# Programa de Pós-graduação em Matemática - PPGM

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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 Abordagem analítica e numérica de técnicas de otimização baseadas na redução de intervalos de incerteza(Universidade Federal de Goiás, 2015-06-30) Smidi, Ali Ahmad; Borges, Romes Antonio; http://lattes.cnpq.br/3888145024042412; Borges, Romes Antonio; Lemos, Glen Cézar; Queiroz, Thiago Alves deMostrar mais In thisstudy,wesoughttopresentanintroductiontonumericaltechniquesaimedto optimize accessibleelementaryproblemstothestudentsofsecondandthirdyearofhigh school.TheoptimizationtechniquesdiscussedinthisworkweretheFibonacciandthe Golden Sectionmethods.Theworkpresentsanddoesmathematicaldescriptionofsuch techniques,fromaninitialknowledgeandbuildingmethodsinquestion.Inaddressinga real problem,weattemptedtointroducetheinterpretationandmathematicalmodeling of theproblemaswellasitssolutionsanalyticallyandnumerically,usingsoftwares simple touse.Inthisregard,itcanbestatedthatthepresentworkprovidesdidactical approachofmainunimodaloptimizationtechniquestoreduceuncertaintyinterval.Mostrar mais Item Uma abordagem matemática no ensino de cálculo estequiométrico(Universidade Federal de Goiás, 2021-03-08) Andrade, Leandro Mendes de; Cunha, Juliana Bernardes Borges da; http://lattes.cnpq.br/5114119986465967; Cunha, Juliana Bernardes Borges da; Santee, Donald Mark; Silva, Ricardo Souza daMostrar mais The present work is a proposal of didactic sequence, with the objective of minimizing some difficulties that the students present when there is interdisciplinarity between Mathematics (basic) and Chemistry, specifically the teaching of stoichiometry. In it we approach the teaching-learning of stoichiometric calculus, working the definitions and mathematical concepts, on the balance of chemical reactions. To try to remedy the difficulties in this content, we initially applied some activities as a survey of knowledge. Then, an intervention proposal was presented and shows an application of Mathematics in Chemistry, which can contribute to the teaching of stoichiometry and basic Mathematics, showing them the importance of studying these subjects and motivating them to teach mathematical concepts that can give them a solution to different problems.Mostrar mais Item A abstração da função exponencial de interações entre engrenagens lego®(Universidade Federal de Goiás, 2020-04-09) Costa, Cristhian Pires da; Silva, Fernando Kennedy da; http://lattes.cnpq.br/8313547891856943; Silva, Fernando Kennedy da; Barbosa, Fernando da Costa; Alves, Deive BarbosaMostrar mais In this paper, the central theme is the abstraction of the exponential function and the exponential type of interactions between gears in the LEGO® Mindstorms NXT Kit. Through the construction of a cart using parts of this kit, was found that it is composed of a 4-speed gearbox, which works with an exponential rate of change. The motivation of this paper was to discover whether it would be possible or not to abstract this function, based on interactions between gears, that in the great majority, are associated only with the proportionality issues and, consequently, with linear functions. With analyzes and studies made based on materials already produced, both on interactions between gears, and on gear shifts made of LEGO® parts, we were able to do the construction of the proposed gearbox. For this, we use gears reductions of spins, which in sequence was able to create a geometric progression, which was associated with the exponential type of function. Thus, this gear is used as an study object of a didactic sequence and of contents, both with regard to its construction (detailed in the didactic sequence) and as to its functioning (explored in the form of exercises). The sequence, as an objective of assisting the teacher in teaching the exponential function is based on the Zabala’s (1995) theory, which is based on Piaget's constructivist conceptions (1978) on the cognitive process construction of knowledge. Based on the choice of using gears and educational digital technologies, through educational robotics, we bring the guidance of Saymon Papert (1985), author of the constructionist theory. And with the positive result of this work, it was possible to see the great mathematical arsenal existing in the interactions between gears, which, when associated with Educational Robotics, allows to fully work on the integral development of the students, by relating in the execution of their activities, in a simultaneously way, such as concepts, procedures and attitudes.Mostrar mais Item A álgebra dos complexos/quatérnios/octônios e a construção de Cayley-Dickson(Universidade Federal de Goiás, 2016-08-30) Santos, Davi José dos; Silva, Fernando Kennedy da; http://lattes.cnpq.br/8313547891856943; Santana, Fagner Lemos de; Galdino, André Luiz; Silva, Fernando Kennedy daMostrar mais This research with theoretical approach seeks to investigate inmathematics, octonions,which is a non-associative extension of the quaternions. Its algebra division 8-dimensional formed on the real numbers is more extensive than can be obtained by constructing Cayley-Dickson. In this perspective we have as main goal to answer the following question: "What number systems allow arithmetic operations addition, subtraction, multiplication and division? " In the genesis of octonions is the Irish mathematician William Rowan Hamilton, motivated by a deep belief that quaternions could revolutionize mathematics and physics, was the pioneer of a new theory that transformed the modern world. Today, it is confirmed that the complexs/quaternions/octonions and its applications are manifested in different branches of science such as mechanics, geometry, mathematical physics, with great relevance in 3D animation and robotics. In order to investigate the importance of this issue and make a small contribution, we make an introduction to the theme from the numbers complex and present the rationale and motivations of Hamilton in the discovery of quaternions/octonions. Wemake a presentation of the algebraic structure and its fundamental properties. Then discoremos about constructing Cayley-Dickson algebras that produces a sequence over the field of real numbers, each with twice the previous size. Algebras produced by this process are known as Cayley-Dickson algebras; since they are an extension of complex numbers, that is, hypercomplex numbers. All these concepts have norm, algebra and conjugate. The general idea is that the multiplication of an element and its conjugate should be the square of its norm. The surprise is that, in addition to larger, the following algebra loses some specific algebraic property. Finally, we describe and analyze certain symmetry groups with multiple representations through matrixes and applications to show that This content has a value in the evolution of technology.Mostrar mais Item Análise da avaliação diagnóstica da aprendizagem do estado de Goiás: um olhar sobre a área de matemática(Universidade Federal de Goiás, 2018-10-31) Rabelo, Fabiano Barros; Borges, Marta; http://lattes.cnpq.br/6407324517825514; Borges, Marta; Bergamaschi, Paulo Roberto; Santana, Fabiana Tristão deMostrar mais The application of large-scale evaluations has undoubtedly become part of the school routine. It is inherent in the teacher's job to prepare the students and analyze their results. This research analyzed the application and evaluation of the results of one of these evaluations: The ADA: Diagnostic Learning Evaluation, promoted by the Secretaria de Educação do Estado de Goiás, in a public school. Considering that the result of this evaluation shows the need for changes in teaching plan in Mathematics in high school and that planning is essential for the teaching activity, the questions analyzed were: How ADA results reflects the teacher's tasks in the classroom and the plan made by mathematics teachers? What actions to improve learning means could be identified based on the results of the ADA? What contributions have the actions taken produced for the improvement of the teaching and learning process of Mathematics? Therefore, a qualitative case study research was conducted through interviews with four participants: a mathematics teacher, a school coordinator, and servers of the Secretaria de Educação Estadual, as well as documentary research on the results of this evaluation. The analysis of the data obtained was done through the construction of an axis of analysis and categorization, through emerging categories such as test questions, application of the Theory of Responses by item (TRI), the results achieved and the teacher training to deal with these results. The means lead us to reflect on the goals of this type of evaluation, emphasizing its objectives and the results obtained, as well as the entire application process, considering the interviewees’ point of view.Mostrar mais Item Análise da função quadrática, com ênfase em seus coeficientes, via GeoGebra(Universidade Federal de Goiás, 2016-10-31) Xavier, José Fábio; Bergamaschi, Paulo Roberto; http://lattes.cnpq.br/6961717072558004; Bergamaschi, Paulo Roberto; Ribeiro, Márcio Roberto Rocha; Junqueira, Manoel MoraesMostrar mais The high school is the final phase of young people in basic education, and at this age are going through the same changes in their lives that will be huge. They live in a highly technological society and study in a school in the last century format. In this work the focus was on when addressing the issue of Quadratic Functions, seen in the first year of high school, to use technology as a motivating element of the teaching and learning process. In the lecture of this text, it is possible to see education as continuous and formative process. Pass by the history of the quadratic equation, and its resolution methods. It addressed the context of the use of technologies such as computational resource for teaching functions. It describes and demonstrates the theorems and proposals concerning the parabola, which is the graph of the quadratic function. In the last chapter the approach occurs within the dynamic geometry environment, GeoGebra. In this chapter you can check the analysis of all the points that make up the quadratic function graphic already applied to the use of the software. It was concluded among other things, the software itself will not solve all problems, but it makes the approach of the truths become more "viewable", however, it reinforces the need for confirmation of statements from expectations.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 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 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 Bingo de Goldbach(Universidade Federal de Goiás, 2018-03-29) Malaquias, Maurício dos Santos Matos; Lima, Igor dos Santos; http://lattes.cnpq.br/6570549108417199; Lima, Igor dos Santos; Barbosa, Fernando da Costa; Costa, Paulo Henrique Pereira daMostrar mais This dissertation is theoretical and has the main objectives of proposing, unprecedentedly, the Goldbach Bingo, alluding to the Goldbach Conjecture and inspiration in the Goldbach Game. The construction of the proposal, for application in the 7th Year of Elementary School, was divided into moments such as Souza's methodology. Finally we did the analysis and justification of the importance of the proposal and the use of games in Mathematics teaching, based on the questions of Cabral and the perspectives of Regina Grando, Tizuko Kishimoto and Cristiano Muniz. Our Goldbach Bingo proposal was designed to help teachers improve content such as even and odd numbers, prime numbers, and the Sieve of Eratosthenes and also the Goldbach Conjecture.Mostrar mais Item Cálculo diferencial: uma abordagem histórico-social e possibilidades de introdução no ensino médio(Universidade Federal de Goiás, 2018-06-22) Oliveira, Cristiano José Rocha Ferreira de; Gonçalves, Tânia Maria Nunes; http://lattes.cnpq.br/7219760130338088; Gonçalves, Tânia Maria Nunes; Borges, Marta; Santana, Fabiana TristãoMostrar mais The poor performance in Calculus courses of the students of the courses of Math and Science in the institutions of higher education has been a constant in the country. A significant number of students accumulates one or more failures in their educational history, being this discipline one of the drivers of student's evasion in higher education. In this present study, we intend to investigate the origins of the problem and its relation to the absence of Calculus in basic education, in particular, in high school. Here we will address the education trajectory along the history of Brazil and its possible sequels in basic education and higher education, specifically in the teaching of Calculus. In a systematic and critical analysis of the above-mentioned assumptions, we conclude with a proposal that can be implemented despite all the historical ills of Brazilian education.Mostrar mais Item A construção de bandeiras: um cenário para exploração da geometria via tecnologia e interdisciplinaridade no ensino fundamental(Universidade Federal de Goiás, 2019-04-17) Oliveira, Inês Naves Cunha de; Freitas, Thiago Porto de Almeida; http://lattes.cnpq.br/5154082262879445; Freitas, Thiago Porto de Almeida; Borges, Marta; Santana, Fabiana Tristão deMostrar mais This work refers to a project carried out with ninety students of the sixth year, of the afternoon shift, of a municipal school, in the city of Uberlândia - MG, from the perspective of learning in Geometry, from the development of an interdisciplinary proposal, in which teachers from three other areas of knowledge contributed to the development of this. The objective was to investigate in which aspects the interdisciplinary practice allied to the use of GeoGebra software could influence the interest and learning of geometric concepts introduced in the sixth year of Elementary School II. The theme "Flags" was elaborated in the idealization, creation and confection, using the flags of Brazil, Minas Gerais and Uberlândia, whose development took place between August and November of 2018, counting on a total of twenty- five lessons. For its execution, a questionnaire was preliminarily applied to trace the profile of study subjects' habits and to diagnose the previous knowledge they had. The information obtained through this questionnaire guided the elaboration and application of the other activities carried out in the classroom, namely: reading and interpretation of official texts (legislation), study of vocabulary and production of texts in Portuguese Language; historical and geographical contextualization of the institution of these flags in each of the respective spheres in History classes, drawing each of them in the Art class and, simultaneously, in the Geometry class, the identification of geometric concepts present in the texts that were explored, constructions of flat figures, measurements and activities using GeoGebra. The methodology adopted was separated into two moments: a first bibliographical one, which aimed to gather information and data about what has already been written about interdisciplinarity and technology for the foundation of this work and the second, a case study that involved teachers partners and students, aiming to relate mathematical knowledge and other contents, technologies and didactics throughout the research process. We used qualitative research in our proposal, and the data were collected from audiotape interviews of students and teachers, annotations made during the interactions, files saved from digital media constructions, printed activities, and the questionnaire answered by the students. The analysis of the obtained results was done after the accomplishment of the planned activities and consisted of the categorization of the information obtained during the follow up of the activities, considering the behavior and comments of the students during the execution of the activities and the perceptions of the project partners teachers. Finally, there was a change in the students' behavior and their receptivity regarding the content applied and the development of activities in the computer lab that became a motivation for the classes. In addition, the involvement of teachers from other areas has led to a narrowing of interpersonal relationships and the perception that working on content interdisciplinarily contributes to a better understanding of students and facilitates their learning process.Mostrar mais Item Construção de geometrias: uma abordagem axiomática(Universidade Federal de Goiás, 2020-05-15) Nascimento, David Lima; Bergamaschi, Paulo Roberto; http://lattes.cnpq.br/6961717072558004; Ribeiro, Márcio Roberto Rocha; http://lattes.cnpq.br/0780755813567262; Ribeiro, Marcio Roberto Rocha; Bergamaschi, Paulo Roberto; Souza, Flávio Raimundo de; Santee, Donald MarkMostrar mais In basic education or in the teaching of geometry, it is shown that there are no reflexions and questions about the construction of geometry: How is geometry born? Or, how to build geometry from nothing? Inquiries about some fundamentals of geometry are fundamental to understanding how mathematics is built. However, it turns out to be a simple task to find ways of approach in basic education that provides these reflexions, since geometry returns to students and is exposed as an absolute truth. It is in this sense, that the present work approaches a process of geometry construction, through the insertion of axioms at a time and is analyzed as its consequences in this geometry. To do so, recover the notion of models in a geometry, which will be attributed to this construction, indicated by the teacher as a tool that can subsidize the reflexions and questions about the construction of plane geometry.Mostrar 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 Contribuições pedagógicas do ensino de pontos notáveis de um triângulo por meio do origami(Universidade Federal de Goiás, 2015-07-28) Araujo, Osmar Rodrigues de; Silva, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; Silva, Élida Alves da; http://lattes.cnpq.br/5863501378045434; Silva, Élida Alves da; Silva, Jhone Caldeira; Rodrigues, Luciana Maria Dias de Ávila; Bergamaschi, Paulo RobertoMostrar mais This work aims mainly to study the pedagogical implications of the use of origami to the process of teaching and learning the notable points of a triangle. For this reason, a qualitative approach was used based on bibliographic research and didactic experiment. A guiding question oriented this work: what are the educational contributions of teaching geometry through origami to understand geometric concepts such as notable points of a triangle? The main bibliographic references are Aschenbach, Fazenda and Elias (1997), Cedro and Moura (2010), D'Ambrósio (1996), as well as documents from Ministry of Education related to the issues highlighted here. The didactic experiment was applied to 35 students of an 8th grade class of a public school in Aparecida de Goiânia, Goiás, Brazil, in February and March, 2015. The analyses of the participants output, the footages and the researcher observations showed that origami is a pedagogical resource that enhances the process of learning the notable points of a triangle. It became noticeable, however, during the execution of the research, how complex is to work with playful in the development of a subject and to plan activities with clear objectives and a methodology appropriate to the level of the students, besides conducting activities that are challenging for them.Mostrar mais Item Da solubilidade por meio de radicais à métodos alternativos – determinando as raízes polinomiais(Universidade Federal de Goiás, 2016-08-25) Holgado, Henrique Semensato; Ribeiro, Márcio Roberto Rocha; http://lattes.cnpq.br/0780755813567262; Lemos, Glen Cézar; Santos Júnior, Porfírio Azevedo dos; Souza, Flávio Raimundo de; Bergamaschi, Paulo RobertoMostrar mais The study of algebra, within the basic education, has become a very important tool for the students in this segment because it allows many problems can be solved through the creation of simple equations. Unfortunately, this area of mathematics has not received the due importance to the story reveals to us and, therefore, their understanding is nothing more than a simple “mathematical formula” . Thus, this work covers a small part of the history of mathematics giving proper credit to employees this area exposing their genius to _nd statements, algebraically, the roots of an equation of degree through operations with radicals and, in addition, other methods that also allow to _nd the solutions of the equations of a algebraic way.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 Dificuldades na aprendizagem e ensino de álgebra: atividades propostas para minimizar essas dificuldades(Universidade Federal de Goiás, 2021-02-11) Estevão, Eduardo José de Oliveira; Gonçalves, Tânia Maria Nunes; http://lattes.cnpq.br/7219760130338088; Gonçalves, Tânia Maria Nunes; Barbosa, Fernando Da Costa; Cunha, Maria Francisca daMostrar mais The difficulties that students possess in the study of Algebra are increasingly evident from Elementary School through to High School. A positive way to intervene in this scenario starts with knowing these difficulties and their origins. The principal aim of this work is to determine which are the main difficulties that crop up in the process of teaching and learning Algebra and subsequently propose activities which minimize them while they promote algebraic thinking. To ascertain these difficulties, a revision of the literature was done, with a descriptive approach, having in mind their causes and origins. Through a qualitative analysis, this research also focused in defining relationships amongst the difficulties encountered. In a systematic and critical analysis of Algebra and Algebraic Education conceptions established over time, as well as the aforementioned relationships, we conclude this work with a proposal of activities that can be used by teachers in the classroom, with the purpose to contribute positively in the teaching process.Mostrar mais Item Dinâmica de máquinas rotativas: um instrumento de aprendizagem no ensino médio(Universidade Federal de Goiás, 2019-05-22) Silva, Sérgio Joaquim da; Silva, Fernando Kennedy da; http://lattes.cnpq.br/8313547891856943; Silva, Fernando Kennedy da; Oliveira, Plínio Jose de; Guimarães, Tobias AndersonMostrar mais In this work, a modeling approach in Mathematics Education is made. Modeling has not yet arrived significantly the schools, probably because many educators have difficulty justifying the use of mathematics taught, or because they have little time for class preparation. In addition to precarious training, there are few materials the Basic Education (High School). This dissertation intends to produce a material that can minimize this need. Therefore, an approach is made on the History of Rotary Machines, taking as a principle the origin of the wheel, from the age of the stone, where it appears the Wheel of Potter's of 3500 BC. Its use in war machines is shown in all the old Roman Empire and arrives until the construction of first Turbine of Aelopile Reaction of Hero. With the advancement of the science of the time, we have the construction of Water Wheels, probably the first tools implemented by mankind to crush seeds, and reports great scientists such as Euler and Bernoulli and Joseph Lagrange, who made great contributions during the scientific revolution, and thus culminates in the invention of First Parson Turbine. The History of the Rotating Machine, facilitates the understanding of its functionalities. There was a theoretical basis of the Ordinary Differential Equations, in which homogeneous linear equations with coefficients are used constants, where its solution is based on functions and equations widely known in High School (Equations of the Second Degree, Polynomial Functions, Trigonometric Functions, and Exponential Functions). Based on Hooke's Law and in the Second Newton Law, it is shown the simplest of vibratory systems and types of movements. In rotor dynamics, the rotor was defined, its elements and the type of movement using the Jeffcott Model, very useful for establishing concepts and definitions. It also seeks to understand the physical meaning of the solutions with their graphical analysis.Mostrar mais Item Diversificação da avaliação em matemática nos anos finais do ensino fundamental para a promoção de uma aprendizagem efetiva(Universidade Federal de Goiás, 2019-05-07) Caixeta, Olemar César; Borges, Marta; http://lattes.cnpq.br/6407324517825514; Borges, Marta; Freitas, Thiago Porto de Almeida; Barbosa, Fernando da Costa; Costa, Priscila Kabbaz Alves da; Santana, Fabiana Tristão deMostrar mais The evaluation is essential for the teaching-learning process and, beginning from this conception, it is necessary to study, reflect and analyze the evaluative practices. As evaluation is a great challenge for the majority of teachers and professionals who offer direct pedagogical support to the teaching profession, this theme must be studied and debated in order to make progress. In this way, the objective of this research was to investigate, apply and analyze how different means and instruments of evaluation adopted in two classes of the eighth grade of a municipal school in the state of Minas Gerais, contribute to the learning process of these students, in order to answer the following question: How can the diversification of means and instruments of evaluation in the classroom can contribute to improving the understanding of mathematics content? This study consists in the approach of a qualitative research, characterized by a Research-action. Data collection began in May 2018 and lasted until December of that year and was performed through a questionnaire, observation, oral and written interactions, application of evaluative activities in the classroom related to the content of mathematics in elementary school, conducting testing in phases and production of portfolios. For the analysis of the produced information, analysis bases and defined categories were created in the development of the research. The students understood the importance of this research, because they participated in a satisfactory way. Therefore, it was possible to verify that there was improvement in the learning of the developed contents and in the attitudes, which are essential in the experience in society. The research results highlight the possibilities of using diverse means and instruments of evaluation as a strategy to facilitate learning, may be used to guide public educational policies to encourage the training of teachers to carry out evaluations as a didactic tool.Mostrar mais