Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-04-19T14:08:32Z No. of bitstreams: 1 PDF - José Vinícius do Nascimento Silva.pdf: 3192736 bytes, checksum: 8225fb32e699246e38f2e356d622bb42 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-07-22T20:25:00Z (GMT) No. of bitstreams: 1 PDF - José Vinícius do Nascimento Silva.pdf: 3192736 bytes, checksum: 8225fb32e699246e38f2e356d622bb42 (MD5) / Made available in DSpace on 2016-07-22T20:25:06Z (GMT). No. of bitstreams: 1 PDF - José Vinícius do Nascimento Silva.pdf: 3192736 bytes, checksum: 8225fb32e699246e38f2e356d622bb42 (MD5) Previous issue date: 2015-08-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The aim of this work is to teach Mathematics, especially algebra and geometry, through learning algorithms and layers method for assemble the Magic Cube of Rubik 3 x 3 x 3 in an interdisciplinary way. The proposal has been applied and developed with high school students from Escola Estaudal de Ensino Fundamental e Médio Dr. Antônio Fernandes de Medeiros located in Malta Pb. In the period from June 1st, 2015 until June 5th, 2015. To achieve this goal we built through learning and hub handling applications with Geometry, Algebra, Combinatorics and Probability and issues arising from tests of Brazilian Mathematical Olympiad of Public Schools (OBMEP). / O objetivo deste trabalho é ensinar matemática, em particular Álgebra e Geometria, através da aprendizagem de algoritmos e do método de camadas para a montagem do Cubo Mágico de Rubik 3 x 3 x 3 de forma interdisciplinar. A proposta foi aplicada e desenvolvida com alunos do Ensino Médio da Escola Estadual de Ensino Fundamental e Médio Dr. Antônio Fernandes de Medeiros localizada na cidade de Malta - PB. Para atingir este objetivo construímos através da aprendizagem e manuseio do cubo aplicações com a Geometria, Álgebra, Combinatória e Probabilidade e com questões oriundas de provas da Olimpíada Brasileira de Matemática das Escolas Públicas (OBMEP).

Orientador: Prof. Dr. Antônio Cândido Faleiros / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2015. / The main goal of this work is to show that it is very benecial to the students to use logical thinking games in the mathematics classes, particularly the one known as Rubik Cube, closely related to the group theory. We present a historical study on the developing of this game, as well as the practical aspects we use in its solution. We also present the group theory and show what are the relations between it and the Rubik Cube. Finally, we show a quiz the students answered after learning this game, in order to analyse in what aspects the game may contributed to the students activities in the school and in the learning process. This non-traditional classes are a good way of increasing the self-esteem of the students and, also, their sociability. It's also a good way of training the logical thinking and concentration, two of the main requisites for learning mathematics, as could be realized in all the groups which did this activities. It is possible to teach notions of group theory to the basic student, because the Rubik Cube may be shown to be a set of elements with a binary operation, which, in this game, is the movements sequence. Furthermore, it is possible to verify the associative, neutral element and inverse element properties. It is usually said that the \Education is the most powerful weapon you can use to change the world"(Nelson Mandela), that is, it is seen as a powerful social transformation instrument. However, our experience shows that goals and laws does not change the reality by themselves. We also need the society as a whole working and contributing, not only the directly interested people, teachers and other school professionals. When we have an education of high quality we can easily see the economic and cultural consequences for our country, as well as in the daily activities. In this work I will present the conclusions I obtained proposing the mathematical games for my students, specially the Rubik Cube, but also other games, like the Sudoku and the Rummikub.

Orientador: Carina Alves / Banca: Cristiane Alexandra Lázaro / Banca: Agnaldo José Ferrari / Resumo: O cubo mágico é um dos quebra-cabeças mais famosos do mundo, e em geral atrai aatenção de muita gente, em especial a dos matemáticos. O desa o, as formas, simetriase movimentos induzem a ideia de estarmos diante de um objeto matemático. E podemosir além. As ações e movimentos no cubo mágico são elementos que atendem a todasas condições da estrutura de um grupo, assim como também se relacionam com umgrupo de permutações. À luz da Teoria de Grupos e dos Grupos de Permutações,iremos analisar algumas sequências de movimentos como os comutadores e conjugados.Existem vários algoritmos que resolvem o cubo mágico e que são fáceis de serem obtidos,por exemplo, na internet. O objetivo desta dissertação, além de trazer uma propostade resolução, é o de proporcionar um caminho para além da simples memorização deum algoritmo, no sentido de compreendê-lo. Consequentemente, a justi cativa para apossibilidade de se resolver um cubo mágico é de ordem matemática e não empírica / Abstract: The Rubik's Cube is one of the most famous puzzle of the world, and generally attractsthe attention of many people, especially mathematicians. The challenge, shapes,symmetries and movements induce the idea of being in front of a mathematical object.And we can go further. The actions and movements in the magic cube are elementsthat meet all the conditions of the structure of a group, as well as relate to a group ofpermutations. In light of the Group Theory and Permutations groups we will examinesome sequences of movements such as commutators and conjugates. There are severalalgorithms that solve the magic cube and which are easy to obtain, for example, at theInternet. The aim of this dissertation, beyond to show a resolution, is to provide a pathbeyond simple memorization of an algorithm in order to understand it. Consequently,the justi cation for the possibility of solving a Rubik's Cube is math and not empirical / Mestre