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1
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ROBERTA PEREIRA MACIEL
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A reflection on the teaching of theorems in schools
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Leader : VIVIANE PARDINI VALERIO
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MEMBRES DE LA BANQUE :
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ANDREIA MALACARNE
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VIVIANE PARDINI VALERIO
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WENDERSON MARQUES FERREIRA
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Data: 23 févr. 2021
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Afficher le Résumé
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This work is a reflection, an analysis on the Teaching of Mathematics in Brazilian schools, more specifically on the teaching of theorems, as they are and can be worked with the students of Basic Education. We started the work by studying the three great mathematical philosophical schools (Logicism, Intuitionism and Formalism) of the late 19th and early 20th centuries, the mathematical rigor and the guiding documents of Basic Education in Brazil (Law of Directives and Bases of Education, Parameters National Curricula, National Common Curricular Base). We selected some theorems worked on in Basic Education to be studied, including their demonstrations and analyzed which can be worked on in schools. We also see how some elementary and high school textbooks work with these theorems. We finished the work proposing activities (lesson plans for the two levels of education) involving an important exercise of verification (proof) of simple mathematical results.
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2
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GUSTAVO BATISTA NOGUEIRA
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Financial Mathematics in Basic Education: An Introduction to Investment Analysis
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Leader : VIVIANE PARDINI VALERIO
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MEMBRES DE LA BANQUE :
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VIVIANE PARDINI VALERIO
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CARLA REGINA GUIMARAES BRIGHENTI
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LUIZ GUSTAVO PERONA ARAÚJO
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Data: 25 mars 2021
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Afficher le Résumé
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This dissertation aims to highlight the importance of Financial Mathematics in the basic formation of a student, working necessary skills to make decisions in purchase and sale operations and investment analysis. We seek to show that some skills developed in basic education serve as a theoretical basis for a more investigative vision, which provides the construction of models and problem solving, providing conditions for the approach to Financial Mathematics contents that, generally, are worked only in higher education. The development of the work led us to the study of two of the main mathematical methods used in the “Investment Analysis” (Net Present Value Method - NPV and Internal Rate of Return Method - TIR), providing to the basic education teachers necessary subsidies for initial teaching of this important branch of Financial Mathematics. The work was accomplished through the description and mathematical analysis of each of the two investment analysis techniques, and later study of some applications (worked algebraically and with the HP-12C financial calculator). It is important to stand out that the whole mathematical theory involved in the work is based on capital equivalence where, through the displacement of capital over time, we developed both methods of investment analysis.
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3
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EDER SILVA DE ANDRADE
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Perceptions on financial mathematics of students in the final years of elementary and high school from two schools inthe south of Minas.
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Leader : RONALDO RIBEIRO ALVES
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MEMBRES DE LA BANQUE :
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RONALDO RIBEIRO ALVES
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ANDREA CRISTIANE DOS SANTOS DELFINO
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ROSICLER APARECIDA DE OLIVEIRA
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Data: 12 mai 2021
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Afficher le Résumé
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It is known that financial mathematics is one of the areas of mathematics with the greatest applicability and relevance in the daily life of the entire population. Therefore, this article aims to present a brief theoretical context and carry out a statistical survey aimed at measuring the knowledge and attitudes of high school and elementary school students from some public and private schools in Coqueiral and Varginha, southern Minas Gerais. The field study methodology was used through the application of questionnaires, through Google Forms from which the presented data came. The results point to a limited understanding of students in relation to their knowledge of financial mathematics, reinforcing the need to turn our attention to this area of mathematics that is often worked only mechanically, without contextualized involvement.
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4
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THAÍS PRESOTTI DE ALMEIDA MACHADO
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MATHEMATICS MODELING FOR TEACHERS: A PRACTICAL APPROACH TO TEACHING APPLICABLE MATHEMATICS
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Leader : JOSE ANGEL DAVALOS CHUQUIPOMA
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MEMBRES DE LA BANQUE :
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COSME EUSTAQUIO RUBIO MERCEDES
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JOSE ANGEL DAVALOS CHUQUIPOMA
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JUAN CARLOS ZAVALETA AGUILAR
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Data: 29 juin 2021
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Afficher le Résumé
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The main objective of this work is to reflect on the use of mathematical modeling as a didactic tool. We present it as an alternative active methodology for teaching mathematics in basic education, seeking to place the student as a protagonist in the construction of their knowledge. Through the mathematical interpretation of real problems, we try to support the teaching-learning process. The mathematics teacher is invited to verify how the construction of a mathematical model can be done during his teaching practice, in view of two examples for secondary education: the modeling of mobile phone rates and the modeling of the propagation of COVID-19 cases in the Brazil.
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5
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DIEGO MOREIRA MACIEL
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A reflection on the intradisciplinarity between geometry and algebra in elementary school
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Leader : VIVIANE PARDINI VALERIO
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MEMBRES DE LA BANQUE :
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FRANCINILDO NOBRE FERREIRA
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VIVIANE PARDINI VALERIO
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ÉDER MARINHO MARTINS
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Data: 16 juil. 2021
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Afficher le Résumé
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The general objective of this work is to reflect on the natural intradisciplinarity between algebra and geometry
in schools, more specifically how geometry contributes to algebra and algebra to geometry in elementary school -
final years. In the course of the work, we explored a total of eight basic mathematical contents, seeking to
understand and highlight this intradisciplinarity. We also explored the GeoGebra software through proposed
activity scripts and we report an experience in the classroom in an eighth grade class. We hope to awaken in our
readers, fellow professors, the perception that algebra and geometry coexist and that this well-crafted coexistence,
evidenced, in our classes can make mathematics much more interesting and pleasurable to teach and learn.
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6
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RICARDO VIEIRA LIMA
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Differential and Integral Calculus: aspects of the discipline in the formation of the Mathematics teacher and proposals for didactic sequences for high school students
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Leader : ANDREIA MALACARNE
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MEMBRES DE LA BANQUE :
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ANDREA CRISTIANE DOS SANTOS DELFINO
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ANDREIA MALACARNE
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FRANCIS FÉLIX CÓRDOVA PUMA
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Data: 21 juil. 2021
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Afficher le Résumé
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Differential and Integral Calculus is a discipline present in several undergraduate courses, not only in the areas of Exact Sciences. Specific contents of this discipline are applied in several areas of knowledge, providing relevant scientific contributions to society. In Mathematics teacher education courses, this subject is mandatory. Given this fact, we intend to analyze in this work the Differential and Integral Calculus in the formation of the Mathematics teacher. For this, we carried out a study of the official documents that guide the implementation of these courses, as well as works that deal with Calculus in undergraduate courses, in particular, in Mathematics licentiate courses. The Calculus and Professional Masters Program in Mathematics in a National Network (PROFMAT) was also the object of investigation in this work. Through the dissertation list, we selected conclusion papers that deal with topics in this discipline and made a survey of the main characteristics of these papers. Finally, this work proposes didactic material and didactic sequences on Limit, Derivative and Integral, which can support the Mathematics teacher in the elaboration of a teaching project for the last years of basic education. The idea is that this project involves students who wants to enroll in undergraduate courses of exact sciences or other courses that include the Differential and Integral Calculus discipline.
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7
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ADRIANA MARTA DE SOUZA
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INTRODUCTION TO THE CONTENT OF TIME SERIES THROUGH REMOTE TEACHING: REPORT OF AN EXPERIENCE.
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Leader : LUCIANE TEIXEIRA PASSOS GIAROLA
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MEMBRES DE LA BANQUE :
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LUCIANE TEIXEIRA PASSOS GIAROLA
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VIVIANE PARDINI VALERIO
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REJANE CORREA DA ROCHA
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GRAZIELA ROCHA DUTRA GOUVÊA
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Data: 22 juil. 2021
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Afficher le Résumé
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The purpose of this work is to report the experience of introducing the content of time series, through remote teaching, using digital information and communication technologies (TIDC's), for students of the Professional Master's Degree in Mathematics in national network (PROFMAT) of the Federal University of São João del Rei, Santo Antônio campus. Synchronous online activities were carried out through the Google Meet platform, approaching the content and presenting several examples of real series. A pedagogical guide was previously presented to the sixteen participating students, containing the necessary information for the development of teaching. The activities were planned using slideshow and Kahoot, Google Forms and Mentimeter platforms for the development of quizzes, questionnaires and word cloud, respectively. GRETL software was also used for exploratory analysis of real time series. Most students considered that it was good to participate in the activities, as well as the approach to the content through online classes. The concepts of trend and seasonality were the best understood and the greatest difficulty was to understand the hypothesis test presented to assess the stability of the variance of a series. Finally, I believe that the activities contributed to enriching students' knowledge, expanding their ability to understand real data that are characterized as time series; that the use of TIDC's was motivating and contributed to the understanding of the content.
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8
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CAYO CÉSAR VIANA DE LIMA
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PERFORMANCE OF STUDENTS FROM THE STATE OF MINAS GERAIS IN THE NATIONAL EXAM OF HIGH SCHOOL IN 2019 CONSIDERING SOCIO-ECONOMIC VARIATIONS
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Leader : CARLA REGINA GUIMARAES BRIGHENTI
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MEMBRES DE LA BANQUE :
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CARLA REGINA GUIMARAES BRIGHENTI
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EVERTON LUIZ DE PAULA
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VIVIANE PARDINI VALERIO
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Data: 26 juil. 2021
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Afficher le Résumé
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This study verifies the general performance of high school graduates in 2019 from schools in the State of Minas Gerais in the Exame Nacional do Ensino Médio, the ENEM. Through data provided by the Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira - INEP, descriptive statistics were used considering the following variables: school administrative dependence, gender, race, income, parents' education, grades in order to relate them to the performance of these students according to their socioeconomic profile. Altogether, the grades of 91540 students from private, federal, state and municipal schools and from the Military Police Tiradentes Schools (CTPM) are counted. The data show that, although most students who took the ENEM 2019 and who completed high school in the same year are enrolled in state schools, these institutions had the lowest averages in all areas of knowledge of the test. The average of the grades of private schools, in turn, was superior to all other institutions in all areas and follows a national standard. The investigation shows how socioeconomic variations contribute to a broader framework through which inequalities constitute barriers to improving school performance and to the democratization of education in Brazil.
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9
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MARCO AURÉLIO NOGUEIRA LEÃO
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A DECADE OF STATISTICS AND PROBABILITY ISSUES AT ENEM: ANALYSIS OF TEACHING TESTS AND PRACTICES
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Leader : CARLA REGINA GUIMARAES BRIGHENTI
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MEMBRES DE LA BANQUE :
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CARLA REGINA GUIMARAES BRIGHENTI
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LUCIANE TEIXEIRA PASSOS GIAROLA
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EVERTON LUIZ DE PAULA
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Data: 28 juil. 2021
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Afficher le Résumé
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Only with the emergence of the National Curriculum Parameters in 1997, the contents of Statistics, Probability and Combinatorics were included in the Basic Education curriculum, initially only for the early years of Elementary School, in 1998 for the final years of Education Elementary and in 1999 for High School. However, it is observed that there is still a gap in probabilistic and statistical education, more specifically in the first two grades of high school, which has a direct impact on the results of the National High School Exam (ENEM). This study aimed to quantitatively analyze the issues related to probability and statistics involved in the ENEM Mathematics test and its technologies, from 2009 to 2019, according to the skills and competences approach. A questionnaire was also applied to high school mathematics teachers in order to help them understand how teaching practices have been organized in relation to the teaching of issues associated with Probability, Statistics and Combinatorial Calculus. Throughout the study, it can be understood that it is essential that schools should train basic education students to take this exam, creating new teaching strategies that can favor the development of probability and statistics skills. In view of the results presented in this work, there is a considerable amount of issues of Statistics, Probability in ENEM tests, and with it the importance that such matters are dealt with even more carefully in basic education, especially throughout the high school.
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10
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MARCO AURÉLIO NOGUEIRA LEÃO
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ANALYSIS OF STATISTICS AND PROBABILITY ISSUES IN ENEM BETWEEN 2009 AND 2019
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Leader : CARLA REGINA GUIMARAES BRIGHENTI
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MEMBRES DE LA BANQUE :
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CARLA REGINA GUIMARAES BRIGHENTI
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LUCIANE TEIXEIRA PASSOS GIAROLA
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EVERTON LUIZ DE PAULA
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Data: 28 juil. 2021
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Afficher le Résumé
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Only with the emergence of the National Curriculum Parameters in 1997, the contents of Statistics, Probability and Combinatorics were included in the Basic Education curriculum, initially only for the early years of Elementary School, in 1998 for the final years of Education Elementary and in 1999 for High School. However, it is observed that there is still a gap in probabilistic and statistical education, more specifically in the first two grades of high school, which has a direct impact on the results of the National High School Exam (ENEM). This study aimed to quantitatively analyze the issues related to probability and statistics involved in the ENEM Mathematics test and its technologies, from 2009 to 2019, according to the skills and competences approach. A questionnaire was also applied to high school mathematics teachers in order to help them understand how teaching practices have been organized in relation to the teaching of issues associated with Probability, Statistics and Combinatorial Calculus. Throughout the study, it can be understood that it is essential that schools should train basic education students to take this exam, creating new teaching strategies that can favor the development of probability and statistics skills. In view of the results presented in this work, there is a considerable amount of issues of Statistics, Probability in ENEM tests, and with it the importance that such matters are dealt with even more carefully in basic education, especially throughout the high school.
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11
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ANA PAULA SOUSA
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AN EXPERIENCE OF USING THE APPLICATION EASY STATISTICS AS A SUPPORT TOOL IN TEACHING STATISTICS AND TOPICS PERCEPTIONS OF MATHEMATICS TEACHERS OF BASIC EDUCATION AND STUDENTS OF HIGH SCHOOL RELATED TO THE USE OF DIGITAL INFORMATION AND COMMUNICATION
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Leader : ANDREA CRISTIANE DOS SANTOS DELFINO
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MEMBRES DE LA BANQUE :
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ANDREA CRISTIANE DOS SANTOS DELFINO
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ANDREIA MALACARNE
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ALESSANDRA QUERINO DA SILVA
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Data: 30 juil. 2021
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Afficher le Résumé
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Due to the situation and the pandemic situation caused by Covid-19, teachers needed to reinvent themselves in their activities and students needed to adapt to the new reality. Regarding education, which had its activities suspended, many doubts arose about how to offer efficient teaching. Linked to this, it was also exposed to the fragility of the educational system, technologically unprepared to serve everyone. In this context, the use of technologies became essential for the execution of teaching practice. Thus, this work sought to understand the perceptions of mathematics teachers and high school students related to the use of digital information and communication technologies as a support tool in the teaching of statistics topics, analyzed in a state public school in the city of Divinopolis-MG. To obtain the necessary information, a survey of data on mathematics teachers and students from a state public school was carried out. It was possible to notice that initially the teachers did not have the necessary skills to conduct the classes, requiring a quick search for qualification. Students consider the use of technology to be important as a support tool in teaching, but refer to in-person classes.
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12
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VALDEMIR MARTINS FILHO
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ACTIVE METHODOLOGIES AND A POSSIBILITY OF USE IN HIGH SCHOOL
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Leader : FRANCINILDO NOBRE FERREIRA
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MEMBRES DE LA BANQUE :
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FRANCINILDO NOBRE FERREIRA
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SANDRO RODRIGUES MAZORCHE
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VIVIANE PARDINI VALERIO
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Data: 13 août 2021
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Afficher le Résumé
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In view of the serious problems faced in the teaching of mathematics and its consequences, there is a need for the search for updating, innovation and the study of procedures aimed at teaching tools. In this scenario, investigations related to new pedagogical practices have conceptualized active methodologies as a viable proposal in the search for better results. Therefore, this study aims to discuss the importance of active methodologies. Therefore, it is essential to discuss the need to update and complement current practices, describe the benefits derived from active practices, identify which factors linked to the methods contribute to the process, carry out a study of actions that are being addressed and finally propose possibilities for implementation in the high school, especially in the subject of mathematics. Thus, a bibliographic research was used as a method of collecting information, using materials developed by scholars in the area. From the analysis of the studies carried out, it appears that the implementation of active practices in the teaching and learning process, contributes positively to the social and professional training of the student, increases the representativeness of the school as a space for training, raises the levels of consolidation of content and promote better working conditions. Such results impose the observation that the adoption of active methodologies can favor the achievement of better results, as well as promoting greater satisfaction for those involved in the educational environment.
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13
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CÉLIA MARIA SOUZA
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Symmetries in Pascal's Triangle
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Leader : FABIO ALEXANDRE DE MATOS
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MEMBRES DE LA BANQUE :
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FABIO ALEXANDRE DE MATOS
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FRANCINILDO NOBRE FERREIRA
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SILVIO ANTONIO BUENO SALGADO
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Data: 13 août 2021
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Afficher le Résumé
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This work makes a compilation of several Pascal?s Triangle properties, as well as their demonstrations. We begin with a little bit of the history of Pascal, their life, and their work in the scientific field, going to some no elementary properties of Fong?s Theorem, the Little Theorem of Hóquei, and Puckl and the Properties of the Davi?s Star. We made an association of Davi?s Theorem with polygons and work the symmetries inside Pascal?s Triangle. Furthermore, we did an association of work?s content and a way to use the interdisciplinarity for their study. Finally, we have a suggestion for classroom activity to be worked with high school students.
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14
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HELIANE SANTOS PENHA
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Resolution of Systems of Linear Equations and Their Applicability in High School
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Leader : JUAN CARLOS ZAVALETA AGUILAR
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MEMBRES DE LA BANQUE :
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JUAN CARLOS ZAVALETA AGUILAR
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JOSE ANGEL DAVALOS CHUQUIPOMA
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SANTOS ALBERTO ENRIQUEZ REMIGIO
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Data: 13 août 2021
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Afficher le Résumé
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This work approaches a perspective for solving linear systems and its applicability in high school, where emphasis is given to the study of the existence and uniqueness of solutions of linear systems as well as analytical and numerical techniques to find solutions, if any, through methods such as: Gaussian elimination, LU factorization, Jacobi method, Gauss-Seidel method. It will also analyze the most common techniques for solving linear systems in high schools. Thus, this work aims to point out the importance of teaching linear systems in high school and to contribute towards making this mathematical content more meaningful to students. The main idea defended in this paper is that when exposed to challenging situations, students feel the need to learn new mathematical techniques and tools, which provide the mastery of skills and competencies that can be applied to everyday situations. The need to learn a new content should come from the students themselves, as soon as they are faced with a situation that challenges and motivates them. Thus, this is a proposal for the teaching of systems of linear equations in which topics contemplated in the Common National Curricular Base (BNCC) of high school are presented as well as complement this subject with other analytical and numerical methods, so that the student has a broader view of the range of methods and problems that can be contemplated. For this, a lesson plan is proposed in which the main theoretical tools are presented, as well as the solution of contextualized problems through different analytical and numerical techniques.
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15
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HELIANE SANTOS PENHA
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Resolution of Systems of Linear Equations and Their Applicability in High School
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Leader : JUAN CARLOS ZAVALETA AGUILAR
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MEMBRES DE LA BANQUE :
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JOSE ANGEL DAVALOS CHUQUIPOMA
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JUAN CARLOS ZAVALETA AGUILAR
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SANTOS ALBERTO ENRIQUEZ REMIGIO
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Data: 13 août 2021
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Afficher le Résumé
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This work approaches a perspective for solving linear systems and its applicability in high school, where emphasis is given to the study of the existence and uniqueness of solutions of linear systems as well as analytical and numerical techniques to find solutions, if any, through methods such as: Gaussian elimination, LU factorization, Jacobi method, Gauss-Seidel method. It will also analyze the most common techniques for solving linear systems in high schools. Thus, this work aims to point out the importance of teaching linear systems in high school and to contribute towards making this mathematical content more meaningful to students. The main idea defended in this paper is that when exposed to challenging situations, students feel the need to learn new mathematical techniques and tools, which provide the mastery of skills and competencies that can be applied to everyday situations. The need to learn a new content should come from the students themselves, as soon as they are faced with a situation that challenges and motivates them. Thus, this is a proposal for the teaching of systems of linear equations in which topics contemplated in the Common National Curricular Base (BNCC) of high school are presented as well as complement this subject with other analytical and numerical methods, so that the student has a broader view of the range of methods and problems that can be contemplated. For this, a lesson plan is proposed in which the main theoretical tools are presented, as well as the solution of contextualized problems through different analytical and numerical techniques.
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