Programa de Pós-Graduação em Matemática - PPGM

URI Permanente desta comunidade

https://repositorio.ufcat.edu.br/handle/tede/24

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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Agora exibindo 1 - 14 de 14

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 Barbosa
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.
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 da
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.
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 de
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.
A elaboração e construção de material pedagógico como metodologia do processo ensino aprendizagem de frações e produtos notáveis
(Universidade Federal de Goiás, 2019-04-26) Mendonça, Glauce Ribeiro de Souza; Santos Júnior, Porfírio Azevedo dos; http://lattes.cnpq.br/5132806149453454; Santos Júnior, Porfírio Azevedo dos; Souza, Flávio Raimundo de; Barbosa, Fernando da Costa
This research deals with the teaching of fractions and notable products, through an applied methodology, using the elaboration and construction of concrete material, such as disks, fractional rulers and squares of varying sizes. The target audience was the students selected, through an Initial Questionnaire, from a class of the First Year of High School of a Public School in the city of Itumbiara-GO, in view of the difficulties presented by them in carrying out activity and / or tasks that need these previous contents. From the selection, a group of students who presented greater difficulties in these contents were chosen to participate in the research in the mathematics laboratory, where these students had the opportunity to participate in the workshops, where the concrete materials were constructed, thus allowing the visualization of the concepts theoretical and practical related to the subject, including theory, definitions and rules. Through qualitative approaches, the results obtained were satisfactory, which allowed us to observe a significant improvement in students final performance.
O ensino da função linear e do torque através de interações de engrenagens
(Universidade Federal de Goiás, 2020-06-30) Vilarinho, Elmo de Abreu; Silva, Fernando Kennedy da; http://lattes.cnpq.br/8313547891856943; Silva, Fernando Kennedy da; Barbosa, Fernando da Costa; Alves, Deive Barbosa
This work aims to introduce educational robotics in the classroom of the first year of high school, through the use of a pedagogical form different from traditional teaching in learning the study of linear functions and torque. For this, a crane was built with the parts of a LEGO EV3 kit by coupling the gears of a gear kit, so that, by applying a constant force of the large lego engine to the driving gear, it transmits the movement to the output gear that is coupled to a pulley that generates torque. It was observed that in the coupling of the gears it is possible to learn various contents of mathematics and physics, such as linear functions, proportionality, composite function and torque. As a result, a didactic sequence was developed that shows the step by step of this work for students and teachers willing to use this teaching methodology. Finally, it can be concluded that this dissertation instigates and encourages students' learning with the use of technology in their daily lives, as has been shown, with the practical application of linear functions and torque generated by gear coupling.
Geometria espacial: uso do aplicativo GeoGebra em smartphones
(Universidade Federal de Goiás, 2018-06-25) Silva, Paulo Cosme Amorim da; Silva, Élida Alves da; http://lattes.cnpq.br/5863501378045434; Silva, Élida Alves da; Souza, Flávio Raimundo de; Barbosa, Fernando da Costa
The use of GeoGebra software in Spatial Geometry classes in Mathematics for 2nd year High School students is the proposal of this work. This software was chosen specifically for its didactic characteristics, which allow a better understanding of the concepts worked in the classroom making them more accessible. The proposed activities deal with Spatial Geometry content and are intended to encourage students to take part in the study developed through the GeoGebra application, which will give them a better performance in their learning. It is expected that this material will give teachers the desire to create new ideas to use this software and other methods in their classes, inserting the teaching of Mathematics in a more current perspective, using technological tools that are common to students' daily lives.
Matemática com tecnologias: cubo de Rubik e robótica
(Universidade Federal de Goiás, 2019-03-14) Barbosa, Cassiano Marques; Barbosa, Fernando da costa; http://lattes.cnpq.br/8953646779705648; Barbosa, Fernando da Costa; Alves, Deive Barbosa; Silva, Élida Alves da
Associating different technologies, especially with playful bias, can provide pleasant moments of knowledge construction to specific audiences, making analogy with Larrosa (2004). In this work, we opted for the playfulness of the Rubik cube puzzle associated to three research scenarios. The mathematical notions scenario aims at a reflection on how to use the art of knowing how to solve the Rubik's cube and the experiences provided by it, associating them in an intrinsic way with the mathematical problems and their solutions. The deepening scenario in learning the Rubik's cube through Educational Robotics is related to the experiences provided by the use of Lego ® and Arduino robotics kits: how to establish relationships among participants through collective work, and to develop an educational activity by means of technological tools in order to appropriate these technologies. These activities were motivated by the construction of robots capable of solving the Rubik's cube. The scenario learning to solve the Rubik's cube focuses on the development of knowledge and experiences about resources and playful activities with the Rubik's cube - structured logical material: logical block. This research sought to understand the contributions to mathematical and technological education and limitations in a constructive research process, using the Rubik's cube in the context of a municipal public school in Uberlândia. The present proposal is of an applied nature with a qualitative approach employing the case study. There are limitations in working with the Rubik's cube, and these may be related to the dialogue between those involved in the process or even materials, but these obstacles do not prevent those who have fallen in love with the art in solving the cube, from continuing to work with the puzzle. From the participation of these passionate students, we observed, through various sources of information, improvements in relation to logical reasoning, agility and motor coordination, interaction with other students, frustration tolerance and group work, as well as designing the mathematics of most pleasurable way.
Matemática, aprendizagem baseada em problemas: metodologia inovadora no 9º ano do ensino fundamental de uma escola pública
(Universidade Federal de Goiás, 2019-03-13) Ribeiro, Geovani Henrique; Barbosa, Fernando da Costa; http://lattes.cnpq.br/8953646779705648; Barbosa, Fernando da Costa; Santos Júnior, Porfírio Azevedo dos; Alves, Deive Barbosa
This research is about the proposal of using Problem Based Learning (PBL) as a methodology that pretends to be innovating as it contradicts traditional approaches, that, today, no longer corresponds to the students’ characteristics nor their necessities inputted by a world into constant and fast social and technological changes. The investigation had as subjects students on the 9th grade on fundamental learning at Escola Estadual do Bairro Jardim das Palmeiras, in Uberlândia/MG. The research directed of answering to the following question: is it possible that PBL becomes a math process learning that attends to the students’ necessities charged by the world and lived by them? It was developed a qualitative investigation, to verify if PBL, supported by technological resources, creates a motivational learning environment, capable of enhancing the learning construction process. The literature’s revision indicates that there are few works using PBL at math area in basic education. The methodology indicated seven steps conceived as adequate to the aim of PBL: to educate participating, critical, self-governing, capable of problem solving students, who accept different opinion, and that access data by digital resources to learn math. With PBL, the problem is the initial target to develop knowledgment, taking the student to be the responsible of building self-knowledge, and the teacher the facilitator to it. The experience of using PBL’s seven steps application, analysis and discussion at math teaching in basic education conducted to an affirmative answer to the research’s goal, as that it put in evidence that the knowledge construction provided students to act as math day-by-day problem’s solutioners. We hope that, afterwards, the result obtained into the investigation in this research encourages and serve as a parameter to other researchers, to look after new paths on teaching math.
O jogo dominó algébrico
(Universidade Federal de Goiás, 2018-04-03) Franco, Felipe Barbosa; Lima, Igor dos Santos; http://lattes.cnpq.br/6570549108417199; Lima, Igor dos Santos; Barbosa, Fernando da Costa; Costa, Paulo Henrique Pereira da
This work is theoretical, and its methodology was initially based on the research and bibliographic review of the Euclidean Algorithm, as well as the use of games in Mathematics education. A proposal was elaborated for the 7th year of Middle School, based on the Algebraic Dominoes of Freitas-Teodoro [8]. This proposal follows the methodology of Souza [22], which has lesson plans defined in four different moments. An analysis was made to justify the efficiency and importance of the Adapted Algebraic Domino restricted to the Use of Games in education based on the work of authors Regina Grando [10], Kishimoto [13], [14], [15], [16], [17] and Cristiano Muniz [18]. In addition, some simulations of plays related to the Algebraic Domino were made, for better understanding of the proposed subject.
O uso da libras na matemática do fundamental: uma proposta de glossário
(Universidade Federal de Goiás, 2019-02-04) Atayde, Suenio Tomáz Spindola; Barbosa, Fernando da Costa; http://lattes.cnpq.br/8953646779705648; Cintra, Vanessa de Paula; Borges, Marta; Barbosa, Fernando da Costa
The present work aims to identify the aspects derived from the process of elaboration and use of a glossary of mathematical symbols, in the search to help its teaching and learning to the deaf students of the 8th grade of Elementary School of a public school in the Federal District, in the Administrative Region of Planaltina. The reason for this proposal is the difficulties encountered by teachers in interpreting the mathematical content to the student in a way that facilitates their learning. Sometimes the existing terminologies are not sufficient to insert or transmit the content, which demands the use of specific signs for the teaching of Mathematics and their respective contents. This is a qualitative research where the case study was developed in the referred school. The methodology adopted for its accomplishment was the formation of a study group composed by the teacher regent, interpreter, hearing impaired students of the 8th grade and the researcher, performing a study of the written and spoken language of the regent teacher and the student listener in the teaching learning process. The specific vocabulary of the necessary mathematical language was raised, considering the National Curricular Common Base (BNCC), the National Curricular Parameters (CPN), reference textbooks and didactic material adopted by the school. A comparison of these terms with their equivalents in LIBRAS was developed. A glossary was compiled that compiled all these signs, both existing and proposed. The final material was used by the deaf students of the selected class, interpreter, regent teacher, and resource room for the hearing impaired for testing purposes. Finally, its evaluation was made and the considerations about its significance were reported. This glossary was offered to the school as a reference material and support for teachers, interpreters and students of the following years.
Possibilidades para melhorar o desempenho dos acadêmicos na disciplina de cálculo
(Universidade Federal de Goiás, 2019-03-26) Teixeira, Sheila Cristina; Silva, Élida Alves da; http://lattes.cnpq.br/5863501378045434; Silva, Élida Alves da; Santana, Fabiana Tristão de; Barbosa, Fernando da Costa
This work is the result of a study about the possibility of improvement in the Calculation’s academics’ performance. It was developed within a first year group of Mathematics Degree students, specifically in the Pre- Calculation subject. This is a quantitative research, which, for data collection, used a socio - economic profile questionnaire, an Elementary Mathematics survey test and the observation of the development of activities in which computational resources were used, being that all these activities were recorded in a daily basis. It was made a bibliographic research about the using of Information and Communication Technology. Relying on technologic development and in the facility to access all the needed resources, we used Maxima software associated with planned Mathematics activities, which assume the investigation by the student, aiming to improve his own performance. Besides, we also aim to analyze how this kind of activity may contribute for a more effective learning process. The final results show methodological possibilities, looking to an intuitive approach of the concepts in an academic environment, which enable the possibilities of several properties visualization, mainly the graphic ones. Besides, the intervention contributed for a change in the students’ attitudes, who turned out to be more active and independent in the learning process.
Robótica educacional livre no 9º ano do ensino básico: uma trilha de implementação de robótica com Arduino para o ensino de Física e Matemática
(Universidade Federal de Goiás, 2021-03-19) Silva, Marcelo Pires da; Baborsa, Fernando da Costa; http://lattes.cnpq.br/8953646779705648; Barbosa, Fernando da Costa; Silva, Élida Alves da; Alves, Deive Barbosa
This research seeks to evaluate/understand how Educational Robotics, in a Free Philosophy/Perspective, can be used for teaching and learning Physics and Mathematics in Basic Education. For this, we work with students from Elementary School II, specifically from the 9th grade, from a public educational institution. The robotic materials used, met the idea of being: Hardware's and Software's, both Free. For this purpose, it was proposed to use Arduino, scraps and other free materials. Classes were developed, didactic sequences with assemblies, so that the participants could carry out the production of the Robots, whose classes were applied in the after of the classes, from one to two classes per week. This work resulted in this dissertation, a research, as a methodology the Case Study method, with qualitative analysis of the data. Our study was based on a Single Case Study, with integrated units of analysis, having as a case the Lessons developed of Free Pedagogical Robotics, which contains two integrated units of analysis: The development and assembly classes of the Line Follower Robot, as well such as the construction and development of ultrasonic robots, through Arduino and Ultrasonic Sensor. For obtaining and storing data, it was used Documentation in the form of Questionnaires, Record in files in the form of Images/Photos, Videos, Audio Files, Interviews, Direct Observations, Participant Observation and the Physical Artifacts produced by the participants. For data analysis, we use the general strategy for data analysis, the theoretical proposition of treating data “from scratch”. For the specific analysis model, we use logical models, from individual to organizational level. From assembling sequences, a transistorized line follower robot was developed, after modification, started to be controlled by Arduino and robots using the Arduino and Ultrasonic Sensor, which was used to determine the speed of sound in a certain environment, and which was modified for calculate distances by means of Ultrasonic Waves and to function as a D/Presence Sensor. Thus, after data analysis, we observed that, in addition to the Free Educational Robotics classes, in addition to promoting learning by manipulating the apparatus, Learning was promoted by attempting to correct the error, caused by behavioral/social engagement, cognitive engagement and emotional engagement, providing learning, socialization, personal and intellectual growth.
Uma análise dos impactos e tendências apontadas nas dissertações de mestrado do PROFMAT, produzidas na UFG - Regional Catalão de 2014 a 2016
(Universidade Federal de Goiás, 2018-05-25) Silva, Felipe Alves da; Silva, Élida Alves da; http://lattes.cnpq.br/5863501378045434; Silva, Élida Alves da; Barbosa, Fernando da Costa; Sousa, Flávio Raimundo de; Baumann, Ana Paula Purcina
Understanding the great need that occurs in the field of Mathematical Education, in regarding to the methodologies and pedagogical practices applied in Basic Education, also arises the scientific research. Second Costa (2007) [2] Scientific investigations make a very important role in terms of the grounding, orientation and evaluation of the practices of use of technologies in the educational context. This Dissertation presents the result of the study of the contents approached in the Master's Dissertations of the PROFMAT program, elaborated in the UFG - Regional Catalão in the period from 2014 to 2016, in view of understanding better the problems studied, the theoretical and methodological frameworks in which they are located, the fields where they were applied, the techniques of collection and analysis of data used and what the trends and impacts caused in the Teaching and Learning of Mathematics. For this reason, the 39 Master's Dissertations produced in the abovementioned period were analyzed, making use of a guiding questionnaire, which is in the appendix. Through the results obtained it was possible to perceive the commitment of teachers of Mathematics of Basic Education in reversing the process of neglect, demotivation, discouragement and inertia of the students and teachers, applying new methodologies and practices of Teaching and Learning Mathematics. It was possible to verify the great satisfaction of the researchers in achieving their goals and in some way can contribute to the intellectual and human development of the students.
Uma proposta lúdica sobre o Summaê no IFG – câmpus Luziânia
(Universidade Federal de Goiás, 2018-08-23) Santos, Wagner Pereira dos; Lima, Igor dos Santos; http://lattes.cnpq.br/6570549108417199; Lima, Igor dos Santos; Barbosa, Fernando da Costa; Costa, Paulo Henrique Pereira da
This dissertation aims to analyze and propose a new adaptation of Summaê to the IFG - Câmpus Luziânia, with the aim of reducing the high rate of reprobation in Mathematics of the first year students of the Technical Courses Integrated to High School in Buildings, Computer Science and Chemistry. Summaê is a playful game of questions and answers and is inserted in one of the active methodologies idealized by Professor Ricardo Fragelli. The adaptation of the original proposal of the Summaê was for the content of exponential and logarithmic functions, where they present different situations and natural phenomena that are part of our daily life, such as: Half-life, rates of proportional variations, compound interest and intensity of a sound. It should be emphasized that the use of games can promote different teaching situations, presenting a mathematical language as well as formal mathematical concepts, as well as associating theory and practice in the subjects addressed.

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