# Programa de Pós-graduação em Matemática - PPGM

## URI Permanente desta comunidade

O Mestrado Profissional em Matemática em Rede Nacional – PROFMAT é um programa de mestrado semipresencial na área de Matemática com oferta nacional. É formado por uma rede de Instituições de Ensino Superior, no contexto da Universidade Aberta do Brasil/Coordenação de Aperfeiçoamento Pessoal de Nível Superior (CAPES), e coordenado pela Sociedade Brasileira de Matemática (SBM), com apoio do Instituto Nacional de Matemática Pura e Aplicada (IMPA). Atualmente, o PROFMAT é integrado por 75 Instituições Associadas e 100 Polos de Atendimento em todas as 27 Unidades Federativas do Brasil. As Instituições Associadas e respectivos Polos estão disponíveis no site nacional do programa: http://www.profmat-sbm.org.br/instituicoes-associadas/.
O PROFMAT visa atender prioritariamente professores de Matemática em exercício na Educação Básica, especialmente de escolas públicas, que busquem aprimoramento em sua formação profissional, com ênfase no domínio aprofundado de conteúdo matemático relevante para sua docência. Os alunos são selecionados anualmente por meio de um processo unificado, regulamentado em edital que descrevem orientações e informações necessárias para a realização do Exame Nacional de Acesso (ENA) ao programa.

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Item Utilização de conceitos básicos de matemática e experimentos de robótica para a compreensão de fenômenos físicos(Universidade Federal de Goiás, 2014-02-03) Nascimento, Gilmar José do; Borges, Romes Antônio; http://lattes.cnpq.br/3888145024042412; Borges, Romes Antônio; Bergamaschi, Paulo Roberto; Oliveira, Plínio José; Junqueira, Manoel MoraisMostrar mais This work aims to enable the understanding of physics conceptions utilizing basic foundations of mathematics. In this regard, the aim is to highlight both those the phenomena that occur in nature as the phenomena which occur in laboratory manipulations. A extensive research is made about mathematical concepts that will subsequently be applied to several types of problems, being possible understand fundamental aspects involving physical quantities. With the goal to experience the in practice applications, robotic prototypes using LEGO MINDSTORMS kits, simulating real situations of nature and confronting of the computations with classical theoretical results are built.Mostrar mais Item Uma proposta do ensino de programação linear no ensino médio(Universidade Federal de Goiás, 2014-07-02) Lyra, Marcelo Simplicio de; Queiroz, Thiago Alves de; http://lattes.cnpq.br/8041183668335400; Queiroz, Thiago Alves de; Guimarães, Tobias Anderson; Santee, Donald MarkMostrar mais This research presents a new approach that aims to introduce linear programming into the high school taking into account the teaching techniques, teacher and student profiles, and the flexibility of the curriculum. The context of the linear programming involves problems with two or three variables, since problems with many variables cannot be easily considered in a high school curriculum, especially due to the time required to solve such problems. The approach is developed under an algebraic point of view, in which the linear problem‟s solutions are obtained by a resolution of systems of linear equations. The approach also considers a numerical and computer simulation software, denominated Octave®, in order to solve those systems of linear equations and, consequently, this software may be used as a tool that allows extending such approach to solve linear programming problems with several decision variables.Mostrar mais Item Demonstrações trigonométricas via geometria plana(Universidade Federal de Goiás, 2014-08-06) Mendes, Cleiton Dias; Oliveira, Plínio José; http://lattes.cnpq.br/8075454624929535; Oliveira, Plínio José; Pereira, Jansen Moura; Santos Júnior, Porfírio Azevedo dosMostrar mais This work has been presented with some trigonometric connections statements only using plane geometry. This proceeding has been realized because we observed that a didactic book only presents algebraic statements. We wish in this way, presents to mathematics teachers and students in high or upper school, trigonometry statements identity using geometry. For this, It has been considered trigonometry cycle only in the first quadrant, given an angle such that α have any α ˂ 90°, extending the reasoning to the other quadrants.Mostrar mais Item Modelagem por meio de funções elementares(Universidade Federal de Goiás, 2014-08-06) Soares, Carlos Alberto; Oliveira, Plínio José; http://lattes.cnpq.br/8075454624929535; Oliveira, Plínio José; Junqueira, Manoel Moraes; Santee, Donald MarkMostrar mais This work aims to propose a different approach for teaching elementary functions in high school context, worrying about concepts understanding, definitions elementary functions characterizations. The didactic-pedagogic proposal presents a mathematical modeling from different regarding daily themes simulators from internet, which encourage students “to see”, hidden functions, and improve learning and teaching. In order to do math more interesting for student, it‟s necessary to experience the practical applications, simulating real nature situations and confronting results with theoretical calculations, to do sure those concepts and functions definitions have become a solid knowledge.Mostrar mais Item Modelagem matemática e as tecnologias da informação e comunicação no processo ensino-aprendizagem(Universidade Federal de Goiás, 2014-08-07) Mastrela, Rogerio; Silva, Jhone Caldeira; Silva, Élida Alves; http://lattes.cnpq.br/5863501378045434; Silva, Élida Alves; Silva, Jhone Caldeira; Freitas, Thiago Porto de Almeida; Lopes, Jaques SilveiraMostrar mais The research reported in this work aims to investigate the contribution of using the methodologies “Mathematical Modeling” and “Information and Communication Technologies” (ICTs) in the teaching-learning process of some mathematical concepts, namely: percentage, rule of three, interest, tables and graphs. These concepts were developed in a way that enable involved students relate them to their quotidian. The study was developed in a class of eighth grade (8th grade) of the Basic School at the Municipal School "Arminda Rosa de Mesquita", located in the rural area of Catalão-Goiás. Questionnaires, field diary and filming were the tools used and analyzed from a qualitative and quantitative approach. This analysis revealed evidences that the used methodologies brought advances in analytical and critical development of the involved students, as well as helped to develop the skills of logical reasoning, problem solving and argumentation. Students acted as builders of their own knowledge through interaction among themselves and with the teacher, who became an advisor. Furthermore, it could be verified that Mathematical Modeling and ICTs make students feel a great pleasure, because they are dealing with everyday situations. And working with computers gave new meaning to the contents studied.Mostrar mais Item Importância do software “Uma Pletora de Poliedros” no ensino de geometria espacial(Universidade Federal de Goiás, 2014-08-08) Garcia Filho, Alceny; Bergamaschi, Paulo Roberto; http://lattes.cnpq.br/6961717072558004; Bergamaschi, Paulo Roberto; Cunha, Juliana Bernardes Borges da; Nogueira, Antônio CarlosMostrar mais The work proposed aims to provide a reflection about the importance of promoting a dynamic teaching. Therefore it proposes the use of a software , A Plethora of Polyhedra, that considers the learning needs of students in order to assist them in the viewing and understanding of space around them and so they can use the geometric and mathematical knowledge in benefit of everyday issues. This is a free software for d ynamic mathematics that gathers resources of spatial geometry such as: rotation, translation, enlargement, reduction, and counting of the number of vertices, edges and faces, which enables the students understand the main presented contents. By manipulating the software chosen, teacher and student can identify their main characteristics and essential elements, not just only through the development and resolution of mathematical expressions algebraically presented. This work also is willing to motivate the activities to be proposed by a theoretical basis and analyze the possible difficulties encountered by students and teachers, and the opportunities for improvement in the teaching of geometry.Mostrar mais Item Utilização de matrizes no estudo de orientação e posição de um braço robótico por meio das coordenadas de Denavit-Hartenberg.(Universidade Federal de Goiás, 2014-08-08) Costa, Carlos Gomides da; Stoppa, Marcelo Henrique; Silva, Fernando Kennedy da; http://lattes.cnpq.br/8313547891856943; Silva, Fernando Kennedy da; Stoppa, Marcelo Henrique; Bergamaschi, Paulo Roberto; Guimarães, Tobias AndersonMostrar mais This work have as the main objective present one a different way to teach the subject matrix multiplication, a way in a ludic form, applied, that can transform the teaching more pleasureable and motivate for the high scholl students, because for many this issue has no practical applications, which for many reasons is the lack of interest in learning such content. The tool used to attract as students so as teachers was the utilization of Kit LEGO® Mindstorms NXT 2.0 for the construction of the robotic arm, or robotic manipulator, that which for this propose, has three rotational joints. The LEGO kit was choosen due its easy interaction with children and adolescents, and to encourage the construction of knowledge stimulating the solution of problems that may arise during the process of building robotic arm.The application of content takes place in obtaining the four parameters Denavit-Hartenberg and those obtained after the placement of reference systems, where three of these parameters are constants obtained by measurement at robotic arm and the fourth parameter is variable dependent on the intended movement or the final position which is to be determined.Mostrar mais Item Programação linear e a geometria analítica(Universidade Federal de Goiás, 2014-08-08) Souza Neto, André Luis de; Queiroz, Thiago Alves; http://lattes.cnpq.br/8041183668335400; Queiroz, Thiago Alves de; Santee, Donald Mark; Guimarães, Tobias AndersonMostrar mais Analytic Geometry has been, over the time, reason of much anxiety among students, because it is an area of mathematics that deals with relationsbetween equations and the Cartesian plane. From that anguish emerges the desire of make such subject accessible to any student and, then, the search for examples experienced by them becomesrelevant. This work aims to facilitate the relationship of students with some of the topics inanalytic geometry, namely: the Cartesian plane, and the representation of equations and inequalities with two and three variables. To develop this work, use the linear programming and a mathematical software become an important methodology, since arise some possibilities contributing to the achievement of the following objectives: to deal with modeling, solve real life problems, and interpret results in practical scenarios.Mostrar mais Item Estudo dos polígonos por intermédio da pavimentação do plano(Universidade Federal de Goiás, 2014-08-08) Coelho, André; Bergamaschi, Paulo Roberto; http://lattes.cnpq.br/6961717072558004; Bergamaschi, Paulo Roberto; Santos Júnior, Porfírio Azevedo dos; Nogueira, Antônio CarlosMostrar mais This paper presents the objective to study the polygons, regular polygons in special, from tessellations of the Euclidean plane (or mosaics, as they are widely known). Thus, it was performed a case study with dynamic approach, with the purpose to promote, in high school, the study of geometry, plane geometry in particular, focusing on polygons. It was sought, from the manipulation of concrete materials, lead students to adopt a participatory posture in the construction of the own knowledge. The research was conducted with a class of second year of high school in a public school in the municipality of Catalão, Goiás. As a result, there was a better understanding of geometric concepts discussed by the students.Mostrar mais Item O ensino de funções lineares: uma abordagem construtivista/construcionista por meio do kit LEGO(R) Mindstorms(Universidade Federal de Goiás, 2014-08-08) Silva, Abrahão de Almeida; Stoppa, Marcelo Henrique; Silva, Fernando Kennedy da; http://lattes.cnpq.br/8313547891856943; Silva, Fernando Kennedy da; Stoppa, Marcelo Henrique; Oliveira, Plínio José; Guimarães, Tobias AndersonMostrar mais This work aims to present a new approach to the concept of linear function using the LEGO ® NXT Mindstorms Kit or Kit NXT within the pedagogical concept of Constructivism / Constructionism and Educational Robotics. It talks about each theory with a view to a change in teacher practice, and a historical survey of educational robotics and robotics. Later mathematical topics that justify the approach to the theory of functions, monotonicity, proportionality, and related linear functions are presented. A proposed work is presented in the form of Teaching Sequence aiming to instigate the teacher changes in how regency, working with educational robotics, using the NXT kit and creativity. Furthermore, within this proposal, it explores the existing mathematics in working gears of an analog watch with the purpose of teaching linear function by means of its operation process. The main aim of the work is to present to the teacher a new methodology for teaching linear function that will be at least different, however it is expected that students and teachers can motivate.Mostrar mais Item O método de Cardano e sua aplicação no ensino médio(Universidade Federal de Goiás, 2014-08-15) Melo, Claudio Umberto de; Santos Júnior, Porfírio Azevedo dos; http://lattes.cnpq.br/5132806149453454; Santos Júnior, Porfírio Azevedo dos; Souza, Flávio Raimundo de; Ribeiro, Márcio Roberto RochaMostrar mais This work presents a study on the Cardano's method applied in 3rd degree polynomial equations of the form x3 + px + q = 0; p; q 2 R and use in the classroom, the 3rd year of high school, working with the procedure without the use of formula to determine a root of 3rd degree polynomial equation. The application of this method searches enable to students a relevant intellectual enrichment for future studies of the exact sciences. In this work not used a diagnostic evaluation to analyse the level of understanding of theme, only search to apply the procedure used by Cardano, in the classroom, and especially present a demonstration of this procedure to an equation in the general form of the 3rd degree. The study brings a historical approach of the resolutions of the equations, after, a theoretical foundation for the study of polynomials, detaching the theorems main, propositions and key de nitions for the study of the polynomial functions. Moreover, detach the study of the characteristics of the roots of an equation of the 3rd degree of analytical and graphical form, where we present an analytical resolution for the 4th degree equations. However, we conclude that the application of this study demonstrates that students have greater facility to nd a root of an equation in the general form, as well as the other roots. Therefore, the procedure used in classroom presents a method to nd at least one root of an equation of the 3rd degree, without the use of formula. KeywordsMostrar mais Item As construções geométricas via geometria dinâmica do software régua e compasso(Universidade Federal de Goiás, 2014-08-21) Silva, Emerson José da; Ribeiro, Márcio Roberto Rocha; http://lattes.cnpq.br/0780755813567262; Ribeiro, Márcio Roberto Rocha; Santee, Donald Mark; Souza, Flávio Raimundo deMostrar mais In this work we revisit the subject Geometric Constructions into ruler and compass, using the dynamic geometry software 'Ruler and Compass' as an auxiliary tool in the teaching and learning of geometry, building examples and suggestions for activities with the software. Brought to the fore the possibility of building into ruler and compass, solutions to several problems that can be presented as algebraic expressions. Yet addressed the possibility of constructing a number, using only ruler and compass and discuss the famous and historical problems of geometrical construction: doubling the cube, squaring the circle and the trisection of the angle. We add appendices which present other possible constructions and also bring suggestions for activities with ruler and compass software. KeywordsMostrar mais Item Técnica de perturbação utilizada para solução numérica de equações do 2º e 3º graus(Universidade Federal de Goiás, 2014-10-09) Hirota, Eduardo Koiti; Borges, Romes Antonio; http://lattes.cnpq.br/3888145024042412; Borges, Romes Antonio; Stoppa, Marcelo Henrique; Junqueira, Manoel MoraesMostrar mais Phenomenon that occur in the nature are essentially nonlinear and the dynamical systems theory aims to obtain a mathematical model that best represents the real physical systems, then nothing more coherent than the description or analysis of these natural phenomenon using models and techniques. In this dissertation, the technique of direct expansion for the development of two differential equations order to solve a nonlinear equation and the approximate determination of the roots of order algebraic equation higher or equal to two, was used. For this purpose, it was initially shown the development of a differential equation of motion subjected to a nonlinear damping, which is represented by the equation of Duffing – Van der Pol. Generally, it’s not easy to obtain an approximated analytical solution for this type equation, but this study was done with the purpouse of illustrating the technique used in the work, solving type solving a problem in which these techniques are routinely used to obtain a solution. Studied for application in basic education, it presents a way to obtain the approximate roots of equations of second and third degrees, using the technique of direct expansion for the sake of comparison. Since there are formulas for resolving this, It was proved that is possible to determine the roots of high-order equations by using the same technique.Mostrar mais Item Razão áurea: como motivação ao estudo de conteúdos matemáticos(Universidade Federal de Goiás, 2014-11-19) Silva, Renato Rodrigues; Santos Júnior, Porfírio Azevedo dos; http://lattes.cnpq.br/5132806149453454; Santos Júnior, Porfírio Azevedo dos; Lemos, Glen Cézar; Galdino, André LuizMostrar mais This work goal to show a possible relationship between the Golden Ratio with nature, animals, architecture, music and also as a motivation to study mathematics content, such as: ratio, proportion and arithmetic average, making the teaching learning more enjoyable. The realization of it proceeded from the literature and field research. The literature describes the history of the Golden Mean and the Fibonacci ratio with the Golden Ratio. The Fibonacci sequence was known for the problem of pairs of rabbits (coniculorum Paia) that is found in the book Liber Abacci (Liber Abaci). Also highlights the relationship between the golden ratio and the nature, proposing that it can be widely used in daily life of the student, promoting a differentiated learning. The field research was the application of the proposed activities presented throughout the study in a rural school of the Federal District, with the purpose to promote the recognition that it is possible to understand the relationship between math and everyday living. Initially the diagnosis 1 (ATTACHMENT A), containing socio-cultural issues and also the diagnosis 2 (ATTACHMENT B) containing specific questions of reason, proportion, arithmetic mean and golden ratio was applied. After applying the diagnosis twelve o'clock classes were taught using contextualized and interdisciplinary methodologies where activities (ATTACHMENT C, D, E, F) were applied seeking to respond to the objectives of this study. In closing the interventions took place applying the same initial diagnosis in order to determine whether interventions have provided new results. In analyzing the results of the second application of diagnosis was realized a significant increase in students' understanding about the content worked. The results show that when there is an understanding of the relationship between mathematics learning and everyday life, students can define new knowledge and relate school learning and their daily lives, which facilitates learning.Mostrar mais Item Atividades lúdicas para o ensino de triangulos em aulas de geometria(Universidade Federal de Goiás, 2015-03-20) Costa, Dayanne Ferreira; Cunha, Juliana Bernardes Borges da; http://lattes.cnpq.br/5114119986465967; Cunha, Juliana Bernardes Borges da; Rodrigues, Clóves Gonçalves; Bergamaschi, Paulo RobertoMostrar mais This work aims to recognize methods and methodologies that seek remedy some di culties in the teaching and learning process in the geometry branch. These methods were applied to a class 7 year of a school on the outskirts of Federal District in 2014, and has the theme "Playful Activities for Teaching Geometry. "With this theme, a brief historical overview was presented on geometry. It then sets a study of this branch of mathematics, speci cally content and properties of triangles. Subsequently described the application site this work and the methodologies used were; concrete material and writing mathematics. Finally, the application is analyzed these methods and methodologies in room school as well as the results achieved. It is concluded that with the methodologies adopted the results were satisfactory, as the students were involved signi cantly.Mostrar mais Item Aprendendo funcoes com experimentos de fisica e atividades interdisciplinares(Universidade Federal de Goiás, 2015-04-27) Silva, Francineia Alves de Souza; Cunha, Juliana Bernardes Borges da; http://lattes.cnpq.br/5114119986465967; Cunha, Juliana Bernardes Borges da; Pinto, Raffael Costa de Figueiredo; Souza, Eduardo Sergio deMostrar mais In this paper we discuss interdisciplinary issues, seeking a better performance by students in external evaluation methods that the school is subject. In order to awaken a taste for mathematics and related sciences, an experiment was conducted with 20 high school students, an education full-time school, located in the center of Morrinhos, Goiás state. First was made an analysis of historical aspects involved in the function context and it’s basic concepts. Later described Physics contents that involve the concept of function, with methodologies for their teaching-learning process. Finally we analyzed the activities developed and concluded that the goal was achieved, as the students stood out to school too, for external evaluations, being awarded the Student Award offered by the Government of Goiás.Mostrar mais Item Matemática lúdica na educação de jovens e adultos do Centro de Progressão Penitenciária do Distrito Federal(Universidade Federal de Goiás, 2015-05-25) Cunha Junior, Lourival Carlos; Lima, Igor dos Santos; http://lattes.cnpq.br/6570549108417199; Lima, Igor dos Santos; Bessa, Vagner Rodrigues de; Gomes Neto, Veríssimo PereiraMostrar mais This dissertation aims to analyze how the use of mathematical tricks, educational games and alternative algorithms for multiplication and Division of integers contribute to learning of multiplication and Division operations between positive integers. Research participants were students of a class of adult and youth education of the 2o segment of the Central Penitentiary Progression of Distrito Federal (CPP-DF). The analysis of the results was made from questionnaires answered by the students and observations by the teacher during class. The introduction of mathematical operations took place initially by mathematical tricks, then were presented alternative ways to perform them later manipulation of new algorithms, unraveling the tricks and finally organizing with mathematical games. The participants demonstrated commitment, dedication and interest in the tricks, games and alternative algorithms. The objective of this work was achieved. We realized that there was in fact an improvement in pupils ’ learning.Mostrar mais Item Um estudo das transformações geométricas no plano via congruência e semelhança de figuras planas(Universidade Federal de Goiás, 2015-05-27) Assunção, Ricardo Gomes; Bergamaschi, Paulo Roberto; http://lattes.cnpq.br/6961717072558004; Bergamaschi, Paulo Roberto; Leandro, Bianka Carneiro; Santos Júnior, Porfírio Azevedo dosMostrar mais The aim of this paper is to study the isometries and homotheties, known geometric transformations of the plane, by means of the congruence and similarity of plane geometric figures. In order to explore and facilitate the understanding of the concepts of these two geometric transformations, some activities with congruent and similar geometric figures are proposed in a manageable teaching materials which were created for this purpose, called isometric plane, and also in GeoGebra software. These activities were applied to a first-year high school class of the Instituto Federal Goiano - Campus Uruta´ı, and some comments (observed results) about this application, they are presented.Mostrar mais Item A importancia da modelagem matematica no ensino-aprendizagem(Universidade Federal de Goiás, 2015-05-29) Renz Junior, Herton; Oliveira, Plinio Jose; http://lattes.cnpq.br/8075454624929535; Oliveira, Plinio Jose; Lemos, Glen Cesar; Borges, Romes AntonioMostrar mais This study aims to present the Mathematical Modeling as an alternative proposal for a signi cant, dynamic and e ective learning. In this sense, the favorable aspects and obstacles to teaching and learning with mathematical modeling will be cited in the course of the work. It begins the conversation with a brief overview of the rise of Mathematical Modeling in the global education and Brazil in order to understand their real importance in the current school setting. The concepts necessary for the mathematical de nition of modeling are presented in the development of work with emphasis on the phases of the Mathematical Modeling proposed by Lourdes Almeida Werle in his book Mathematical Modeling in Basic Education . The paper also describes the mathematical modeling as a tool in the teaching of mathematics, highlighting the ve steps to implement the methodology of teaching by modeling suggested by Maria Salett Biembengut and Nelson Heim, in the book Mathematical Modeling in Education . It also highlights the materialization of the Mathematical Modeling as Jonei Cerqueira Barbosa, identifying three possible cases of distribution of the modeling tasks for teachers and students. The paper describes the importance of using the classical mathematical models in the initiation of mathematical modeling activities. The mathematical model proposed by Thales to calculate the height of a pyramid, described by Johannes Hisrschberger in the work history of philosophy in antiquity, and the model of Malthus to keep up with population growth, reported by Rodney Carlos Bassanezi, are mentioned to be aware of evolution of the classic mathematical models. The proposal of the classical mathematical model to calculate areas by division into plane gures is suggested for elementary education, secondary and higher education, realizing the idea that, by adaptations, the same theme can be explored at di erent times of mathematics teaching. Finally, the work presents three activities in the classroom with high school students so that they could live in practice the importance of Mathematical Modeling in teaching and learning.Mostrar mais Item Aplicacao de determinante: area de poligono convexo e volume de piramide(Universidade Federal de Goiás, 2015-06-17) Araujo, Elismar Jose de; Freitas, Thiago Porto de Almeida; http://lattes.cnpq.br/5154082262879445; Freitas, Thiago Porto de Almeida; Leandro, Bianka Carneiro; Oliveira, Plínio JoséMostrar mais This work will concentrate on making a rereading of the theories that surround the procedures for calculating the area of a convex polygon, as well as the volume of a pyramid whose base is a polygon convex, with its vertices properly represented in a coordinate system, in the plan or in space, respectively. Addresses some topics on arrays and determinant and some of its applications, in particular the study of polygon area and the volume of the pyramid. Based on applying a decisive factor for the calculation of the area of a triangle with its vertices represented in a coordinate system, presents a new theorem to calculate the area of any polygon convex, as well as, a new formula to calculate the volume of any pyramid with convex basis as a direct application of the volume of the tetrahedron with its vertices represented in an orthogonal system. For both, it was essential to the concept of coordinates in the plane and in space, vectors in the plane and in space, and some of its properties, being essential for the demonstrate the volume of the tetrahedron and the area of the triangle, using determinant. Keywords: Volume. Area. Convex polygon. Pyramid. Triangle. TetrahedronMostrar mais