Mestrado em Matemática em Rede Nacional - PROFMAT

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    A plataforma de atendimento no processo de ensino e aprendizagem de matemática com alunos deficientes Intelectuais
    (Universidade Federal de Goiás, 2021-03-22) Vasconcelos, Cladis Henriques; Guimarães, Daniel da Silveira;; Guimarães, Daniel da Silva;; Borges, Marta; Costa, Wanderleya Nara Gonçalves
    In view of the importance of teaching instruments in the mediation of learning, research was done on the use of the Service Platform in the teaching and learning process of mathematics with students with intellectual disabilities, in order to verify the benefits pointed out by the teachers who implemented this new how to use the projector. Therefore, it was necessary to compare the exercises performed on the Service Platform with the exercises that students do in a conventional way on a white board at school and investigate how the Platform instigates the learning of these students. A case study research was conducted in 2019, in two days with alternation of classes on the Service Platform and in a traditional way, with the execution of exercises, on both days of research, whose material produced was used for data analysis. Interviews were also conducted with the teachers who created the platform. Therefore, it was found that there was an increase in the percentage of correct answers in the Service Platform, managing to improve the correct response rates in conventional activities used in the school. In addition, it was observed that this assisted technology was the object of transition from real content to its abstraction, by students with intellectual disabilities. Thus, with a qualitative and quantitative analysis, it was found the learning of mathematics with the use of this learning device, concluding that the Service Platform contemplates the learning of students with intellectual disabilities.
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    Formação inicial do professor de matemática: fatores relacionados à preparação dos licenciandos para a docência na educação básica
    (Universidade Federal de Goiás, 2021-03-11) Alves, Wilson Júnior; Gonçalves, Tânia Maria Nunes;; Gonçalves, Tânia Maria Nunes; Borges, Marta; Lima, Thaynara Arielly de
    According to the data collected in the study "Profession Professor", prepared by the organization Todos pela Educação, a third of Basic Education teachers think that their initial training did not prepare them for the challenges encountered in the beginning of their careers. This fact was responsible for the main objective of the research developed and presented in this dissertation: to determine if, currently, the initial training of future mathematics teachers will allow them to face the challenges that arise in the beginning of their careers. To this end, a documentary research was carried out on the profile of undergraduate students in mathematics, and the profile of teachers and their initial training. Based on this research and on the curricular matrices of undergraduate courses in Mathematics that obtained a grade 5 in the 2017 National Student Performance Exam (ENADE), it was found that these courses seem to help future teachers overcome obstacles encountered by mathematics teachers. in Basic Education in Brazil. However, only time will tell, as these courses have been redesigned in the last two years
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    Videoaulas como recurso extraclasse no ensino de análise combinatória e probabilidade: um estudo de caso do ensino médio
    (Universidade Federal de Goiás, 2021-02-19) Vaz, Dhyego Rodrigues; Freitas, Thiago Porto de Almeida;; Freitas, Thiago Porto de Almeida; Guimarães , Daniel da Silveira; Viola , Denise Nunes
    Nowadays, it is becoming increasingly necessary to use diversified materials for extraclass education in order to instill the student's curiosity regarding mathematics in high school. This work presents the actions developed in the research project “video classes as an extraclasse resource in the teaching of combinatory analysis and probability a high school case study” within the scope of the Professional Master in Mathematics in the National Network - PROFMAT from the Federal University of Goiás - Regional Catalão. The project was developed with students from the third year of high school at a public school in the city of João Pinheiro / MG, with a focus on teaching probability content. It should be noted that the context of the COVID-19 pandemic required the creation of remote alternatives for the execution of the project, and this brought elements to rethink teaching practice in addition to complementing the training that came from the master's degree. The research described in this work aimed to investigate the impacts of using video classes as extra-class material for the development of mathematics skills, according to the Common Base National Curriculum, of students in the third year of high school. In this context, 09 video classes were developed and used as extra-class material interspersed with the virtual classes with the participants, addressing counting and probability, considering motivational aspects for high school students. For data collection, 11 questionnaires were applied: one at the beginning (survey of the participants' characteristics), 9 during the development of the classes previously planned and linked to the elaborated video classes, and one at the end (with questions that deal with the content of probability addressed throughout the period and reflections on the methodology used). In addition, in a logbook, the professor-researcher recorded the relevant facts arising from classes developed remotely. The collected data were analyzed, after the intervention carried out with the participants, based on the categorization of the information obtained. This work brings in its results the opinions of the students about the methodology used, the evolution of the learning of the content and its relation with the development of the referred abilities of the Common Base National Curricular. There was an evolution in the learning of all participants, as well as great acceptance and adaptation of the methodology used.
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    Uma abordagem matemática no ensino de cálculo estequiométrico
    (Universidade Federal de Goiás, 2021-03-08) Andrade, Leandro Mendes de; Cunha, Juliana Bernardes Borges da;; Cunha, Juliana Bernardes Borges da; Santee, Donald Mark; Silva, Ricardo Souza da
    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.
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    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;; 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.
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    Modelagem matemática no processo de inclusão: uma conexão entre educação matemática e educação inclusiva
    (Universidade Federal de Goiás, 2021-03-05) Oliveira, Lucas Aparecido de Castro; Santos Júnior, Porfírio Azevedo dos;; Santos Júnior, Porfírio Azevedo dos; Freitas, Thiago Porto de Almeida; Alves , Deive Barbosa
    This work reports the experience that was developed in classes of the 9th year of Elementary School II, in which we re-signify the reality of the school society, during the development of the Mathematical Modeling teaching methodology. From the difficulties of the wheelchair student mobility through the school space, the motivation to build an investigative process emerged, relating the content of Mathematics and accessibility at school, seeking to develop greater awareness regarding inclusion. In this sense, this work it aimed to investigate how much the teaching methodology Mathematical Modeling can contribute to the teaching-learning process, from the problem of accessibility of a wheelchair user in the school space. The research was carried out in line with the qualitative participant research, seeking to develop activities in the classroom through the teaching methodology Mathematical Modeling. For data collection and analysis we used the following instruments: researcher's diary; questionnaires; informal semi-structured interview; in addition photos and written records prepared by the students in carrying out the activities. In the moments with the classes, the following research activities were developed: introduction to the initial theme/problem; motivational video; conversation wheel (chat); identification and reflection on the initial problem; investigation and research to solve the initial problem; application of mathematical content; and construction and socialization of models of possible solutions. The lived experience went beyond what was expected, the contributions of the teaching methodology Mathematical Modeling encompassed the relationship between student and content, teacher-student and student-student, providing a cooperative work environment, engagement in the task of “learning to learn”, besides stimulating the perception of the issue of affectivity in the action of teaching and learning mathematics, and the videos were as a way to change the perception and engagement of students in research activities. The students were able to investigate and apply the mathematical content: geometric shapes; length measurements; proportion; similarity of triangle; Pythagorean theorem; percentage; elementary angles and operations. The research contributed to my education, providing a different look for students and the problems of society. It sowed a seed regarding inclusion in the school environment, showing the importance of awareness, especially, when people do not live or experience the difficulties of a person with a disability. And with the teaching methodology Mathematical Modeling applied in class, students showed better results than previous in two months. In this way, recommended this teaching methodology to professional colleagues, because despite all the work invested in the accomplishment, believed it is worthwhile.
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    Uma experiência com o ensino aprendizagem de estatística durante a pandemia: percepções e desafios
    (Universidade Federal de Goiás, 2021-02-24) Dias, Fabrício Fernandes; Cunha, Juliana Bernardes Borges da;; Rodrigues, Cloves Goncalves; Cunha, Juliana Bernardes Borges da; Bergamaschi, Paulo Roberto
    This work describes a research carried out with students of the third grade of high school, from a public school in the state, located in the city of Goiatuba - GO, which aimed to: verify the perception of students in the teaching-learning process of mediated content technologies during emergency remote education. For the development of the research, eight synchronous virtual classes were carried out using, as support, several technologies. At the end of the classes, a semi-structured questionnaire was applied in order to verify, in the student's view, satisfaction with the skills related to the content of statistics taught with mediation of technologies during remote emergency teaching. In view of the results, it can be noted that the students showed a preference for synchronous virtual classes as a transmission tool and, with respect to the skills related to the content of statistics, demonstrated some difficulties in applying the concepts in solving problems. It was also notable, the low adhesion of students to synchronous virtual classes. Therefore, a new research was carried out, through a survey, with the objective of investigating which social and economic context the student is inserted in, as well as the existence of material and technological limitations and which are its relations with the teaching-learning process during the emergency remote education. In view of the results obtained, it can be noted that there were several aspects, such as housing, economics and technological accessibility that influenced the low adherence of students to virtual classes during remote teaching, limiting the teaching-learning process during this period.
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    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;; Gonçalves, Tânia Maria Nunes; Barbosa, Fernando Da Costa; Cunha, Maria Francisca da
    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.
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    Uma investigação sobre a ideia de número
    (Universidade Federal de Goiás, 2020-12-18) Silva, Fabrício Oliveira; Ribeiro, Márcio Roberto Rocha;; Ribeiro, Marcio Roberto Rocha; Rocha, Rogério Azevedo; Santos Junior, Porfirio Azevedo dos
    In this assignment we aim to stimulate reflections about the millenary inquiry regarding what number really is. We aimed to show how historically controversial this question might be, which finds diversified comprehensions in the fields of philosophy, mathematics and the philosophy of mathematics. We came up with a historical pathway related to the construction of the idea of number, since the paleolithic period, reaching the end of the Nineteenth Century, when the mathematicians reevaluated the basics of mathematics and raised the ideas up to the level of the most rigorous languages involving logic. Frege (1884), in his book "The Fundamentals of Arithmetic", intended to explain and justify the real nature of the numbers idea, without appealing to geometry. Besides him, we have put a spotlight on the beautiful ideas as well as the important contributions of Bertrand Russell, Hilbert, Dedekind and Peano on the construction of the idea of number. The rational approach of the concepts and their validation through rational methods, without making use of sensorial experiments, are either philosophical and mathematics studies. In this assignment, we intended to bring some light to these ideas, acknowledging the relevance of a deeper and more structured comprehension of the idea of number.
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    Processo de ensino e aprendizagem de matemática nas escolas prisionais: perspectivas e possibilidades
    (Universidade Federal de Goiás, 2020-04-20) Souza, Naiane Ferreira; Silva, Élida Alves da;; Silva, Élida Alves da; Freitas, Thiago Porto de Almeida; Santana, Fabiana Tristão de; Santana, Fabiana Tristão de
    A related research in this work aimed to understand the limits and possibilities of presenting a teaching and learning process in mathematics, in the Youth and Adult Education modality, in the view of teachers and students who have links with temporary schools. We sought to reflect, discuss and identify, based on the current laws that guarantee cultural and social rights to rights, a legitimacy of access to educational assistance, or the role of school education in the process of re-socialization of the detainee and the factors that influence learning of the math of the arrested student. A chosen methodological proposal can be characterized as qualitative research, whose investigation procedure was carried out through the analysis of bibliographic materials, documents, national educational indexes and questionnaire analyzes. The questionnaires were subject to detention, which has access to the school, in a prison in the state of Minas Gerais and teachers who work or already work in provisional schools. The results of this research point to the challenges encountered in prison education, such as the lack of didactic resources and show the relevance that schools inserted within the prison units present in the perspective of the detainee's resocialization. We present a didactic sequence on the creation of a bottle sofa that can be used by mathematics teachers working in provisional schools.
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    Uma visão geral sobre a análise real no país e uma proposta em sequências didáticas para a disciplina em cursos de licenciatura em Matemática
    (Universidade Federal de Goiás, 2020-08-06) Batista, Állison Pinto; Bergamaschi, Paulo Roberto;; Bergamaschi, Paulo Roberto; Ribeiro, Márcio Roberto Rocha; Nogueira, Antônio Carlos
    The present approach aims to understand the difficulties and criticisms faced the teaching of Real Analysis in Mathematics Degree courses and to present a proposal aimed at discussing the concepts of Real Analysis with a greater emphasis on the properties of sets and functions addressed in Brazilian Basic Teaching. Based on the bibliographic survey regarding works aimed at discussing the teaching of Real Analysis and the documentary survey of Pedagogical Projects of Mathematics Degree courses offered by Brazilian Federal Institutions of Higher Education, we resort to works and titles aimed at the study of the History of Mathematics to understand possible reasons for the criticisms evidenced in current works. We analyze the proposals for disciplines of Real Analysis of Pedagogical Projects in order to discuss the subjects there covered and the focus given to the disciplines, registering categories based on the wordings there available for this purpose. Based on this information, we observed criticisms of the approach of the Real Analysis disciplines and proposals to improve disciplines' approach in order to promote a meaningful understanding and aligned with the professional purpose of the graduate. We observed how an impression of rigor reached the improvement of research in Mathematics and brought consequences to the discipline conception of Real Analysis discipline in force. From those raised observations, we propose an approach through didactic sequences for some topics studied in Real Analysis, in order to highlight some concepts and issues arising from Basic Education itself, and we hope the proposed approach motivate a change in the conceptions regarding the curricular components of Mathematics teaching courses in the near future.
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    Probabilidade e jogos digitais: uma experiência com o software GeogGbra no ensino médio
    (Universidade Federal de Goiás, 2020-03-27) Moura, Tarcisio Junqueira; Freitas, Thiago Porto de Almeida;; Freitas, Thiago Porto de Almeida; Bergamaschi, Paulo Roberto; Camargo, José Ivanildo Felisberto de
    This paper describes a survey conducted with students of third year high school, students from a state school in the city of Uberlândia, in the perspective of an alternative practice to be inserted in the mathematics classes. The objective was to investigate the use of technology and digital games in teaching and learning probability. For the development, didactic sequences involving digital games were elaborated through dices constructions in GeoGebra software permeated by probability issues. The research of this work has a bibliographic and field character, since bibliographic research took place that culminated in the elaboration of didactic sequences about digital games with constructions in GeoGebra, manipulated by participants in the probability study. The participants were the protagonists of the fieldwork in the exploration of the digital games, in the computer lab, with the interaction of the research professor. In the activities, the students expressed their opinions, expectations and experiences about their contact with the mathematical content in question and the didactic proposal performed by them. The construction of the dices in the digital environment and the elaboration of mathematical issues from the game created showed possibilities of exploring the creativity of teachers to seek or create alternative and modern dynamics for the teaching of mathematics. We carried out analyzes with data produced according to students' records, both in the resolution of probability questions and in their reflections about the activities. Students' successes and errors were analyzed in an attempt to understand their knowledge regarding probability. Their reflections and opinions about the activities were categorized, in order to express common ideas. It was noticeable that the insertion of the technological resource, with the use of digital games, pleased the students, provided moments of study, fun and much interaction between them. It was also possible to notice that such dynamics strengthened the teaching and learning probability and enabled students to see the content in their practices even outside the school, and further develop their reasoning for situations that require probabilistic knowledge.
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    GeoGebra e a metodologia de resolução de problemas: aplicações na inscrição e circunscrição de sólidos geométricos
    (Universidade Federal de Goiás, 2020-03-17) Reges, Nilivan; Freitas, Thiago Porto de Almeida;; Freitas, Thiago Porto de Almeida; Borges, Marta; Colnago, Marilaine
    This work is the result of a research project carried out with twenty students from the 3rd serie of high school, from the morning shift, from a private school in Caldas Novas-GO, which had as objectives: to investigate, apply and analyze a proposal for teaching solids geometries developed in the Problem Solving Methodology from app GeoGebra. From the guiding question: "What effects are produced in the learning of high school students, in relation to Spatial Geometry content, from the articulation of the Problem Resolution Methodology with Dynamic Geometry environments?", were applied, in the month from June 2019, initially, a questionnaire to identify the profile and habits of the research participants and a diagnostic activity that could guide the direction that the research would take. In the same period, three didactic sequences were elaborated, the first sequence referred to the basic notions of Flat Geometry, the second to the calculation of area and volume of polyhedra and round solids, and the third to the construction and manipulation of inscribed geometric solids and circumscribed. For the application of didactic sequences, in the month of August 2019, it was used the multimedia rooms, the computer lab and the sports court of the educational institution, on the counter and in the morning period (as some teachers gave in) your classes). In the process of data collection, they used the following instruments: photographs, footage of activities, reports, diagnostic activity and questionnaires. In addition, tables and graphs were built that included the analysis procedures, describing the Methodology of Resolution of Problems in the learning, through the construction of the solids in GeoGebra where the researcher was mediator of these activities. In the end, with the results obtained, it can be noted that GeoGebra combined with the Problem Resolution Methodology is a facilitating tool in the process of solving problems that involve solid enrolled and circumscribed, leading to the conclusion that, in turn, can benefit the process of teaching and learning mathematics in this area, especially with regard to its manipulation, concepts, visualization, construction and assimilation
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    GeoGebra: uma proposta para o ensino de funções trigonométricas
    (Universidade Federal de Goiás, 2020-04-02) Machado, Maxiel de Mesquita; Borges, Marta;; Borges, Marta; Santee, Donald Mark; Santana, Fabiana Tristao de
    This dissertation aims to present a teaching proposal that makes it possible to explore and better understand important aspects of the teaching of Trigonometric Functions, using the educational software GeoGebra. The main question is: What potential does this educational technological tool have to contribute to teaching and learning the concepts of Trigonometric Functions? This issue is relevant since several external assessments (Basic Education Assessment System (SAEB), Diagnostic Learning Assessment (ADA), Goiás Education Assessment System (SAEGO)) carried out in High School in the state of Goiás point out that there is, at national and local level, a gap in the teaching and learning of Mathematics. Thus, it is believed that the use of digital technologies can contribute to making Mathematics teaching more attractive to students. This is a research with a qualitative approach, exploratory and bibliographic, in which activities were developed, initially to improve and understand the software and, subsequently, didactic sequences aimed at students in the 2nd grade of High School, with tasks at an increasing level. requirements related to the Sine, Cosine and Tangent Trigonometric Functions. In the elaboration, the dialogue with didactic books and alternatives was sought to dynamically explore the potential of the software, in order to promote the understanding of both the steps and the content covered, through the suggested constructions. It is believed that the ideas presented here may serve as support for various works and projects related to the teacher's own practice or even students of exact science courses who still have difficulties with the subject. With the proposal, it is expected to add more formative possibilities for the teaching of Mathematics and, in particular, for teaching and learning with the help of digital technologies, especially GeoGebra.
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    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;; 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.
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    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;; 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.
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    Construção de geometrias: uma abordagem axiomática
    (Universidade Federal de Goiás, 2020-05-15) Nascimento, David Lima; Bergamaschi, Paulo Roberto;; Ribeiro, Márcio Roberto Rocha;; Ribeiro, Marcio Roberto Rocha; Bergamaschi, Paulo Roberto; Souza, Flávio Raimundo de; Santee, Donald Mark
    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.
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    O estudo de funções no ensino médio: uma abordagem sobre as contribuições do software Graphmatica como recurso metodológico para a prática do professor
    (Universidade Federal de Goiás, 2020-02-04) Nunes, José Ferreira; Cunha, Juliana Bernardes Borges da;; Cunha, Juliana Bernardes Borges da; Souza, Eduardo Sérgio de; Santee, Donald Mark
    This is a methodological proposal for the teaching of Mathematics, content of functions, for students of Basic Education, who used the software Graphmatica. This study was carried out based on an applied field research of a theoretical and practical nature, with quantitative and qualitative approaches through the collection of data through the application of questionnaires and justified expositions about functions and Graphmatica. The research started from the problematic of the difficulties encountered by the educators in the insertion of the Graphmatica resource as pedagogical practice. The central axis consists of the inquiry about this problem, which sought to answer which pedagogical advantages Graphmatica software presents, when used as a methodological tool in the teaching of functions, for high school students. In this perspective, it aims to present Graphmatica software as a tool capable of assisting the teacher in the construction of tables and graphs and to explore the results that can be obtained with these constructions, with the second year students of the Secondary School of the State School Dom Lustosa of Patrocínio, Minas Gerais. The research was based on questions that demonstrate the conjunctures of the researched school, the usefulness of computational resources for education, the importance of the Graphmatica software to aid the learning of functions. The activities developed were lectures and practices on the resource in question and applicability of questionnaires, held in the classroom and computer lab. It is concluded that the findings presented in this research declare in favor the use of the Graphmatica software in the teaching of mathematics, specifically in the content of functions. It is noteworthy that, despite limitations in teaching practice, this resource contributes satisfactorily to educators in their educational practices, especially for those who work directly with students in Basic Education. It is recommended, the use of the software Graphmatica in the study of functions, since it allows a better learning of the student, in front of the objectives proposed by the content. It should also be noted that the software is a resource that is freely available to anyone who is interested.
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    Problemas matemáticos com cálculos algébricos: da resolução à formulação no 8° ano do ensino fundamental
    (Universidade Federal de Goiás, 2019-09-27) Silva, Sérgio Luis; Borges, Marta;; Borges, Marta; Silva, Élida Alves da; Lima, Rosana Catarina Rodrigues de
    The present study aims to analyze the contributions of the formulation and problem solving as teaching methodology in the study of algebraic calculus for elementary school students. The research had a quatative approach and was carried out through a case study if 8 th grade elementary school students in a state public school, located in city of Patos de Minas – MG. The research it was made on months August to October of 2018 and the data colletion was performed through two questionaries and material produced by students. Initially a sequence was given eight class about the subject and question. After there classes was apply the first questionary to check the acquired knowlegdes in the classes taught. Subsequently, the activities of Problem Solving and Formulation were developed, in the perspective that the students themselves, divided into groups, formulated the questions, always mediated by the teacher's guidance. At the conclusion of the formulation phase, written evaluations were prepared by the teacher, which were solved by the students. Finally, the second questionnaire about the activities worked in this period was applied. The produced data were analised starting of methodology to formulation and solving of problems in content of algebraic calculus by construction guilding aixes and categories emergents of field material. That work aims to analyze how question formulation can develop students' understanding when studying algebraic calculus from the perspective of Formulation and Problem Solving. The results indicate that the students, in general, even with little knowledge of the methodology, were quite receptive to the proposed activities, showing interest and motivation. Was possibily to verificate too that students don ́t accustome to tasks of this nature, which leads to questions difficult to understand. On the other hand, with the medition of researcher teacher, themselves felt a necessited of retruturation that questions for the application to his classmates. Finally, three essential points in the developed activities: the first refers group activities, in which several students became protagonists in the process of making, learning and promoting knowledge among the participants. The second point the improvement in the teacher-students relationship, due to the mutual involvement in the activities. And the third regards the best assimilation of algebraic calculus content by most students, mainly regarding the use of variables in an action plan in solving a problem and in operations with algebraic expressions, with conexions behind the algebra and the geometry linked to algebraic calculus.
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    Um estudo de caso de aplicação do GeoGebra em uma escola da rede particular com foco em geometria espacial
    (Universidade Federal de Goiás, 2019-07-23) Gonzaga, Ivanete Lopes; Santos Júnior, Porfírio Azevedo dos;; Silva, Élida Alves da; Silva, Jean Carlo da
    The study of spatial geometry is necessary in the life of everyone since ancient times, in various everyday situations it is necessary to use geometric knowledge to solve problems. With the difficulty that educators have to make spatial geometric visualization simpler, the present study evaluated the influence of software on the understanding of spatial geometry and consequences of the use of this tool in the teaching-learning process, answering the following question: “The use of technologies through software can influence the learning of space geometry? ” To this end, a qualitative and quantitative exploratory research was carried out, whose methodological procedures combined comprehensive bibliographic research, such the fundamental theoretical foundation, field research and case study. The activities were developed in seven stages, in a private school in the city of Paracatu-MG, with a group of 20 high school students. The results showed that the use of the software, allowing the construction and analysis of the properties of solids, allowed the students to understand, from its planning and movement, simpler ways to solve most questions, without the need to memorize specific formulas. leaving them very satisfied and motivated to assume themselves as protagonists of their learning.