Mestrado Profissional em Matemática em Rede Nacional (IME)
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Navegando Mestrado Profissional em Matemática em Rede Nacional (IME) por Por Orientador "Dias, Ivonildes Ribeiro Martins"
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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 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 Teorema de Napoleão: origem, demonstrações e aplicações(Universidade Federal de Goiás, 2015-08-06) Gonzaga, Gean Carlos Sousa; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Silva, Sílvia Cristina Belo e; Lourenço, Kélem GomesThis paper addresses the theorem of Napoleon on historical, conceptual perspectives, and focusing on demonstrations and applications properties as well. In the rst chapter, are discussed aspects of the history and Napoleon Bonaparte biography. In the second chapter are addressed notions of Plane Geometry, Linear Algebra, of Rigid Transformation of Complex Numbers and Related Transformations. In the third chapter, statements are presented, generalizations (especially the so-called Barlotti Theorem), properties and applications in exercises.Item Uma aplicação web como recurso didático em aritmética(Universidade Federal de Goiás, 2020-03-13) Lima, Felipe Viterbo de; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Leandro, Bianka Carneiro; Lima, Thaynara Arielly deIn this work, we aim to show the efficiency brought by a given web application that was developed with the purpose of serving as a pedagogical resource, in the mathematics teaching, specifically arithmetic. The conclusions of the present study come from the analyzes carried out and the results obtained during the period of experimentation of this application. Here will be described in detail the functionalities existing in this software, how it was disseminated and how the evaluation made by its users will also be presented. In order to have a good understanding of the mathematical context involved in this dissertation, it is worth mentioning that its target audience is composed of students and teachers who already have knowledge of the main basic concepts related to the arithmetic theory of numbers.Item Criptografia(Universidade Federal de Goiás, 2015-08-06) Mata, Tulio Fernando da; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Silva, Sílvia Cristina Belo e; Lima, Thaynara Arielly deThis paper makes a brief reading on the crisis experienced by the mathematics education in Brazilian public schools in recent years, analyzing some of the reasons and motives of this crisis and trying to point out ways that this teaching will become better, more e cient and above all presenting mathematics as a fundamental importance for today's world science, pointing their applicability in everyday situations that may arouse the interest of students and present themselves as challenges to their ability to think and learn. In order to show the applicability and the importance of mathematics shows the encryption, if elected as a basis for analysis the cryptographic method RSA, one of the most widespread throughout the world, to present it as a tool that uses mathematical algorithms to encoding and/or decoding of data, enabling the protection and con dentiality of sensitive information transmitted via satellite in commercial and banking transactions. The paper presents the general importance of cryptography in the context of a globalized and technological world of today, as well as within the story, noting even its decisive contribution to the Allied victory against the Germans in the 2nd World War. It presents also the mathematical basis for encryption, prior knowledge of mathematics that are used to encrypt messages and or data, and presents examples of encoding and decoding simple messages. Finally, a general approach on the encryption is done, since its concept and common de nitions, pointing secured requirements for its use and the main types of algorithms for encryption and decryption codes, also called cryptographic keys.Item O mistério e a beleza dos números primos(Universidade Federal de Goiás, 2017-12-14) Mota, Karla Valéria Caldas; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Lima, Thaynara Aryelly de; Adorno, Ticiane Proença BuenoIn this work, we address one of the most instigating subjects in mathematics: prime numbers. The purpose of this is present the history of prime numbers, their applications, curiosities and thus, to stimulate educators and learners about its importance.Item Equações polinomiais: da equação de 1º grau à teoria de Galois(Universidade Federal de Goiás, 2017-05-30) Oliveira, Daniell Ferreira de; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Souza, Mário José de; Souza, Flávio Raimundo deThis paper aims to improve the understanding of Mathematics teachers regarding the solution of polynomial equations by means of radicals, focusing on the theory of Galois. The reader _nd in this document a little of Galois's life story, radical resolutions of degree n 4 equations, group, ring and body theories, as well as Galois Theory.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 Geometria analítica: estudo da reta e da circunferência, uma abordagem vetorial como proposta de ensino para alunos do ensino médio(Universidade Federal de Goiás, 2015-08-06) Silva, Sidival; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Silva, Sílvia Cristina Belo e; Lima, Lidiane dos Santos MonteiroAccording to studying of vectors [1], straight and ats are considerable useful to the students of the last year in high school, mainly those who wish to attend Engineering, Physics, Mathematics or Chemistry. This present paper has as its main focus the study of the straight and of the circumference under a vector approach. Initially the necessary vectors concepts are introduced so the subject can be comprehended under de nitions and propositions, so the reader (high school's student) take ownership of the vector's ideas in plan and space and, above all, understand all the main vectors' properties, with which will be de ned the equations of the straight and of the circumference. It introduces the de nition of the equipolency given by Giusto Bellavitis see it at [2] (that is basically the vector's de nition that is known nowadays) and also the de nition of linear dependence and independence, angle between two vectors, opposite vectors and internal product. It is also observed that all de nitions and mentioned properties in the plan are valid in space R3. Finally it is de ned the straight's equation (using the idea of product by scale) and, the circumference equation (using the rule de nition).Item A ruptura entre o ensino de Matemática nos níveis básico e superior e a adoção de uma perspectiva contrária para a sua minimização(Universidade Federal de Goiás, 2019-12-16) Tomé, Ricardo; Dias, Ivonildes Ribeiro Martins; http://lattes.cnpq.br/8664599889120339; Dias, Ivonildes Ribeiro Martins; Rodrigues, Eunice Cândida Pereira; Silva, Jhone CaldeiraAs a teacher in Basic Education, for over 12 years, for along time, I tried to justify the contents I taught, from the yours contextualizations. However, I realized that to understand mathematics it would not be enough to contemplate it only by observing its presence in our daily lives, since Mathematics itself as a human creation is far beyond this limitation, since it deals with subjects that are only justified by its usefulness, within Mathematics itself, and that are unquestionably relevant to its own development. Thus we proposed to conduct a discussion that argued for the inclusion of aspects of Scientific Mathematics in the teaching of Mathematics in Basic Education. Therefor we, seek to discuss current education and some of its elements, to show that initiatives are being developed in this sense, specifically, some OBMEP projects, as well as to try to understand past situations in which this same perspective was adopted, even claiming what they called “modernization of Mathematics teaching”.