Mestrado Profissional em Matemática em Rede Nacional (IME)
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Item Lançamento oblíquo: uma abordagem matemática(Universidade Federal de Goiás, 2016-03-31) Almeida, Francisco Fabio Monteiro de; Lima, Lidiane dos Santos Monteiro; http://lattes.cnpq.br/3020743359147341; Lima, Lidiane dos Santos Monteiro; Lima, Thaynara Arielly de; Souza, Flávio Raimundo deThe main goal of this work is to verify that we can assign the oblique launch a mathematical approach. To reach this conclusion, we address important issues of mathematics and physics, as linear functions and quadratic functions , and uniform and uniformly varied movements. These concepts were presented to facilitate understanding and implement an equation that allows to determine the moment of rise, the maximum height and horizontal reach, knowing an shot's angle, the initial velocity and gravity's acceleration.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 Tomada de decisões e o aprendizado de matemática financeira: uma experiência com aplicativos para smartphone(Universidade Federal de Goiás, 2018-10-05) Amim Júnior, Jair Elias; Faria, Elisabeth Cristina de; http://lattes.cnpq.br/5007480938176936; Faria, Elisabeth Cristina de; Vargas Júnior, Valdivino; Moraes, Moema GomesThe present work was a technical report that introduced the course and the results of the investigate work accomplished in the Professional Mathematics Master’s Program in National Network (Profmat). I proposed a method of teaching Financial Mathematics focused in the use of financial applications for smartphone, having as main objective to verify the students' development in relation to the made decisions in situations that are offered to them the possibility to choose the applications to assist in the resolution of problems. As main benchmark was used the heuristics of problem solving proposed by George Polya (1995), the use of smartphones and Applications as Pedagogic tools, according to Voltolini (2016) and Soares (2016): the creating of a virtual learning environmoent, according to Shitsuka (2012), and the critic mathematics education associated with resolution of problem, according to Skovsmose (2000). From the application of the method it resulted an electronic textbook of studies as education product, whose title is "Financial Mathematical with Use of Applications for Smartphone." Aimed for teachers of the Basic Education, the electronic textbook has theoretical summaries and links for the resolutions of the exercises in videos posted on YouTube. A qualitative research was carried out in four meetings, and the instruments of data collection were questionnaires, record sheets and videos captured by the participating students themselves. This allowed to observe the capacity of the students' autonomy in the choice of the applications. The critical glance that they developed when analyzing interest rates and options of payments, serves with foundation for the construction of a financial education to be used in daily routine.Item Introdução à análise convexa: conjuntos e funções convexas(Universidade Federal de Goiás, 2013-03-18) Amorim, Ronan Gomes de; Cruz, José Yunier Bello; http://lattes.cnpq.br/8377200040018415; Sandoval, Wilfredo Sosa; Cruz, José Yunier Bello; Pérez, Luis Román LucambioThis paper presents the main ideas concerning convex sets and functions. Our aim is to deal, didactically, with the main topics concerning convexity, as well as the consequent exploitation of the envolved mathematical concepts. In this sense, we have made a bibliographic revision approaching important theorems, lemmas, corollaries and propositions designed both to first readers and to those who want to work with applications arising from convexity. We hope that this study may constitute an important research source either for students, teachers or researchers who wish to learn more about convex sets.Item A matemática da educação financeira(Universidade Federal de Goiás, 2016-08-07) Andreatini Neto, Alessandro; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Souza, Flávio Raimundo de; Lima, Thaynara Arielly deThis paper aims to promote a re ection about the didactic potential interfaces between nancial education and math content covered in high school through a course of nancial education. O rst course module presents a tool to organize spending so systematic . In the second module discusses the di erent types of loan and credit. The third module has been the most common investments and how they workItem Geogebra como recurso facilitador do processo de ensino-aprendizagem de curvas planas(Universidade Federal de Goiás, 2018-05-07) Araújo, Cláudio Lourenço; Smith, Ole Peter; http://lattes.cnpq.br/9938244088922275; Smith, Ole Peter; Pina, Romildo da Silva; Silva, Silvia Cristina Belo eThe objective of this work is to contribute to the teaching-learning process of planas curves, in high school as wellas in higher education. To achieve this goal, we present the concepts, de_nitions and studies of planas curves, addressing algebra and geometry through Geogebra Software. Using this tool, we will approach mechanically generated curves (roulettes) and discuss some concepts. The theme provides us with a re_ection on the use of Geogebra software as a facilitating tool in the teaching-learning process. The possibility of being able, on a single screen, to analyze the algebraic and geometric behavior of planas curves contributes to the construction of mathematical knowledge. To this end, we will conduct a brief discussion on the use of Geogebra Software in teaching. Then we will present the main concepts of _at curves such as parameterization, tangent vector, normal vector, Frenet system, arc length, reparametrization, curvature, evolute and involute. In the discussion of all these concepts, Geogebra is present, in order to assist in the discussion and to show the possibilities of its use. Finally, we discuss a proposed activity in the classroom.Item Refletindo sobre os números complexos - da sua história às suas aplicações(Universidade Federal de Goiás, 2019-03-25) Assis, César Lopes de; Santos, Maria Bethânia Sardeiro dos; http://lattes.cnpq.br/9592720615600301; Santos, Maria Bethânia Sardeiro dos; Silva, Jhone Caldeira; Souza, Flávio Raimundo deThe present work aims is to increase the knowledge of teachers and students on the complex numbers, highlighting their importance in the study of geometry, trigonometry and providing a perspective on their construction and concepts. Initially, we present the reasons for choosing the main theme of the work, complex numbers. The, the reader will find data obtained with a reserch with secondary and higher education teachers, on the importance of studying complex numbers. Subsequently, historical facts that were relevant in the process of evolution of complex numbers. The paper also presents the theories of Gauss and Argand, and addresses the idea of complex numers and their representation on the Cartesian plane. In the end, relevant aspects of the correspondence are between complex numebers, trigonometry, and analytic geometry. The work is intended to lead the reader to reflect on the methodologies for teaching content and the impacts of these methods on student learning.Item Ensinando Geometria Plana na EJA(Universidade Federal de Goiás, 2018-11-20) Azevedo, Luciano Bráulio Caetano de; Lima, Lidiane dos Santos Monteiro; : http://lattes.cnpq.br/3020743359147341; Santos, Maria Bethania Sardeiro dos; Souza, Flávio Raimundo deThis work is aimed at showing that the teaching of Flat Geometry at Young People and Adults Education can be done in a pleasant way, so that students may have interaction with Geometry, applying its concepts in their daily lives. Initially, we dened the concepts of Flat Geometry focusing on: Angle, triangles and Special Quadrilaterals. Then we inserted a chapter to talk a little about EJA * legislation and nally we introduced a didactic sequence with the goal of connecting the Theoretical Part with the Practical Part.Item Representações em matemática: observações para o ensino e a aprendizagem em geometria(Universidade Federal de Goiás, 2016-04-25) Bastos, Charles Lourenço de; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Souza, Mário José de; Rodrigues, Eunice Cândida PereiraThis work observations are made about some ways in which it is possible to teach and learn geometry through the representations. For this, we treat the mathematical language, understanding of the modes of representation and the teaching of geometry combined with other areas of Mathematics in Basic Education. The literature search included a brief study of geometry teaching in the public schools, exploring the presence in textbooks of history of mathematics, problem solving and representations. We note also, some of my teaching practices that relate dierent ways of representing and representations through real objects and computing resources.Item A teoria elementar dos inteiros de Gauss(Universidade Federal de Goiás, 2019-11-08) Batista, Paulo Henrique Alves; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Rodrigues, Paulo Henrique de Azevedo; Veras, Daiane Soares; Dias, Ivonildes Ribeiro MartinsThis work refers to the importance of the arithmetic properties of the integers in the comprehension of the abstracts structures as Gauss integers Z[i] subset of complex numbers(C) a alarm information is the little relevance that this topic receives by math teachers of elementary school, This research is a bibliographic work in order to promote a theoretical survey by the main results which are around the sts Z and Z[i], This work has the intention of mobilise the math teachers who might have math dominium on Z arithmetic properties, because they will give them the possibilities to estabilish a parallel between Z and Z[i] and consequently to describe the equalities and differences between the analysed structures, The research was divided in three chapters, Initially were exposed the main results referents to the set Z and a priori of properties that will be valid to the set Z[i],then it will be done a detailed approach about the characteristics of Z[i] and a suggestion of math application of Z[i] that could be developed at the elementary education, in high school third grade concerning to the determination of all possible Pythagoras theorems derived from a value previously fixed to the hypotenuse right triangule , During al the work its visible the intense search on a strict mathematical achieved by intentional form, in order to promote to the math teachers the opportunity if knowing or deepen the math knowledges through other abstracts structures, in this case the set Z[i].Item O efeito transformador das atividades lúdicas nas aulas de matemática(Universidade Federal de Goiás, 2014-09-26) Bispo, Leandro Pinto; Chaves, Rogerio de Queiroz; http://lattes.cnpq.br/2029572406153004; Chaves, Rogerio de Queiroz; Silva, Sílvia Cristina Belo e; Santos, Maria Bethânia Sardeiro dosThis work aims to analyze the results of the use of challenges and tricks based on mathematical principles as a motivational method in high school classroom. The activities contain elements that help to improving concentration, stimulate thinking ability, arouse interest in mathematics classes and thus increase participation of the students in the classroom. Each activity is described in detail, including a summary of its mathematical content, the average classroom time required, as well as a suggestion on how to perform it in class. Besides the direct assessment of the results by the teacher, a more objective evaluation of the e ects of these activities on the student's perception and attitude towards mathematics and its study was made by means of questionnaires answered by the students before and after the development of the project. Analysis of the data from the answers is also presented.Item Equações diofantinas lineares em duas incógnitas e suas aplicações(Universidade Federal de Goiás, 2013-03-01) Borges, Fábio Vieira de Andrade; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Rodrigues, Paulo Henrique de Azevedo; Seimetz, Rui; Oliveira, Ricardo Nunes deThe main objective of this assignment is to help students and also teachers with the resolution and understanding of problems involving the Linear Diophantine Equations with Two Incognits through the elaboration and application of didactic activities in order to contribute to the study of this kind of equations. Through the tasks it was aimed to dothe integration of Arithmetic with Algebra and Geometry by using some computational programs which worked as support to the graphical visualization of the entire solutions. In the first chapters the essence of the Elementary Theory of Numbers will be better known, since the mathematical tools which will be used to solve linear Diophantine equations will be displayed and demonstrated, some of them already known, like the greatest common divisor (g.d.c). Then the Diophantine equations and theirapplication methods for the solution of daily problems will be introduced. The Conclusion of this study highlights the importance of algebraic and geometric interpretation of Linear Diophantine Equations, and also emphasizes that the contact with problems of this area contributes to the students reasoning abilities development in a creative way. It is important to emphasize that this issue can be introduced in high school.Item Modelagem matemática no ensino de trigonometria(Universidade Federal de Goiás, 2020-03-10) Borges, Leila Bernardes; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Silva, Jhone Caldeira; Assis, Aline Mota de MesquitaTrigonometry, being one of the branches of mathematics that it developed for needs especially in the field of navigation and astronomy, it is still today considered by students and teachers, as an abstract content, full of formulas to be memorized and difficult to apprehend. This proposal seeks to develop teaching in this area of mathematics, in particular the concept of sine and cosine, emphasizing the transition from the right triangle to the trigonometric circumference, so through Mathematical Modeling as a teaching strategy.Item Jogo do par ou ímpar(Universidade Federal de Goiás, 2014-07-03) Borges, Pablo dos Santos; Vargas Júnior, Valdivino; http://lattes.cnpq.br/1795859800919467; Vargas Júnior, Valdivino; Souza, Flávio Raimundo de; Diaz, Mário Ernesto PiscoyaThe following work was carried out over the game of odd or even. By exploring this game, we analyze a dispute between two players, one being a strategist and another layman. In the rst part were successive bets, in which the strategist had advantage over the layman. Then play until someone stay without money. The methodology is investigative and directed by activities that seek to show the importance of this knowledge in cognitive training of the student, giving it a theoretical re ection on the practice experienced and stimulating logical reasoning mathematical experiences. The work was divided into parts. Before starting the detail work, we use a theoretical basis directed to Game Theory and Probability. In the course of this, we present the relevant problems of work results. Shortly following section, we have four draft classes using the game of odd or even. One of which was performed at the High School students.Item Resolvendo os cubos prisioneiros(Universidade Federal de Goiás, 2015-03-27) Borges, Robinson; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Seimetz, Rui; Dias, Ivonildes Ribeiro MartinsThis work shows how an educational toy (game) can stimulate the teaching of mathematics. This game becomes a starting point for several discussions, is a pedagogical tool that relates to concrete, direct and simple way, various parts of mathematics. This is a game easy to use, easy to manufacture and which favors the systematization of logical reasoning. By using this teaching tool the student is required to take decisions and also notes that every decision has implications in the upcoming decisions. The desired solution is obtained with the aid of a spreadsheet. We work with a general case and for that we used twenty-four variables. To reach the desired solutions toy was converted into codes, axes were used as directions and guidelines senses them, counting rule, application of the fundamental theorem of arithmetic and foundations of probability.Item Números primos: pequenos tópicos(Universidade Federal de Goiás, 2013-03-15) Carvalho, Glauber Cristo Alves de; Melo, Maurílio Márcio; http://lattes.cnpq.br/9171320863927413; Melo, Maurílio Márcio; Medino, Ary Vasconcelos; Cruz, José Hilário daThis paper presents a brief history about the numbers. After some important definitions to understand the texts. Following, we encounter the world of prime numbers. This part is presented some important properties, findings and open problems. The study of these figures have managed to find some formulas to generate them, which are presented throughout the text. It presents some numbers especias such as Fermat primes, Mersene, Shopie German and others. Finally, we have an application that uses many properties presented.Item Cálculo das fórmulas de Euler e Pick no geoplano e no GeoGebra(Universidade Federal de Goiás, 2016-12-09) Carvalho, Wesley da Silva; Vieira, Ewerton Rocha; http://lattes.cnpq.br/9011778118531233; Vieira, Ewerton Rocha; Lourenço, Kélem Gomes; Souza, Flávio Raimundo deIn this dissertation, we first state Euler's polyhedral formula for a set of points with Euler characteristic 2. We address the two known ways to prove Euler's Theorem: beginning with the classical proof by using Euclidian Geometry and afterwards we take the advantage of Spherical Geometry to give another proof. Furthermore, we address a version of Euler's formula for planar polyhedron, as well as, Pick's formula and the equivalence between Euler and Pick's formula. In the end, we provide application of Euler and Pick's formula, via two pedagogy tools Geoplano and GeoGebra, by giving examples to teach in classroom.Item Aritmética com Python(Universidade Federal de Goiás, 2018-10-11) Cavalcante, Rogério da Silva; Lima, Thaynara Arielly de; http://lattes.cnpq.br/3324489027928883; Lima, Thaynara Arielly de; Rodrigues, Eunice Cândida Pereira; Smith, Ole PeterWe aim to show how effective the technological resources can be when used for teaching. We chose to use the Python programming language in mathematics teaching, specifically arithmetic, showing how logic moves naturally between computing and mathematics, thereby showing a natural interdisciplinarity between these subjects. We propose programs built from the demonstrations of some classic results of arithmetic, aiming to integrate the teaching of these results to the teaching of basic tools of a programming language.Item Introdução à teoria ergódica de bilhar(Universidade Federal de Goiás, 2019-09-16) Coenga, Thiago Marcel Duarte; Alarcon, Eduardo Arbieto; http://lattes.cnpq.br/5960048699820842; Alarcon, Eduardo Arbieto; Hall, Bryon Richard; Ferreira, Júlio CésarThe work aims to describe the movement of a particle inside a pool table through a billiard application and to determine a formula for varying the motion of that particle. Another objective was to show the application of this knowledge in basic education.Item A história da matemática como estímulo ao ensino-aprendizagem(Universidade Federal de Goiás, 2016-12-07) Costa, Cleomar Luiz da; Lourenço, Kélem Gomes; http://lattes.cnpq.br/6219440124523685; Lourenço, Kélem Gomes; Lima, Thaynara Arielly de; Vasconcelos, José Eder Salvador deMathematics accompanies man since the beginning times and it is present in most everyday activities. It’s considered a difficult discipline to understand, many people get away, instead of seeking for ways to allow the interest for its study. Usually the mathematics teacher comes across students who have difficulty to assimilate mathematical content, as those who have an aversion to discipline. Therefore, the teacher must look for ways to motivate his students and the history of mathematics is considered by experts as an effective source to arouse such interest. In this sense, this work aims to demonstrate how the use of history of mathematics can help the teacher to stimulate the student's appreciation for this study. This is a literature review whose main method was a literature research with the National Curriculum Parameters of high school and elementary school, to specialized books on the subject, and the articles, dissertations and theses published on the internet. Amid numerous mathematical contents taught in secondary and fundamental education, this study highlighted nine of them, considering them more present in the daily lives of those who study or not study mathematics. The contents were: basic concepts, count, number, algebra, basic operations, sets, fractions, geometry and functions. The study concluded that when using the history of mathematics as a teaching resource, the teacher wakes up students’ interest and curiosity, becomes classes more dynamic and engaging, and these possible discoveries, besides historic rescue, the importance of each mathematical content as a facilitator of everyday life. However, it is necessary that the teacher seek knowledge for this, and this work has also the objective of providing support for those who seek this information.