve his knowledge in this area, and limited to basic operative properties, taking care not to exceed the learning capacity of students at this stage of teaching. An application of modular congruence will be presented in everyday situations, and in solving basic problems of divisibility in order to make learning more interesting and attractive to the student.Item A álgebra dos polinômios(Universidade Federal de Goiás, 2020-05-28) Sousa, Reginaldo Jacinto de; Dias , Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias , Ivonildes Ribeiro Martins; Martins, Ivonildes Ribeiro; Assis, Aline Mota de MesquitaIn this work, we will approach the definition of polynomial using the concept of sequence, which allows you to remove the ambiguity from the symbol x, and we will study the algebraic structure of the polynomial rings, the concept and criteria of polynomial irreducibility and factoring of a polynomial in the product of irreducible polynomials, aiming to provide mathematics teachers who work in high school, a deepening in the study of abstract algebra. Obtaining, some suggestions of applications in the classroom, for example, the study of the rationality of a given number.