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RODRIGO DIAS MATOS
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FLAT GEOMETRY: UNUSUAL PROPERTIES AND THEOREMS IN EVERYDAY BASIC EDUCATION
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Data: 15/12/2021
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The main objective of this work is to provide support material and also to deepen the discipline of Plane Geometry, more specifically in the study of problem solving involving areas of plane figures, and in this way contribute to Basic Education teachers and students who participate or intend to participate in Olympic competitions such as the Brazilian Mathematics Olympiad for Public and Private Schools – OBMEP, also serving as support material for students of the Professional Master's Degree in Mathematics – PROFMAT in the MA 13. This work will address unusual properties and theorems. in the curriculum of the subject of mathematics in Basic Education, more of great importance in the study of Plane Geometry and in the context of the current Olympics, such as the Theorems of Stewart, Ceva and Menelaus, which refer to remarkable segments in a triangle, and which are fundamental for the solution to many problems in this area.
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MARCEL BRITO SOARES
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TEACHING PROBABILITY IN THE 8TH YEAR THROUGH ACTIVITIES
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Data: 15/12/2021
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This work aims to present a didactic sequence for the teaching probability through activities with an approach to conceptual aspects and on the resolution of issues involving the subject, in order to favor the participation of students in math classes and learning the concepts present in each activity. the rationale theory served as the basis for the "construction" of the didactic sequence that was adapted from the author's dissertation, based on the Teaching of Mathematics by Activities. The sequence consists of five activities that include the differences of deterministic and random experiments, space concepts sampling and events, the classical definition of probability and the interval of probability variation. The sequence can be applied in the 8th and 9th years of the Elementary School.
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NELIO SANTOS NAHUM
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COUNTING METHODS: A TEACHING PROPOSAL USING PROBLEMS FOR HIGH SCHOOL.
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Data: 03/09/2021
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This research work approaches the counting methods studied in high school. With an emphasis on bibliographical research in books and scientific articles, and based on the use of a activities sequence, it was possible to build a teaching proposal using problem solving that seeks to value logical thinking, the mounting of strategies, rather than by the use of standard examples solved mechanically. The motivation for proposing this approach arose from concerns derived from the teaching experience in basic education and from the knowledge acquired in the Professional Master's Degree in Mathematics in the National Network (PROFMAT), which has enabled a meaningful teaching vision from the dialogue with other works of textbooks that are used daily at schools. In this sense, we seek to investigate and understand the counting methods, starting from a proposal that directs the use of problems, stimulating the ingenuity and understanding of the situation described. The propose addressed favors the use of the Basic Principle of Counting (BPC), with which problems can be solved regardless of the type of grouping involved (arrangement, permutation and combination).Thus, four sequences of activities are presented, along with methodological proposals for teaching and learning of counting methods. The construction occurred in line with the guidelines of the BNCC and with the contributions of analyzes of the works of Hazan, Dante and Morgado. The research was concluded taking into account that the approach of counting methods based on problem solving enables significant learning.
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RENERSON RENNEE MALATO DE SOUZA
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PROGRESSIVES: PROBLEMS AND SOLUTIONS.
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Data: 30/07/2021
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This work is a study of progressions, that is, arithmetic (PA), geometric (PG), harmonic (PH), arithmetic-geometric (PAG) and geometric-arithmetic (PGA) progressions. Furthermore, to introduce progressions, topics such as finite induction and first order recurrence were discussed. This research was developed through the process of constructing mathematical formulas, theorems demonstrations and exercise resolutions. The objective is to improve the understanding and understanding of demonstrations involving progressions, in addition to instructing and listing methods, paths and examples on how to promote the study of progressions at a deeper level, that is, to expand the possibilities of mathematics in the teaching-learning process of the progressions. According to the bibliographical study developed, it is possible to show that the demonstration processes involving progressions have an important relationship with the construction of the cognitive and logical development of mathematics. The method used in the research had the combination of being exploratory, explanatory and descriptive. Finally, the research found that the studies of progressions through problem solving contribute to the development of logical, cognitive and interpretive reasoning for both students and teachers in their teaching-learning process.
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MICHELLEN ALESSANDRA CALDAS SOUZA
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The Study of the Unknown in the 1st Degree Equations Through the Analysis of Textbooks.
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Data: 19/07/2021
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This work aims to verify whether textbooks satisfactorily address the Incognita in the knowledge and resolution of 1st Degree Equations. Thus, it seeks to analyze how textbooks approach the study of Equations of the 1st Degree, especially the Incognita, in the seventh year of Elementary School, according to the dimensions of Algebra presented by the PCN and the competencies and skills proposed by the BNCC for the that year. Thus, initially, a historical approach was made about Algebra and the emergence of Equations, based on the works of several authors. This work also reinforces the importance of using letters as Incognita for learning Equations, and highlights the student's need to understand the algebraic language as well as the meaning of Incognita for a better knowledge and resolution of 1st Degree Equations. For this purpose, textbooks from the seventh year of elementary school were analyzed in order to check whether they satisfactorily contributed to the algebraic development of the students.
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SEBASTIAO JUNIOR MONTEIRO COSTA
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STUDY OF GEOMETRIC SOLIDS IN THE AMAZON CONTEXTUALIZATION: THE ETHNOMATHEMATICS OF MATAPI BASKETBALL AND THE THEORY OF VAN HIELE
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Data: 15/06/2021
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O ensino da geometria, assim como de modo geral, o da matemática está pautado em possibilitar ao aluno a construção do conhecimento a partir do que é adepto a ele, ou seja, ensinar e aprender Matemática de acordo com o modo de vida do aluno, contudo o que tem se observado é que os alunos apresentam dificuldades de compreender os conceitos de geometria, principalmente quando se trata de sólidos geométricos. Por isso, o objetivo principal do trabalho é compreender as relações da geometria espacial para que possam descobrir formas e representações das mesmas, a partir da confecção do matapi, partindo do próprio cotidiano do aluno como uma alavanca para obter conceitos matemáticos para os alunos do 8º ano do Ensino Fundamental da Escola Irmã Stella Maria – Anexo 1, localizada no rio Furo Grande, nas ilhas de Abaetetuba/PA e em consonância com o modelo de aprendizagem da Teoria de Van Hiele, no qual auxilia na identificação de competências e na orientação no decorrer da aprendizagem para o desenvolvimento do pensamento geométrico a níveis mais elevados de compreensão, respeitando os níveis do pensamento geométrico em que o aluno se encontra. Para o desenvolvimento deste trabalho foi utilizado a metodologia de estudo bibliográfico, juntamente com a realização de uma atividade de caráter pedagógico em sala de aula, dos quais as asserções foram analisar como a prática proposta – confecção do matapi – deram importância ao interesse do aluno por utilizar um recurso comum do seu dia a dia e apresentar conceitos geométricos, como também as necessidades individuais e os níveis de desenvolvimentos, pautadas na teoria de Van Hiele, os dados foram coletados e analisados por meios do questionário de sondagem (para averiguar os conhecimentos prévios dos alunos sobre o tema). Por meio da realização deste trabalho constatou-se que os estudantes tiveram uma visão distinta sobre a Geometria - principalmente da geometria espacial - valorizando a construção humana, ao assimilarem que a matemática não é apenas composta por equações, e sim que é possível aproximar o ensino da matemática à cultura local, interligando os saberes tradicionais com os saberes adquiridos em sala de aula, através da prática.
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JOCIEL MACHADO NUNES
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THE RELEVANCE OF COMPLEX NUMBERS IN BASIC EDUCATION.
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Data: 11/06/2021
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This work addresses the study of the complex number and application in the area of geometry, with the aim of showing that such knowledge can be relevant in basic education. Historically, the development of complex numbers took about 300 years to formalize as a set of complex numbers where it was possible to obtain a solution for equations of the type and another with similar characteristics. The solutions of this type of equation were described by Euler as being of the type and , thus enabling the construction of the set of complex numbers, where $ i $ is called an imaginary unit of the number $ z $. However, this set came to be better understood when K. F. Gauss and Jean-Robert Argand independently discovered that Z could be represented geometrically. It is a fact that the number z is not a priority in basic education in Brazil, largely because of the new tendency of content flexibility that appears less and less in the entrance exams and is not required in the National High School Exam. However, it is important that the elementary school student knows the advantage of using the set to better understand non-real 2nd degree equation roots. The formalism of set z is treated in undergraduate courses with various applications in the areas of mathematics, physics, engineering and etc. Although not useful in basic education, it is necessary to approach the concept of the number z as an algebraic operator responsible for rotating a vector 90º. From this approach it was possible to apply some problems in the area of geometry, such as in the lunar movement (application of the 2nd Moivre formula), angle between lines, cube root of a non-real number, systems solutions to two variables involving complex numbers with emphasis on plane geometry. In this sense, there is a great advantage in considering the applicability of complex numbers in other areas of knowledge and due to this advantage, it could be part of the content at the level of basic education. Thus, taking into account the algebraic and geometric aspects in the solution of several problems in which it is necessary to know the set z, the teacher would undoubtedly have one more resource to address some contents that are intrinsic in basic education and that requires looking for methods that facilitate learning. It is concluded with the research that the set of complex numbers has the advantages of expanding the learning using the concepts of complex number as an algebraic operator and with the advantage in applications in geometry and other segments of scientific knowledge.
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SIMEY DA COSTA NEGRAO
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HISTORICAL METHODS OF MULTIPLICATION AND DIVION AS A FACILITATING RESOURCE FOR TEACHING
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Data: 10/06/2021
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The work has as a general objective to show the multiplication and division techniques, allowing the student the historical knowledge of some methods used by ancient civilizations that can be developed for the solution of everyday problems. In this case, the multiplication and division methods developed in some ancient civilizations and the use of Napier Bars or Bones are developed and based, constituting a facilitating resource for the teaching and learning process. The study based on theoretical research, based on literature by authors such as Eves (2004), Boyer (2012), Rooney (2012), among others, that favor the necessary principles in which mathematics is inserted in the historical conception and in the instruments that are fundamental to understanding and application in everyday school life. Exploratory research brings together reports of teaching activity developed in a hybrid way (in person and online) in classes of the 5th and 6th grades of Elementary School with the use of Napier Bars in solving mathematical questions, as well as the conclusions about this one practice. The research is concluded considering the need for a methodology that encompasses activities of multiplication and division operations in order to improve the teaching and learning process in the Mathematics discipline.
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DANIEL DE DEUS NEGRAO MAUES
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A proposal for teaching financial mathematics using App Inventor 2.
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Data: 04/06/2021
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The objective of this work was “To propose, through Active Methodologies, the teaching of Constant Amortization Systems - (SAC) and French Amortization System - (SAF) using the application“ Capitalizacao ”, created on the block programming platform MIT App Inventor” aimed - there is a need for better financial education for the Brazilian population linked to a teaching strategy that involves new methodological trends. In this sense, it was guided in this dissertation to make a proposal involving hybrid teaching and meaningful learning using the technological tool, the “capitalization” application. Therefore, it was necessary to seek previous studies with methodological experiments using new trends for the teaching of financial mathematics, thus the reading of dissertations related to financial mathematics and the use of technological tools in the teaching methodology was carried out. It was observed in the literature abstracts present in this dissertation that the methodological proposals are similar to the objective chosen in this work. Still as information, research was done on financial education seeking to give meaning to the teaching of the formal content of financial mathematics which was presented and used for the elaboration and structuring of four activities for the teaching of financial mathematics, emphasizing the SAC and SAF. Thus, based on the information collected in the aforementioned research, a comparison was made with the proposal chosen in this dissertation, where it was found that the methodological proposals of the analyzed dissertations show similarities to the objective of this work. This fact provided an indication of the proposal's validity. carried out in this dissertation which must be applied later in the face-to-face.
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