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 Análise combinatória: uma questão de lógica e linguagens(Universidade Federal de Goiás, 2013-03-01) Alvim, Karina Guerra Cardoso; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Seimetz, Rui; Vieira, Elisabeth Cristina FariaThe objective of this work is to address the Combinatorial Analysis as a theme that can be treated in the classroom, without the utilization of mathematical formulas in problem solving. For this it will presented a method of reasoning that, basing on logic and languages, underscores the importance of: To read, interpret and analyze texts that are presented in the mother tongue; Formulate conjectures, make choices and seek strategies of count; and Make the correct translation between languages maternal and mathematics. Expected to show from this approach that the Combinatorial Analysis, besides its importance in various elds of knowledge, may also be seen by students and teachers as a challenging and stimulating content.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 O uso da calculadora simples em sala de aula(Universidade Federal de Goiás, 2013-04-11) Arruda, Dilermano Honório de; Mota, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539; Mota, Jesus Carlos da; Seimetz, Rui; Smith, Ole PeterO objetivo deste estudo é apresentar uma ferramenta que todos possuem, que é fácil de carregar e que portanto tem alcance popular. Nas primeiras seções apresenta-se algumas operações matemáticas elementares executadas com uma calculadora simples. Começa-se por estudar a operação de divisão de inteiros e como encontrar o resto na calculadora, como operar com frações em uma calculadora e responder na forma de fração, como encontrar a fração geratriz de uma dízima periódica ou ainda como extrair a raíz "n-ésima"de um número real. Para cada operação destas há a preocupação de se expôr também suas devidas aplicações e, quando necessário, de se realizar estudos matemáticos mais profundos como, por exemplo, no caso das congruências módulo m nas dízimas ou derivadas para raízes n-ésima. Em iterações com a adição, por exemplo, trabalha-se o uso adequado de algumas teclas para um procedimento rápido no estudo das progressões aritméticas, juro simples e funções polinomiais do 1o grau. Já na seção de iterações com o produto, propõe-se um estudo das progressões geométricas, funções exponenciais e juro composto. Iterando com as fórmulas de Maclaurin, veremos como é possível utilizar a calculadora simples para encontrar valores das funções trigonométricas circulares e hiperbólicas, bem como os valores dos logaritmos decimais e neperianos. Esse trabalho mostra ao leitor que pelo conhecimento matemático pode se otimizar a calculadora simples, responder questões que antes os cálculos ficariam apenas indicados, ganhar tempo nos cálculos e utilizar o tempo restante para melhor elaborar a estratégia de resolução, e demais vantagens que o leitor descobrirá.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 O número de ouro e construções geométricas(Universidade Federal de Goiás, 2013-03-22) Azevedo, Natália de Carvalho de; Cruz, José Yunier Bello; http://lattes.cnpq.br/8377200040018415; Cruz, José Yunier Bello; Seimetz, Rui; Martins, Ivonildes RibeiroThe golden number and its geometry remote from Ancient Greece. The golden number is a real number that can be represented geometrically by dividing a segment in extreme and mean ratio. It is related to the act of determining a point C on a segment AB in order to obtain equal ratios between AB : AC and AC : CB. Its value is obtained by numerical solution of the quadratic equation obtained from this equality. From ruler and compass constructions of the golden mean other geometric constructions are made: triangles, rectangles, pentagons and spirals. The golden number has been present in arts, architecture and nature for years, and it presented in this work as a tool for study, focusing on presentation to high school students.Item Concepção, organização e realização de olimpíada interna de matemática, em tempos de ensino remoto(Universidade Federal de Goiás, 2021-12-21) Barbosa, Marco Antônio; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Rodrigues, Eunice Cândida Pereira; Souza, Mário José deThe aim of this thesis is to analyze the implementation of a Mathematics Olympics in a private school in the city of Goiânia, Goiás. Considering the COVID-19 pandemic and having Olympic competitions like the Goiás State Mathematics Olympics (OMEG) and Public Schools’ Brazilian Mathematics Olympics (OBEMEP) canceled, which were influential in the weekly training sessions, motivated the coordination to suggest the challenge of creating and implementing a competition associated to the school itself. The project has been developed between the years 2020 and 2021, 2021 being the second edition and having students from the latter years of middle school (6th to 9th grade) as participants. The classes were held remotely, consisting of two classes per week, through zoom.us and the tests, both for the first and the second round, were held on a specific platform belonging to the school. The preparation followed the specifications of OBEMEP regarding both educational content and the specifics of the test for the first and second round. The classes have been developed in accordance with the National Common Curriculum Base (BNCC), which defines the regulatory compliance meant to achieve the essential educational objectives supposed to be developed during the basic education period, and inspired in the problem-solving methodology. The process described includes all stages from its original idea to prizes. Worth mentioning are classes and references, the challenges encountered in dealing with a remote class system - until then unknown to Basic Education, the promptness of the work ensured by the Mathematics department and the success of the students, who were dedicated to studying mathematics, in spite of the difficulties stemming from the pandemic. Furthermore, this paper hopes to inspire Mathematics teachers from Basic Education to implement in their own schools internal competitions which promote commitment to studying and the dissemination of mathematics and Olympic competitions.Item Uma análise sobre as novas modalidades de financiamento imobiliário(Universidade Federal de Goiás, 2020-06-16) Barra, Willian do Amaral; Lemes, Max Valério; http://lattes.cnpq.br/6512955169729670; Lemes, Max Valério; Moreira, Fernando Ricardo; Lourenço, Kélem GomesThis dissertation presents a discussion on the importance of Financial Mathematics and Financial Education in relation to practical everyday situations, such as when contracting real estate financing. In August 2019, a decision by the National Monetary Council changed the rules for contracting real estate financing, with this, new financing modalities emerged. We will perform some simulations of real estate financing comparing the current modalities, assessing the advantages and disadvantages of the credit lines offered. To support the discussions on financing, we will present some concepts and examples related to financial mathematics, such as interest rates, compound capitalization system, uniform series and amortization systems. Concepts and laws that regulate the real estate financing system will be presented in order to assist the reader in making strategic decisions.Item Números binomiais: aplicações ao ensino e extensões(Universidade Federal de Goiás, 2021-08-24) Barros, Gabriella da Silva; Vargas, Tiago Moreira; http://lattes.cnpq.br/1884655261136497; Vargas, Tiago Moreira; Vargas Júnior, Valdivino; Lima, Thaynara Arielly de; Belisário, Hugo Leonardo da SilvaIn this work, we approach the binomial coefficients, which are seen in basic education in the 2nd grade of high school, when students are presented with the contents of combinatorial analysis. When binomial coefficients are presented, students study the definition and emer-gence of these coefficients in the Triangle of Pascal and Newton’s Binomial. In order to expose the binomial coefficients, we present and demonstrate some of their relevant properties and some of their extensions. Initially, we present the counting principles, after exposing the defi-nition of the binomial coefficients and their properties, we also present the relationship of these coefficients with the Fibonacci sequence and the Lucas Theorem. In addition, we pro-pose some activities that can be used by the high school mathematics teacher that use the bi-nomial coefficients as well as their properties. We finish with a construction of the Pascal Tri-angle and the development of the Newton Binomial in the Geogebra that can be used by the teacher during the presentation of these contents.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 Geometria de Moulton x geometria euclidiana: trilhas de aprofundamento para o ensino médio(Universidade Federal de Goiás, 2023-03-24) Borges, Charlles de Morais; Smith, Ole Peter; http://lattes.cnpq.br/9938244088922275; Smith, Ole Peter; Silva, Geci José Pereira da; Souza, Flávio Raimundo deWith the advent of the approval of the National Common Curriculum Base for Secondary Education - BNCC, which brings learning based on Skills and Competences, and made the content no longer the protagonist of the teaching-learning process, this is what the present work addresses . For this, we present a little of the trajectory of this BNCC homologation process, its main paths and resolutions. We present how this Base was structured, enunciating the expected Skills and Competences, as well as proposing an educational product in the form of a Deepening Track in Mathematics, for the student's formation. The purpose of the deepening trail proposed here is to present the model of geometry proposed by Moulton, as a way of provoking a comparison with the geometry proposed by Euclid, evidencing the existence of other geometries, the so-called non-Euclidean geometries that, in most cases , are not introduced to students until the end of high school. Thus, through skills already acquired in Elementary School in relation to the study of Plane Geometry, lead the student to review already known concepts and propose challenges, so that through scientific research, he can further develop his skills and competences that lead them to propose solutions and conjecture new ideas about the proposed subject. We begin with a presentation of primitive concepts and postulates of the Euclidean model, and then we present primitive concepts of the model proposed by Moulton. We show how its structure was defined for the plane, the behavior of straight lines and their equations, how to calculate the distances between two points and also how to determine the measure of angles between straight lines. For this, we make use of Cartesian Geometry, structured by René Descartes, as a link in the comparison between these two models. The concepts to be worked on are already well known in Euclidean Geometry and, from this other model, we are going to show some of the transformations and modifications undergone by these classic figures of Plane Geometry, namely: parallel and perpendicular lines, the triangle and its notable elements , circle, ellipse, parabola and hyperbola. With the intention of making a broad initial exploration of the transformations and modifications undergone by these figures, we will also present the step-by-step of a constructive process of some conics, using dynamic geometry software, in this case, Geogebra, in order to also develop computational and programming skills, which are expected in the new National Base.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.