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Dissertations |
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1
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RODOLFO DOS SANTOS SILVA
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Ethnomathematics and Geometry in Textile Arts: Analysis through Didactic Engineering
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Advisor : VANIO FRAGOSO DE MELO
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COMMITTEE MEMBERS :
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EDIEL AZEVEDO GUERRA
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GIVALDO OLIVEIRA DOS SANTOS
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JOSE DA SILVA BARROS
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VANIO FRAGOSO DE MELO
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Data: Mar 14, 2024
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Show Abstract
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This work aims to develop the concepts of areas of plane figures Through a Didactic Sequence guided by the methodology of Didactic Engineering, bringing to light a study between plane geometry seen in the basic education classroom, with geometry in production artesanal, such as fillet. Furthermore, a theoretical survey will be carried out on Ethnomathematics with the aim of justitying artesanal production as a Branch of Ethnomathematics.
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2
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FERNANDO LOPES DO NASCIMENTO
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CALCULATION OF POLYGON AREAS IN A DYNAMIC APPROACH USING GEOGEBRA SOFTWARE IN THE 9TH YEAR OF ELEMENTARY SCHOOL
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Advisor : LUIS GUILLERMO MARTINEZ MAZA
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COMMITTEE MEMBERS :
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GABRIEL ARAUJO GUEDES
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LUIS GUILLERMO MARTINEZ MAZA
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VIVIANE DE OLIVEIRA SANTOS
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Data: Mar 27, 2024
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Show Abstract
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In this dissertation we will present a didactic sequence for teaching polygon areas using the GeoGebra software. For this purpose, a bibliographical study was carried out. Some concepts of plane geometry were covered, especially such as polygon area formulas, making use of the area formula demonstrated in the Dissertation made by (Lima, 2014) [17], where demonstrating a formula through Determinants, using the coordinates of the points in a Cartesian graph, whose area is the sum of the halves of these determinants. Projections of area formulas using this method were shown. Polygon constructions were made in the GeoGebra Software, calculating the areas to check whether the results generated by the formula were correct. Finally, a didactic sequence was made to apply the concepts mentioned.
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3
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JOSÉ JERFFESSON CAZÉ DE ANDRADE
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THE IRRATIONALITY OF √𝟐 BY THE METHOD OF REDUCTION TO ABSURD IN HIGH SCHOOL
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Advisor : EDIEL AZEVEDO GUERRA
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COMMITTEE MEMBERS :
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MARTA ÉLID AMORIM MATEUS
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EDIEL AZEVEDO GUERRA
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VANIO FRAGOSO DE MELO
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Data: Apr 1, 2024
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Show Abstract
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In this work, we investigate the learning difficulties inherent to the use of the method of reduction to absurdity in the first year of high school to demonstrate the irrationality of the number √2. This is a qualitative research, having as a theoretical-methodological reference the Method of Learning Mathematics through Problem Solving by Lourdes Onuchic. Among the results obtained, we highlight the following: the presentation of the demonstration of the irrationality of √2 at the beginning of high school with good learning results is possible, but it requires special and careful teaching strategies in the introduction of rational principles and direct and indirect demonstration methods
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4
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ARIEL SANTOS DA SILVA
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THE EXPERIENCE OF EMPATHY IN THE EXPERIENCE OF TEACHING PRACTICE AND MATHEMATICS LEARNING
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Advisor : EDIEL AZEVEDO GUERRA
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COMMITTEE MEMBERS :
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EDEL ALEXANDRE SILVA PONTES
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EDIEL AZEVEDO GUERRA
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JULIANA ROBERTA THEODORO DE LIMA
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Data: Apr 1, 2024
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Show Abstract
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This work addresses the topic of empathy between educator and student. More precisely, we will address the following investigative question: how do mathematics teacher’s experiences of empathy experienced as students affect their learning processes and how can teachers of this discipline have a more empathetic position towards their students? To answer this question, descriptive qualitative research was carried out based on the phenomenological method according to the variant proposed by Sanders for empirical phenomenological research. In this research it was observed that teachers recognize the importance of empathy in learning mathematics, this recognition being based on the belief that if they had had empathy from their teachers, that is, if teachers had paid more attention, presented more openness to identify the learner’s difficulties and had established more affective relationships with the students, the teachers could have achieved better results in terms of the student’s learning processes
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5
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YUDI JOÃO MANOEL SILVA DE OLIVEIRA
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Numerical Analysis and Methods for Approximate Calculation of Areas and Volumes
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Advisor : MARCIO HENRIQUE BATISTA DA SILVA
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COMMITTEE MEMBERS :
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JOSE ANDERSON DE LIMA E SILVA
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MARCIO HENRIQUE BATISTA DA SILVA
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MARCIO SILVA SANTOS
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Data: Apr 3, 2024
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Show Abstract
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In this work, we comprehensively address the importance of numerical techniques in estimating areas and volumes in various situations. We emphasize the relevance of these techniques in complex contexts where direct approaches are impractical or inaccessible. Numerical analysis, through mathematical and computational approaches, plays a crucial role in determining areas and capacities, especially in challenging geometries. The text explores the integration of skills related to the teaching of areas and volumes throughout Basic Education, aligned with the National Curricular Base (BNCC). In the scope of numerical analysis, fundamental concepts are presented from an accessible standpoint. Among these concepts are the definite integral, numerical integration methods, numerical error, and convergence, which are essential for the efficient calculation of areas and volumes. Furthermore, specific methods are discussed, such as the rectangle method, trapezoidal method, and Simpson's rule for areas, as well as methods involving cross- sectional areas and cylindrical shells for volumes. The article also proposes the investigation and comparison of numerical methods, aiming to contribute to the appropriate selection of these techniques in different applied contexts. In summary, this work provides a comprehensive view of the importance of numerical techniques in estimating areas and volumes, highlighting their applicability in challenging situations and offering a solid foundation for the selection and application of these techniques in various educational and practical contexts.
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6
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WESLEY HANDERSON BARRETO DA SILVA MARTINS
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The Use of Geogebra in Proving Plane Geometry Theorems.
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Advisor : JOSE CARLOS ALMEIDA DE LIMA
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COMMITTEE MEMBERS :
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JOSE CARLOS ALMEIDA DE LIMA
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ANDRE LUIZ FLORES
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GABRIEL ARAUJO GUEDES
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Data: Apr 29, 2024
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Show Abstract
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Mathematics education has been undergoing a process of change that has intensified mainly during the COVID-19 pandemic, as today's society is immersed in what is called Education 5.0. In this type of "education", the approach is more focused on the digital technologies used in the educational process to guarantee a better socio-emotional development for the student. The National Common Curriculum Base (BNCC), through its general competences, learning objectives, in the competences and skills of various curricular components, recommends the use of digital technologies aimed at the students' experiences. It is in this sense that the use of GeoGebra, as a technological resource, can guarantee a better approach to mathematical concepts, as it is a dynamic software and tends to help in understanding the contents. The choice of the approach of using GeoGebra in the area of Geometry is due to its presence in everyday life, but also in various mathematical or physical contents and in various professions. The main objective of this work is to demonstrate Plane Geometry concepts using GeoGebra software for high school students, in addition to analyzing its potentialities and limitations in exploring Plane Geometry concepts and solving questions of the Brazilian Mathematics Olympiad of Public Schools (OBMEP). For this, the methodology used is of a qualitative nature, bibliographic and exploratory. Finally, the results obtained through the demonstrations of the theorems and the solutions of OBMEP questions show that GeoGebra can be used as a methodological resource in the teaching of Mathematics and mainly in the demonstration of Plane Geometry theorems.
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7
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JEFFERSON DAVID MOREIRA DOS SANTOS
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SageMath as a didactic tool in teaching of real functions for high school: a practical approach
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Advisor : GREGORIO MANOEL DA SILVA NETO
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COMMITTEE MEMBERS :
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ÁLVARO KRÜGER RAMOS
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ANDRE LUIZ FLORES
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GREGORIO MANOEL DA SILVA NETO
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Data: May 2, 2024
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Show Abstract
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This work proposes to show the advantages of using SageMath as a digital tool prac- tice by basic education teachers and students, providing support in classes on functions polynomials for the 1st year of high school. Specifically, in the manipulation of algebraic expressions and interaction with function parameters in the software. At the same time, to use introductory concepts from the Python programming language to build algorithms, in order to model and solve mathematical problems, and thus, visualize the respective graphics and representations.
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8
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ISABELLA MACIEL TORRES
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A pedagogical proposal in Financial Education
focused on credit operations
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Advisor : JULIANA ROBERTA THEODORO DE LIMA
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COMMITTEE MEMBERS :
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ISNALDO ISAAC BARBOSA
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JULIANA ROBERTA THEODORO DE LIMA
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NIVALDO DE GOES GRULHA JUNIOR
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Data: Sep 30, 2024
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Show Abstract
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Financial education is defined as a cross-cutting theme by the
National Common Curricular Base (BNCC). Although it is addressed from different perspectives in various curriculum components, beyond Mathematics, there are some gaps in the curriculum re- garding current topics related to various types of credit operations. Research indicates that the majority of the Brazilian population has some type of debt to pay. Therefore, this work begins by collecting data on the indebtedness of the Brazilian population. Ad- ditionally, it emphasizes the importance of laws that define strategies for preparing the population for everyday consumer relations through education. As a result, an alterna- tive educational material will be proposed, covering the most commonly used financial instruments by the population: credit operations, credit cards, financing, among other modalities. Finally, the responses of 3rd-year high school students to a survey focusing on their knowledge of financial topics and their ability to manage household finances will be highlighted
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9
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CAIO CÉSAR SILVA DE LIMA
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USE OF STATISTICS TO UNDERSTAND QUALITY INDICATORS OF PUBLIC EDUCATION IN ALAGOAS
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Advisor : AMAURI DA SILVA BARROS
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COMMITTEE MEMBERS :
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AMAURI DA SILVA BARROS
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GIVALDO OLIVEIRA DOS SANTOS
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ISNALDO ISAAC BARBOSA
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JOSEALDO TONHOLO
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Data: Dec 19, 2024
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Show Abstract
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This dissertation aims to discuss and analyze the evolution of public education in the State of Alagoas, showing the tools used by the government entities, studying the methodology of collecting, tabulating and organizing data with the help of Statistics, observing and discussing results in elementary school education (6th to 9th grade) and secondary education (1st to 3rd grade), presented through graphs and tables. The study is justified by the concern with the low performance rates that students have been presenting in the latest results of the Basic Education Development Index (IDEB) and by the need to help teachers, principals and the academic community in general to understand and identify critical points, so that states, cities and the federal government can identify patterns and trends that indicate where and how public policies can intervene to improve the quality of education. In this study, a bibliographical research was carried out on scientific articles, books and official federal government documents for the theoretical basis, a data collection on the INEP portal was carried out as well in order to create graphs and tables of the results obtained by schools in Alagoas. The results reveal that there must be concern among the competent authorities regarding the evolution of the indexes presented in this study.
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10
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HERIVELTON FABRICIO MENDONCA BARBOSA
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EVALUATION METHODS IN MATHEMATICS TEACHING: BUILDING A MEANINGFUL LEARNING ABOUT WHOLE NUMBERS IN THE LIGHT OF NATIONAL COMMON CURRICULAR BASE (BNCC)
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Advisor : ADINA ROCHA DOS SANTOS
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COMMITTEE MEMBERS :
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ADINA ROCHA DOS SANTOS
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ANDRE LUIZ FLORES
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JÔNATHAS DOUGLAS SANTOS DE OLIVEIRA
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Data: Dec 19, 2024
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Show Abstract
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his dissertation study employed a bibliographic review aimed at analyzing evaluation methods in MathematicsTeaching, focusing on the 7th grade of Elementary School. Seeking to propose improvements for the teaching ofWhole Numbersgrounded in the National Common Curricular Base (BNCC), this research seeks to contribute with a special focus on this numerical set, due to the inherent difficulties of understanding it in Basic Education. Using tools that foster and encourage learning, reflections were made on the evaluation methods, emphasizing the importance of planning and the construction of this organization obtained in the evaluations so that the evaluation becomes a learning tool. The primary contribution of this work to the teaching of Mathematics lies in the importance of the interaction between teacher and student, grounded in the students' cognitive knowledge as a path to their formation. With the creation and use of tools such as games involving the numerical set and with the breakingofthetabooofinterdisciplinarityofMathematicswithotherareasof knowledge,usingsustainablematerialsthatareeasilyacquiredinschool environments and in the students' communities, these adapted games and digital tools such as Khan Academy (2024), as a basis for this study, references from Jussara Hoffman (2009), D'Ambrosio (1989), Sant'Anna (2013), BNCC (2019) and others were used.
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11
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JOAO HENRIQUE DA SILVA SOUSA
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TEACHING CREATIVE MATHEMATICS FOR A GROWTH MENTALITY FROM PROBLEM SOLVING: A SYSTEMIC AND PEDAGOGICAL APPROACH
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Advisor : ISNALDO ISAAC BARBOSA
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COMMITTEE MEMBERS :
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ISNALDO ISAAC BARBOSA
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AMAURI DA SILVA BARROS
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ELTON CASADO FIREMAN
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JÔNATHAS DOUGLAS SANTOS DE OLIVEIRA
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Data: Dec 19, 2024
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Show Abstract
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Education in Brazil is undergoing an innovative transformation in teaching and learning, seeking to adapt to the social, technological and intellectual demands of a constantly changing world. Traditional teaching, focused on memorization and repetition and centered on the teacher, has proven to be ineffective, especially in the area of Mathematics, where the lack of connection between the content learned and its practical application demotivates students.To meet current demands, teaching methods that promote autonomy, responsibility, critical sense, creativity and protagonism of students in building their life projects are gaining prominence. In this context, strategies such as elaborating and solving problems and redefining mathematical concepts emerge as essential tools for developing these skills, with a special focus on creativity in Mathematics, which is the theme of this research.Based on these principles, this research seeks to answer how problem-solving methodology can contribute to the development of mathematical creativity in Basic Education students. To this end, the work intends to analyze didactic and methodological concepts, guiding basic education Mathematics teachers based on the ideas of authors who influenced this area of study in Brazil and around the world. This is detailed research on the subject, in which we consider questions such as: how do teachers teach? How do students learn? Do these relationships complement each other? What techniques and methodologies should teachers adopt? The focus will be on mathematics teachers in primary and secondary education. Therefore, we gave this work the title “Teaching Creative Mathematics for a Growth Mindset through Problem Solving”, using a systemic pedagogical approach.
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12
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JAZIEL DE LIMA CAVALCANTE
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TEACHING MATHEMATICS FOR EJA TEACHERS THROUGH THE QUANTITATIVE SURVEY OF COATING IN CIVIL CONSTRUCTION: A PRACTICAL AND INTERDISCIPLINARY APPROACH
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Advisor : ISNALDO ISAAC BARBOSA
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COMMITTEE MEMBERS :
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ISNALDO ISAAC BARBOSA
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ANDRE LUIZ FLORES
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EDEL ALEXANDRE SILVA PONTES
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Data: Dec 23, 2024
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Show Abstract
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This dissertation presents an innovative pedagogical proposal that integrates mathematics teaching in Youth and Adult Education (YAE) with the practical activity of quantitative assessment of coatings in civil construction. Through a practical and interdisciplinary approach, the study aims to support YAE teachers by providing tools that contextualize mathematical content to the realities of students, aligning with the guidelines of the Brazilian National Common Curricular Base (BNCC). The research reviews the historical trajectory of YAE in Brazil, discusses the challenges faced by this educational modality, and highlights the importance of contextualization in mathematics teaching. Methodologically, educational materials and a detailed step-by-step guide are presented for calculating various coating services, such as plaster, render, screed, and painting, based on a real architectural plan of a single-family residence. The results emphasize the potential of this proposal to make mathematics teaching more accessible, relevant, and engaging for both teachers and students in YAE, reinforcing its practical application and social transformation through education. The dissertation concludes with recommendations for adopting the methodology in diverse educational contexts, contributing to the development of meaningful and inclusive pedagogical practices.
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13
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THIAGO DOS REIS SILVA
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First-Order Linear Recurrence Relations – a proposal to model problems in high school through recursive formulas
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Advisor : LUIS GUILLERMO MARTINEZ MAZA
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COMMITTEE MEMBERS :
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ALEXANDRE FAISSAL BRITO
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ISNALDO ISAAC BARBOSA
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LUIS GUILLERMO MARTINEZ MAZA
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Data: Dec 30, 2024
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Show Abstract
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This work focuses on the study of numerical sequences, with particular emphasis on first-order linear recurrence relations. We explore how these relations can be applied in various mathematical areas, including geometry. The main goal is to enable students to make meaningful connections between distinct mathematical concepts, fostering a deeper understanding of sequence theory. The effectiveness of this approach is evaluated through two tests, one administered before and one after the intervention. These tests demonstrate an improvement in students’ performance regarding their understanding of numerical sequences. The applications discussed cover both elementary and secondary education, with specific adaptations for each educational level. The primary focus is on developing recursive reasoning and transitioning from recursive formulas to closed formulas, allowing for the precise and efficient calculation of any subsequent term in the sequence. We began our investigation by modeling a specific problem, starting from initial information established as the foundation. Subsequently, we adopted a formal approach grounded in rigorous methods to demonstrate relevant properties and construct the necessary formalizations and proofs. To illustrate the practical application of the developed knowledge, we explored the resolution of three distinct problems: the Tower of Hanoi, the problem of coins arranged in regular hexagons, and a challenge involving colored liquids organized in bottles. Each of these examples concretely demonstrates the versatility and depth of the techniques addressed. It is important to note that existing literature often presents only superficial outlines for deriving recursive formulas, especially in the context of numerical and non-numerical sequences. The focus is frequently on the final result without delving into the underlying steps and fundamental ideas. This study aims to offer a comprehensive understanding of the process of deriving recursive formulas and how to obtain closed formulas from them. Throughout the work, we demonstrate how to transition from specific problems to numerical sequences and closed formulas, providing a detailed and systematic view of this process.
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