This study is based on the observation of low student engagement in Mathematics classes, especially in the teaching of Geometry, and aims to investigate the feasibility of gamification as a strategy to make lessons more interactive and to promote students’ appropriation of concepts in the 8th grade of Elementary School. The research was conducted in a public school in the city of Petrópolis, Rio de Janeiro, with a class of 29 students, and is characterized as a qualitative investigation of a descriptive and exploratory nature, situated within the field of action research, since the intervention was planned and implemented by the teacher-researcher throughout the school year. The proposal consisted of the development and implementation of a gamified didactic sequence focused on teaching contents such as polygons, number of diagonals, sum of interior angles, and angle bisector, integrated into regular expository lessons as a complementary strategy. The results indicate that gamification proved to be a promising pedagogical strategy in the teaching of Geometry, fostering active participation, teamwork, strengthening the bond between teacher and students, and increasing students’ interest in the lessons.

Geometria Cantada (Singing Geometry) is an Investigative Didactic Sequence (IDS) that uses music and concrete materials to review elements, terms, and concepts related to the mathematical object circle, which is present in several competencies of the Brazilian National Common Curricular Base (BNCC). With the goal of promoting meaningful learning, this strategy aims to break away from the standardization of mathematics classes, which have traditionally consisted of two main components: lecture-based instruction and exercise solving. In this context, this study aims to analyze the potential of Geometria Cantada to: promote learning through the natural investigative instinct of human beings; foster interest in mathematical content through its connection with everyday life; reduce math-related anxiety; and encourage a modern pedagogical practice supported by artificial intelligence. In addition, the IDS and each of its designed activities have their own specific objectives. The proposal is grounded in the definition of IDS by Costa et. al. (2024), Ausubel’s (2003) theory of meaningful learning, Boaler’s (2018) growth mindset, the mathematical modeling approach highlighted by Biembengut (2014), and the concept of humans-with-media proposed by Souto et. al. (2025). It also incorporates an intersectional perspective in education, alongside feminist, multicultural, inclusive, and environmental approaches. The research is qualitative in nature, with an exploratory and ethnographic approach, conducted with 7th- and 8th-grade students from a public school in the municipality of Piraí. The instructional resource was structured into three stages, comprising four activities: investigation of circular objects using music and concrete materials; step-by-step musical analysis through text or drawings; presentation of analyses; and a group discussion. During implementation, aspects such as student engagement, participation, content understanding, and interaction were observed. Data analysis was based on these elements, complemented by daily notes. The results indicate that Geometria Cantada contributed to increased student interest, encouraging active participation and the construction of meaning related to geometric concepts. Furthermore, the proposal demonstrated potential to reduce math anxiety and promote a more collaborative and inclusive learning environment. It is concluded that Geometria Cantada represents a viable and innovative teaching strategy, capable of integrating different dimensions of the educational process and contributing to the development of meaningful, critical, and contextualized learning.

This master's thesis aims to investigate the relevance of using origami as a teaching tool for geometry, specifically as a resource to support the calculation of the perimeter and area of plane figures such as squares, rectangles, and triangles. The study will be conducted with a first-year high school class at a public state school located in the Campo Grande neighborhood of Rio de Janeiro, Brazil. The main objective is to promote more meaningful learning and facilitate students' understanding of geometric concepts. By working with paper folding, the study seeks to stimulate students' spatial visualization, logical reasoning, and creativity, making mathematics lessons more engaging, interactive, and enjoyable. Before the intervention, students will complete a questionnaire containing questions about the perimeter and area of squares, rectangles, and triangles, as well as their interest in mathematics and the difficulties they experience in contextualizing the proposed exercises. The methodology includes a hands-on workshop involving origami activities associated with mathematical concepts, as well as classroom observations, diagnostic and formative assessments, and systematic records of the activities. The data will be analyzed qualitatively based on classroom observations, students' work, and interviews. This study aims to contribute to the development of innovative pedagogical practices that enhance the understanding of geometric concepts in high school. The proposal is grounded in Freirean pedagogy, particularly by encouraging students to take an active role in their own learning process. In this way, the project promotes a more active, participatory, and meaningful educational experience, aligned with the principles of emancipatory education, in which students not only acquire knowledge but also recognize themselves as active constructors of their own learning

This work investigates the impact of creative insubordination on the mathematics assessment process in the final years of Elementary School, seeking to demystify the learning of the subject and make it more meaningful and inclusive. The justification for this research lies in the need to rethink assessment practices, since traditional approaches are often limited to classifying students, often disregarding their learning trajectory and contributing to demotivation. Creative insubordination emerges as an alternative to promote fairer and more effective evaluations. Therefore, the guiding question of this study is: how can the adoption of assessment practices based on creative insubordination contribute to improving students' mathematical learning? The main objective is to analyze the contributions of an innovative assessment methodology in changing students' attitudes towards Mathematics, as well as investigating its relationship with the discipline and the impacts of the strategies adopted. Methodologically, the research is applied in nature, with a qualitative approach and exploratory character. Experimental, bibliographic and survey procedures were used, including questionnaires and comparative tests between traditional evaluation methodologies and those based on creative insubordination. The study is based on the concepts of authors such as Luckesi, D'Ambrosio, Lopes, Souza, Brião and Freire, who discuss educational assessment, creative insubordination and innovative methodologies in the teaching of Mathematics. The results show that the adoption of insubordinate assessment methodologies, such as the "written-with-glue test", favors a change in students' attitudes, encouraging greater autonomy, engagement and conceptual understanding. These findings reinforce the relevance of creative insubordination in the construction of more effective and equitable pedagogical practices in the teaching of Mathematics.

This dissertation sought to investigate the effects on the learning of high school students related to Spatial Geometry content and the use of digital technologies such as GeoGebra and 3D printers. One of the motivations for this research was the fact that the school in which the author of this research works as a teacher was recently equipped with a Maker room, equipped with computers and a 3D printer. This is a recent phenomenon in the state of Rio de Janeiro, in which many other state public schools have been equipped with these technological resources. The research also sought to investigate the relevance of Geometry for the training of high school students, the difficulties inherent to their learning and how it stands out in assessments such as the National High School Exam (ENEM). Through the assumptions of Van Hiele's Theory, regarding the learning of Geometry, a didactic sequence was created that integrates both the use of concrete materials and also digital technologies, such as GeoGebra and 3D printers, the latter, carried out in the Maker room environment of the research field school. The proposal sought to connect theory to practice, seeking to allow students to visualize and manipulate geometric solids, thus contributing to the improvement of spatial geometric thinking. The results indicated significant progress in some students, but also revealed that others had difficulties, suggesting the need for more adaptive and personalized pedagogical approaches.

This work approach the application of mathematics in the performance modeling of drugs, which allows determining precise dosages and time intervals, maximizing efficacy and minimizing side effects. This practice is in line with Specific Competence 3 of the BNCC, which emphasizes the application of mathematical knowledge in real situations. Exponential and logarithmic functions are essential to understand pharmacokinetics, ensuring the efficacy and safety of drugs. Understanding these functions is critical to modeling and solving problems related to drug concentration in the body, using properties and graphs. Computational tools such as the use of Excel and GeoGebra facilitate the visualization and detailed analysis of pharmacokinetic concepts. We will work with two classes, one being an experimental class where we will apply an initial questionnaire to obtain information about the medications used by students and their families. This questionnaire will help to contextualize the activities of the experimental class and another class will be the control class in which we will adopt the traditional teaching and learning methodology. At the end of the experiment, we will apply an evaluation to compare the performance of the two classes. After the evaluation, a qualitative and quantitative analysis of the students' responses and performance will be carried out. With possible improvements for future implementations of the project.

This dissertation aimed to analyze the learning of 6th-grade students in the topic of Measurement, through the implementation of didactic activities conducted beyond the traditional classroom environment. The research was based on the hypothesis that contextualized methodologies, grounded in the theory of meaningful learning and the concept of creative insubordination, could enhance both student engagement and understanding. This study is justified by the need to review mathematics teaching methodologies, given the low performance observed in national assessments. The research was carried out in a public school located in the city of Volta Redonda, with a 6th-grade class. A qualitative approach was adopted, with a sequence of practical activities organized around four thematic axes (length, mass, time, and capacity). Data collection involved observations during the activities, the application of a learning test, and the conduction of a focus group with students, allowing for triangulation between the different instruments. The results showed that most students achieved satisfactory performance, with scores close to the target of 75%, and demonstrated greater engagement and interest in class. Furthermore, the reports indicated a positive shift in the students’ perception of mathematics as a tool present in everyday life. Despite challenges such as curricular rigidity and large class sizes, the proposed approach proved to be both viable and effective. It was concluded that creative teaching practices connected to students’ realities can make mathematics instruction more meaningful, contributing to students’ holistic development and offering concrete support for teachers seeking to innovate their methodologies in the teaching of Measurement.

This work addresses the teaching and learning of fractions by high school students in the Youth, Adult, and Elderly Education (EJAI) program at a state school in the South-Central region of the State of Rio de Janeiro, Brazil, using contextualized activities in their daily lives. Noting that several EJAI students have difficulty dealing with fractions, partly due to the distance from school and the lack of strategies that make Mathematics meaningful, the research was based on the use of contextualized activities and concrete materials as a connection between formal knowledge and everyday experience, aiming at a humanizing and meaningful learning, as advocated by Arroyo (2017), Freitas (2018), Conrado (2020), Pelizzari et al. (2002), and Brito (2023). The research question was: Can the use of activities with fractions related to the daily lives of high school students in EJAI help in understanding this content? Therefore, the main objective of this work was to analyze the contributions of using activities with fractions related to the daily lives of high school students in EJAI at a state school in the South-Central region of the State of Rio de Janeiro, Brazil. The dissertation methodology consisted of a bibliographical search on the study of fractions in the daily activities of EJAI students and an action research study conducted with nine students from high school classes of EJAI at a state school in the South-Central region of the State of Rio de Janeiro, Brazil. Regarding the procedures, two initial questionnaires were administered to assess the participants' prior knowledge of fractions and their perceptions of how they use this content in everyday life. Following this stage, some activities involving the use of fractions in everyday situations were conducted using concrete materials. Following this, two final questionnaires were administered to assess the participants' learning about fractions after completing the activities and to gather their impressions after the experience. The activities contributed to their understanding of fractions, although some conceptual difficulties identified in the initial questionnaires persisted in the final questionnaires. The research reinforced the importance of a humanizing approach that values students' prior knowledge and life experiences, as advocated by Arroyo (2017), promoting a meaningful curriculum that connects with the realities of EJAI students. The results of this research are expected to contribute not only to strengthening students' understanding of fractions but also to inspiring other pedagogical practices in Mathematics Education, respecting the particularities and knowledge of EJAI students.

This study aims to support students in preparing for the entrance exams of the Naval College (CN) by concentrating on the most frequently encountered topics in plane geometry, particularly the areas related to plane figures. The research underscores the significance of mastering geometric concepts for student development, as well as the challenges many students face when engaging with this material. To provide a more focused and effective geometric learning experience, the incorporation of autonomous resources and tailored pedagogical pathways is essential, as the appeal of these approaches plays a critical role in the teaching-learning process. In this context, digital tools can enhance students' understanding of the geometry topics prominently featured in the Naval College entrance exams.
The primary objective of this study is to evaluate the impact of digital pedagogical strategies as supportive tools for learning the most relevant geometry topics for the Naval College exams. Specifically, the study aims to create digital content and implement applications and pedagogical methods that make learning these topics
more accessible and dynamic.
The research methodology will include a comprehensive bibliographic review of pedagogical strategies, analysis of teaching practices in geometry, and an examination of the evolution of CN exams. The initial phase will involve assessing the prior knowledge of geometry among 9th-grade students at a private school in Nova Iguaçu, Rio de Janeiro, through a diagnostic test. Following this, the identified pedagogical strategies and applications will be implemented as tools to facilitate teaching.
Finally, the study will gather students' feedback on the effectiveness of the introduced tools and assess their progress. Both qualitative and quantitative analyses will be conducted to evaluate student performance and to interpret the collected data.

This research paper proposes a differentiated pedagogical approach for teaching geometry to
students with Autism Spectrum Disorder (ASD) in high school, using didactic workshops as
the main methodology. The research is qualitative and aims to explore the knowledge of four
students with ASD from a state school in Baixada Fluminense, Rio de Janeiro. The purpose
of the workshops is to assist teachers in teaching fundamental geometric concepts, such as
shapes, angles, area, perimeter and geometric solids through manipulative materials such as
Tangram, Golden Material and Acrylic Geometric Solids. Despite the growing discussion
about inclusion, its implementation in Brazilian education is still a challenge, especially in
high school, which receives students every year with several different cognitive difficulties,
and many have learning gaps in mathematics, including the interpretation of geometric
problems. Workshops can be a way to work on inclusion, teaching geometry in a more playful
way and promoting interaction among students with ASD. Therefore, pedagogical workshops
appear to be a promising strategy since their practical and manipulative nature, with sensory
exploration and direct interaction with materials, can facilitate the internalization of abstract
concepts, making the content more accessible and engaging. In addition, the research also
aims to investigate the potential of workshops to optimize the pedagogical relationship,
promoting more individualized, flexible learning adapted to the needs of students with ASD,
strengthening the teacher-student bond and an environment of trust.

This academic work aims to map and analyze thematic and methodological trends in Brazilian research on mathematics teaching in the context of Ethnomathematics in the Youth and Adult Education (EJA) teaching modality, as well as contributing to educational practices and future research in this context. This is a documentary research with a qualitative approach, taking into consideration an analysis material from 14 dissertations related to the object of study, defended in Brazil, from 2007 to 2022, available in the bibliographic database from Brazilian’s digital library of theses and dissertations (BDTD) using the descriptors “Ethnomathematics and EJA”. From the analysis of the summaries of these materials, six categories were adopted: Professional context (4); Everyday knowledge (3); Analysis of scientific production(1); Mathematics curriculum (1); Contextualization (3); Numeracy practices(2). The analysis of the research showed us the importance of Ethnomathematics discussions being inserted  in Education. Furthermore, the research revealed that teachers have been adopting Ethnomathematics in the EJA modality in their pedagogical practice,they really understand the relevance of contextualizing the teaching of mathematics through the students' knowledge. Due to the diversity of possibilities, the surveys highlight the dynamic and comprehensive nature of the Ethnomathematics Program, contributing to its development. The educational product developed as part of this dissertation is a collection of activities carried out from the researches analyzed for EJA,based on Ethnomathematics. This research reiterates the importance and necessity of keeping  the continuity and deepening of studies in this field, with the purpose of generating knowledge that enables educators and teachers responsible for teaching Mathematics in Youth and Adult Education to effectively conduct their pedagogical practices, taking into account the sociocultural particularities of students.

This work proposes the integration of financial mathematics as an ally, offering practical activities that demonstrate the direct application of these concepts in students' daily lives. Justified by the need to fill gaps in the literature, the work focuses on the analysis and application of this approach in a State School in Rio de Janeiro. The Finvest_Educa application is introduced, developed to provide information about financing and investment to students, aiming to positively impact their future financial decisions. The implementation of the application in classes for third-year high school students, characterizing the research as applied, involved data collection through class recording, learning monitoring and a questionnaire to assess students' intention to share the knowledge acquired. Analysis of the results reveals the possibility of a cultural transformation in the financial habits of young participants, highlighting the potential of the Finvest_Educa application as a valuable educational tool. Thus, this research contributes to the literature by exploring financial education in a school context, offering information about the effectiveness of the application in changing students' behavior in relation to their personal finances.

The proposed work aims to improve understanding of the contents of combinatorial analysis and probability through activities that simulate some casino games. An application was developed for mobile devices with the aim of simulating situations involving these games. Firstly, these games (roulette, poker, and blackjack) will be explained with their rules. After presenting these games, we will address the combinatorial analysis and probability content necessary to solve the problem. All content presented in the class will be exemplified using the most varied casino games with the aim of stimulating the curiosity of all students. We will present a mobile app called Casmath, built using App Inventor software. This game consists of a question-and-answer quiz related to situations involving combinatorial analysis and probability in roulette, poker, and blackjack games.In order for this class to be applied, a didactic sequence was created with eight lesson plans, where each class lasts 1 hour and 40 minutes each.Therefore, this work shows that Casmath can be used to assist in teaching combinatorial analysis and probability. 

The globalized world requires people to make decisions regarding their finances, especially if the nuances of the economy are taken into account. In Brazil, from the recent past, consumers from classes D and E have deposited around 60% of their income solely on supermarket purchases (Cavalcanti; Ribeiro, 2022). Furthermore, products have been increasingly offered in proportionately more expensive scales in relation to their quantity. This research work aims to analyze the use of critical thinking in family budget estimates by students in the 8th year of elementary school at a public school in Queimados (RJ). The specific objectives are: (1) to investigate the use of critical thinking by participating students in family budget estimation situations; (2) develop a didactic game on the topic covered; and (3) classify these students' aptitude for critical thinking in financial mathematics. The methodology is, according to the nomenclature of Mattos (2020), defined as applied, qualitative, exploratory and ethnomethodological. There is the creation and application of an educational product - a didactic game - that simulates supermarket spending, covering the incidence of reduction, price increases and discounts, in a playful way. The theoretical framework includes the LDB - Law of Guidelines and Bases of National Education (Brazil, 2017a), and the competencies defined by the BNCC - National Common Curricular Base (Brazil, 2017b). Data analysis was carried out considering the students' critical reasoning, valuing “the means”, that is, the paths used by them to solve problems. As a result, despite the initial deficiencies, a significant evolution was observed in the learning of proportionality and percentage content, and in the students' perception of these contents, in terms of how to best apply them in their daily lives, based on the inputs provided in this autonomous approach, with occasional interventions by the research professor, when requested. The expectation of this work is to contribute in the future to the financial re-education and development of critical reasoning of this year's elementary school students, helping them with regard to their citizenship, with more conscious financial decision-making.

The main theme of this research is the resolution of quadratic polynomial equations with an unknown through the Equafácil application. The proposal was to carry out an experiment with students with special educational needs, such as the use of applications in the teaching of mathematics. This strategy has gained prominence due to its potential to make learning more interactive, personalized and effective, for this reason the use of technology in the classroom was sought through the use of this application, in view of the difficulty that many students have to develop a solving process of this type of equation. Therefore, this research has a qualitative character, and had the participation of students from the 9th year of Elementary School and students from the 1st year, 2nd year and 3rd year of High School who have some type of special needs. The didactic strategies used the principle of the Universal Learning Design (UDL), which provides for the adaptation of methodologies and the adoption of innovative strategies in  the teaching and learning of all students. The results of the analysis of the collected data showed that the use of the Equafácil application  is a great facilitator for this process, making it a useful tool with easy access and very interactive.

This work intends to approach the application of educational board games through a look at the 
integral education of mathematics. The objective is to investigate the impact of board games on 
students' interest and learning regarding basic mathematics operations in integral education, having 
as a product the selection and development of board games for learning basic mathematics operations.
The methodological approach to be used for the development of the project consists of using research 
instruments (Observation, Questionnaire, Interview, Tests and Field Diary), with group activities in 
previously defined and directed game stations, where we will seek to have a look critical and 
participative, aiming to capture the affectivity of the participants in a qualitative and quantitative way, 
with the record of the facts. This research is justified by the possibility that board games help to 
reduce the difficulties of students found by the author in the classroom, in learning the basic concepts 
of mathematical operations, making use of the integral system, taking advantage of time at school 
in a way efficient, teaching in a playful way, seeking to expand the teaching-learning process and 
equity in learning, resuming, on the part of students, the interest in wanting to learn. With this, 
we intend to answer the following question: "How can board games help in learning the basic operations 
of mathematics in the early years of elementary school II, in a public school in the municipality of 
Resende that offers full-time education?". As a theoretical reference, we sought and analyzed several 
projects with similar subjects, that is, referring to the use of games in teaching mathematics content 
in general and in the theory of product development, which served as a basis and were essential for 
the development of our project. With all that has been said, we believe that the use of educational 
games, in differentiated and welcoming environments, with a more playful look and closer to the 
students, can generate favorable conditions to improve learning in general, providing conditions for 
our young people to can react to existing natural and social difficulties and fight for their personal,
intellectual and moral development, becoming full citizens in the broadest sense of the word.

This work seeks to contribute to Mathematics Education, through the development of activities that encourage increased student engagement in Mathematics classes, which has decreased considerably after the period of removal from the routine of face-to-face classes due to the Covid-19 pandemic. As a methodological strategy, a didactic sequence was elaborated based on the theory of Gamification with manipulable materials, without the use of digital technologies. This research had as target audience the students of a 7th grade class of a municipal school in Rio de Janeiro. A qualitative approach was used to analyze the research data, which were collected through forms and observation of students in class. We sought to compare student engagement in math classes and their relationship with the discipline before and after applying the sequence of gamified activities. Among the results obtained in this research, a significant improvement in the students' relationship with the teacher stands out.

The in-person return to classes, after the social distancing caused by the COVID-19 pandemic, brought great challenges for teachers and students. Unfortunately, several of these students were left without access to the subject content, which accentuated the learning deficit. There was also harm to interpersonal relationships in the school environment. Therefore, the main objective of this work was to analyze the teachinglearning and socialization processes of students at the middle school in activities involving Art and Mathematics, in the study of plane geometric figures. The theoretical framework was composed of the Base Nacional Comum Curricular (Brasil, 2018), the Parâmetros Curriculares Nacionais (Brasil, 1997, 1998) and works by Barros (2017), Conceição and Moreira (2019), Silva (2021), Santos (2006) and Campos (2020), among others. The methodology consisted of action research with a qualitative approach. The research subjects were 17 sixth and seventh-grade students, who attended the Mathematics Learning Laboratory of a Transformative Public Education Center (CEPT), in the Municipality of Maricá – RJ, in the year 2022. Firstly, participants responded to two questionnaires: one of them, about study habits and resources during the social isolation imposed by the COVID-19 pandemic and about their expectations regarding the activities that would be carried out in the laboratory; the other, for initial verification of learning about plane geometric shapes. Afterwards, several activities were carried out, involving the study of plane geometric shapes, using some works of art by the Dutch painter Piet Mondrian and the manipulation of plane geometric figures in the construction of mosaics with E.V.A. (Ethyl, Vinyl and Acetate). Finally, participants answered two new questionnaires: one to verify their learning about plane geometric shapes, similar to the first; the other, about study habits after returning in person and their impressions about the activities carried out in the laboratory. In relation to learning the content covered, there was a significant improvement. Furthermore, the majority of participants improved interaction among themselves and with the teacher-researcher, increasing confidence in their abilities and in the teacher, which are important and necessary factors for the social and academic development of students. It is hoped that this research can serve as a source of reference for anyone interested in the subject.

This work aims to bring a teaching proposal to high school classes addressing a
specific topic of Graph Theory that deals with shortest paths and the Dijkstra and
Bellman-Ford algorithms used to determine them. As algorithms are something
abstract, it was decided to bring to the present work notions of the Pascal
programming language, a language of easy understanding for beginning
programmers. In this work, students will have contact with the Pascal programming
language, will know the origin and importance of Graph Theory and will have access
to the theory's basic notion, presuppositions for the study of shortest paths, their
algorithms and related Pascal programs. Activities related to the daily lives of
students were proposed, in order to provide mastery of the basic concepts of both
the Pascal programming language and Graph theory, in particular, algorithms aimed
at solving problems involving shortest paths. Finally, a change in the behavior of the
student is expected in the search for the new.

This dissertation aims to approach Financial Mathematics in a playful, through the use of games in the second segment of elementary school. To the throughout the work, and with the help of theorists such as Piaget and Viogostsky, we demonstrate how games can be great allies in the learning process, forming a positive attitude in the face of mistakes and a proactive attitude. In addition, we discussed how the application of games related to Financial Mathematics can help build student autonomy in this area and help them make more serious decisions in the future about your economic life. In order to apply the ideas and proposals presented above, we built a playful activity for the ninth grade of elementary school, at the Monteiro Lobato municipal school, in the public school system in Nova Iguaçu. In this dissertation, we analyzed the use of the ludo game adapted to Financial Mathematics, observing its limitations and possibilities of use for the second segment of elementary education.

During mathematics classes it is essential to communicate well between the people involved and correlate the objects of studies to their real meanings. We envision the real possibility of adequacy between the meanings present in the mother tongue with the rigorous concepts of mathematics, with this we proposed a research involving teachers, mainly the basic education of public schools and, through studies and readings of linguists, semanticists and theorists of education with the aim of consensus between writing in the mother tongue and mathematical notation. We made an intervention from a linguistic perspective in the concept of multiplication, bringing different ideas of multiplication respecting language, mathematics and normative documents such as PCN and BNCC. Language, in any teaching and learning process, has a very important role and would not be different in the construction of mathematical concepts, especially students at the beginning of their school life, seeking to assimilate the contents and make connections with the knowledge already acquired by out-of-school relationships. In this aspect, we discuss the results obtained in the research with the education professionals, we present proposals of table by gradual construction process for the understanding of these fundamental concepts and activities to be carried out in the classroom. We believe that language, both in the oral or written parts, can be a great ally for mathematics classes. The mother tongue and mathematics working together helping each other in the construction of knowledge.

This dissertation sought, through the Ethnomathematics Program, methodologies for conducting Mathematics classes in the Teaching of Youth and Adults. The work was justified by the challenges that EJA modality imposes in the academic formation to face them and, specifically, the Mathematics discipline concentrates obstacles for the student's development.Given this, how to approach school Mathematics content that can meet the daily demands of students of Youth and Adults Education? Thus, the objective was to analyze research from the last five years on Ethnomathematics in the EJA modality to observe the applicability and effectiveness of using Ethnomathematics concepts. The bibliographic research aimed to find theses and dissertations that applied the concepts of the  Ethnomathematics Program in Youth and Adult Education. To obtain a theoretical basis, a brief history of Brazilian education, focusing on the EJA modality, a study on popular education was carried out, which provided subsidies in the evaluation of problems in adult education. But the deeping of Ethnomathematics occurred with the contribution of the authors Ubiratan D'Ambrosio, Maria Cecília Fantinato, Darlinda Moreira, Sandra Matos, Sebastiani Ferreira and  Sônia Maria de Vargas. When analyzing the studies that the research provided, it was possible to see the importance of contextualizing mathematical content for students with old age. The works showed ways to make classes more accessible to students. With the development of the study, the role of the teacher proved to be still essential. For even suffering from the loss of autonomy, the professional can reinvent yourself in the face of new methodologies and offer your students significant contributions to their daily lives.

Nowadays, the society is highly technological, the information flow is constant and the technological advances happen easily. This facts requires from people constant learning of simple and complex things. In this new context, the mathematical knowledge becomes responsible for developing in the students the competences that will help them to live in this new reality, putting them as leading figure in the process of knowledge construction. Into this perspective, we give special attention to the Problem Solving Methodology and the Critical Mathematics’ Theory. Since the formal mathematics education has its beggining in the children early years’, we aim to study which beliefs and conceptions the teachers of this teaching cycle present in relation to these theories and connect it with the orientations presented in the PCN (Brazil, 1997) and BNCC (Brazil, 2018). We felt the need to understand some of the aspects of these professionals’ formation and the specific orientations of its pedagogical pratice, so we could produce a qualitative research. This research was developed through a form that was given to the early years’ teachers of three cities of the interior of the state of Rio de Janeiro, with the main goal of investigating their conceptions and beliefs in respect of the Problem Solving Methodology and the Critical Mathematics’ Theory. In our analysis, we found out that the teachers show a superficial knowledge about these theories, hindering the students development of basics’ competences that sets up the formative character of the education these days. A workshop was produced in a way to work on these theories, so they can bring some reflections to the teaching practice.

This present work introduces relative aspects regarding loss of purchasing capacity, loss of purchasing power of household income, linked to payment of taxes (taxation) and the rise in prices (inflation).
Definitions of taxes, inflation and types of taxes applied to household income are presented, in addition to the presentation of comparisons on how much money is spent on paying taxes and rising prices - taxation and inflation,
respectively.
Finally, the theme is approached so that you can view the value on income of taxation and inflation when there is, in the commercial operation, a specific tax, ad valorem by “inside” or ad valorem for “outside”.

This work approached the difficulties to solve problems involving geometrical solids by High School Students. The explanation for this research occurs because of the fact that Space Geometry is present in daily; although, at school environment, the learning difficulties in this area it´s well-known. For this reason, the school must prepare students for other areas from Mathematics. The leading question from this research was: Which are the main type of mistakes committed by students from High School in the resolution of surface area and geometrical solids bulk problems. As shown, the general objective was analyze the principal types of mistakes committed by students from a second degree class of High School from public Network in the resolution of surface areas and geometrical solids bulk problems. The research was based on the National Curricular Parameters and on Polya´s, Dante´s and Cury´s works, among other authors. For a select class, was implemented a diagnosis questionnaire, with questions about surface areas and geometrical solids bulk. After that, were executed activities with manipulate materials, involving planning and installation of geometrical solids, which were worked known aspects. After the students solved, in groups, three lists with conceptual problems about contents already mentioned. Furthermore, the methodology of analyses mistakes was used, according to Cury, to analyze the difficulties found by students in the resolution proposed problems. They also wrote comments, evaluating the activities performed. The main results were: wrong answers and partial rights answers was predominant and a considerable part of the results with no answers or without a fundament. Besides that, there were many mistakes on interpretation of statement, arithmetic’s and conceptual mistakes, involving confusion in quantities or unit of measure. Even though the difficulties, with this research, it was possible to understand the value of observe mistakes that were committed by students as an important allied to rethink the teaching practice and for conceive new experiences and learning opportunities.

The present study has as main focus to analyze if the use of Manipulable Materials motivates and helps in the 

learning of Integer Numbers in a class of the 7th year of Elementary School. Approaching this methodology is 

justified because students tend to have many difficulties when they start making calculations involving whole 

numbers and consequently successive errors lead students to become unmotivated. To better understand the

 concepts that will be addressed in this research and the difficulties encountered by teachers and students with 

regard to Whole Numbers, a chapter on motivation, a chapter on Integer Numbers and a chapter on Manipulable

 Materials will be presented, in addition to the methodology used as well as the analysis of the data obtained. 

The present study consists of quantitative and qualitative research, based on data collection through an 

experimental research with 60 students from a Municipal School in Rio de Janeiro. To analyze whether there was

 any impact on the students' motivation, a motivational questionnaire was applied before and after the activities

 with the Manipulable Materials. To analyze whether there was an improvement in students' learning in relation 

to Integers, a pre-test and a post-test were applied. The students carried out the activities with four different 

options of Manipulable Materials. With the survey of information throughout the research and the analysis of 

the information, it was possible to conclude that with the use of Manipulable Materials it is possible to motivate 

and assist in the learning of the Integer Numbers. 

This research analysed math skills were considered insufficient or underdeveloped in high school students from twelve classes public school of the State of Rio de Janeiro. The main goal was proposed a intervention in these math skills using for that playful learning and problem-situations. The methodology used performe an investigation about the importance of development math skills for high school students, as well as, the student avaluation of a instrument to intervention. The justification for carrying out this research was the possible difficulties to integrate determined math contents predicted at different times of basic education which may discourage the teacher's action in the intervention to recover skills considered essential for the continuation of academic life and/or professional after the completion of high school, as evidenced in the research carried out with teachers that is treated in chapter 2 of this work. Thereby, this work had intent answer a question: Is it possible to develop skills expected to be worked on in previous stage, without, however, compromising the program planned for the current phase of development? For the development of the arguments in the present work, authors such as Hoffmann, Perrenoud, Luckesi, Pires, and others, were used as a theoretical reference, as well as, the legal documents provided for in Brazilian legislation, such as the “Base Nacional Comum Curricular” and the “Lei de Diretrizes e Bases da Educação Nacional”. Reflecting on the importance of math skills for life in society, as also, the instruments available for the identification of possible acquisition failures of these skills, allows those involved in the education trajectory to see the need for continued assessment, reevaluation and recovery of learning. Through that research, and with the intervention activities proposed here, it was possible to observe the possibility of integrating diverse contents of mathematics in basic education, seeking to rescue skills that were undeveloped without prejudice to the development of the new skills provided.

The teaching of mathematics is marked by a certain resistance, “cognitive block” when understanding and applying the contents.This question involves the didactics of mathematics used in the classroom. It is up to the
teacher to have languages and methodologies to reach students. Mainly, students who have Attention Deficit Hyperactivity Disorder (ADHD). This dissertation aims to approach the teaching-learning process of mathematics
with an emphasis on the student diagnosed with Attention Deficit Hyperactivity Disorder (ADHD), considering the learning difficulties.

To this end, we must understand the proposals for inclusion of students with Special Educational Needs (SEN), taking into account that children and young people have the right to learn mathematics and to be confronted with rich and diverse learning experiences, we must look for, then, propose active methodologies for the development of the expected learning for those who present the disorder.

Finally, it should be noted that the mathematics teacher's commitment to education will be much more significant when he establishes an interpersonal
relationship with his student, a relationship that constitutes, on the one hand, the core of the activities of the teaching-learning process.

This dissertation presents the State of the Art of the dissertations produced in Mestrado Profissional em Matemática em Rede Nacional (PROFMAT) related to Mathematics Education in the Youth and Adult Education (EJA) modality. PROFMAT aims to serve mainly Basic Education teachers in order to offer professional training complementary in mathematics with an emphasis on in-depth mastery of content related to school mathematics. The research aims to examine the pedagogical practices used in the works, the curricular contents developed, the levels of education, besides quantifying the national distribution of the production of dissertations in the program related to EJA. It is used as a theoretical foundation some notable topics of EJA in Brazil, such as its history of implementation, the legislation that regulates EJA, the curricular contents and specificities mathematics of this modality.

We also sought to list some models of didactic materials and teaching methodologies used in mathematics classes, as well as describe the PROFMAT format and design. The investigated information was presented in a quantitative way by means of tables and in a qualitative way by dissertations. Among the data verified in the dissertations, the low of works related to EJA when compared to the totality of dissertations produced, as well as the preponderance of pedagogical practices based on the use of playful materials and digital technologies.

This work is expected to awaken in readers the importance of a differentiated methodology for teaching mathematics at EJA, as well as raising awareness of researchers in the area of Mathematics Education on the need to develop more research aimed at students of this modality, which has a fundamental role to play in offer students, who have faced socio-economic difficulties that made it impossible for them to study throughout their childhood or adolescence, conditions to obtain with quality the basic level of education provided for in public education policies for all adult individuals.

This essay is meant to be a dialogue. The point of interest of this dialogue is to investigate and reflect on the possibilities of recovering the essence and meaning in the classroom, especially in the discipline of mathematics, under the research paths and practices in the program of Ethnomathematics. The objective was to investigate paths and proposals of the program in Ethnomathematics that enables a pedagogical practice that is possible, and able, to restore meaning and understanding to the contents of the discipline of Mathematics within the classroom. The methodology sought directions to meaningful learning and approximations within the program of Ethnomathematics under socio-affective relationships to the mathematics of sense, aided with the possibilities and procedures of Oral History. This research is justified in contributing to theoretical basis and to guide educational, stimulating, and democratic practice. Finally, how to bring essence and meaning to the classroom through dialogue with pioneering and contemporary researchers from the program in Ethnomathematics? We sought dialogue to solve. Interviews were conducted with six authors, pioneers and contemporaries from the program: Ubiratan D’Ambrosio, Eduardo Sebastiani Ferreira, Pedro Paulo Scandiuzzi, Cristiane Coppe Oliveira, Olenêva Sanches Sousa e José Roberto Linhares de Mattos. Also, theorists such as Abreu, Coppe, Costa, D’Ambrosio, Fantinato, Farias, Ferreira, Frege, Freire, Freitas, Gerdes, Hernández, Knijnik, Mattos, Moreira, Santos, Scandiuzzi, Silva, Sousa e Vygotsky.  To reflect on the pedagogical possibilities for mathematics education under the eyes of the Significant and Sensorial Mathematics, aligned with the Ethnomathematics program and Oral History leads to the proposed expectations, since such alignments reverence the aspects of valuation, appreciation, recognition, and respect.

Keywords: Ethnomathematics program. Oral History. Significant Mathematics. Sensorial Mathematics.

The present work aims to show and evaluate two tools, developed through the use of the Arduino microcontroller integrated with a mobile application created in the visual programming environment of MIT (Massachussetts Institute of Technology), which can assist in teaching trigonometric reasons in the ringht triangle. The research was done with 56 students from the ninth grade of Elementary School, in a State School located in the municipality of Nova Iguaçu and divided into four classes of 100 minutes each. In the first class, a pre-test was applied to evaluate the students' knowledge about the subject that had already been studied. In the second, the necessary applications were installed for the development of the activities as well as the accomplishment of the activity with the tool, named by the author, Plan of Trigonometric Ratios with the objective of working through the investigation the concept of the Sine, Cosine and Tangent reasons in a triangle rectangle. In the third the activity was held in the patio with the use of the Theodolite (Built with the Arduino), aiming to calculate the height of the building of the school using the trigonometric reasons. In the fourth and last class, a post-test was applied to evaluate the evolution of learning after the activities were carried out and a Motivation questionnaire was applied, based on the motivational test of Gontijo, in order to verify the motivation conceived to the students through the use of Arduino as a teaching tool. Finally, an analysis of the test results and a survey of the information obtained in the Motivation questionnaire was carried out, observing an improvement in the students' learning and the motivation aroused by the use of the teaching tools used in the classes.

This work of literature review aims to establish connections of the contents of Newton's binomial under a combinatorial perspective for high school students,and it also deals with a didactic sequence on the subject, which can be applied in the classroom by the mathematics teacher.As a High school teacherwas observed that students havepresented several deficiencies in mathematics, especially in combinatorial and probability.Many know only formulas, do not understand their applications, while others have complete ignorance in such matters, and most of them can’t solve common problems of counting Elementary school. However, it was aroused interest on part of the students, even those with no aptitude for the exact disciplines, when exercises were applied that were associated with daily situations, such as the Mega-Sena game.It is verified the student absence of interest in the High Schools, majority, is fruit of the little value given by the teachers to the subjects. There is no doubt that the study of Newton's binomial is fantastic, provided there is an understanding of how binomial expansion occurs. The purpose is to contribute to new approaches of action and, consequently, to be an exciting topic for students, thus developing significantly their ability to gather ideas and reason logically.

This work proposes the construction of a low cost air track developed using the Arduino microcontroller that can be a pedagogical tool to assist the study of affine and quadratic functions. This research was developed in a school in the west zone of the Rio de Janeiro city, where two ninth grade classes participated in the survey. In all this work had 6 times of 50 minutes in which students were able to interact with the pedagogical resource elaborated in this work, were proposed five different experiments, three of uniform rectilinear motion and two of uniformly varied rectilinear motion. The students underwent a pretest and a posttest in order to qualitatively verify the improvement in learning that the air track can offer. Finally, the students performed a motivational test in which they tried to understand how much the air track contributes to the motivation of the student body to learn mathematics and in a more specific way the related and quadratic function contents.
Analyzing the results, we found that 77% of the students observed enjoyed performing experiments on the air track and that 82% of these students agree that activities relating theory and application help them understand mathematics.

The present work is based on the investigation of the influences that the use of concrete materials and origami

 cause in the teaching-learning process of the students of the elementary years. Being structured from the 

difficulties of the same facing the internal and external evaluations of the teaching process and abandonment over 

the years present in Geometry Teaching in the Brazilian educational scenario. The objectives are based on the 

official curriculum guidance documents and the work appropriates concrete, manipulable and tactile resources 

to verify the presence or absence of advances in relation to the contents of Spatial Geometry treated with the 

classes. The research was carried out with two classes of a municipal school of Rio Bonito - RJ totaling

 41 students (24 of the 7th grade A and 17 of the 7th grade B), where these classes were verified through activities

 - six activities at the same time. All - designated as pre-tests and post-tests and with the students divided into 

groups were practiced as building a cube and an origami tetrahedron and making a descriptive sheet about the

 concrete materials presented. The results designate how stripping of teaching resources in the classroom is

 beneficial to substantiate the contents to the students.

This work deals from the development process of an RPG computer for only one person and that this serves for math practice. It arises from the need for teachers to create different forms of mathematics teaching, escaping from the usual chalkboard and chalk, in order to motivate students and thus keep the student studying mathematics for longer. For its elaboration was carried out a research of some concepts of games educational, educational software, RPG games and game development platforms. Also featured was the RPG Maker MV Engine and its features in which the game was developed. As a result, an electronic RPG game was created for the practice of mathematics and this was classified pedagogically and evaluated its applicability by high school students. Where we could observe that it is possible to create an electronic educational game for math exercises that is attractive to students, improving the dynamics of math classes. We also see that other possibilities can be explored with the use of games such as: persistence, kindness and situations that the student needs to make decisions that can change their future.

The aim of this dissertation is to present a proposal of a didactic sequence for Linear Diophantine Equations to be applied at the final years of middle school. It is also expected that after some classes about the subject the students will be able to identify real word problems that can be modeled and solved through Linear Diophantine Equations. In order to achieve this objective essential topics for the understanding of the contents involved in the elaboration of the didactic sequence, such as: integers, divisibility, Euclidean division, greatest common divisor, Euclid's algorithm and modular arithmetic will be reviewed. Thus, this work is justied since in some selective processes of military competitions, Naval College, Military College and EPCAr, and also in the tests of the Brazilian Mathematics Olympiad of Public Schools - OBMEP, have some questions that can be solved with this tool, and due the fact it is a possible topic for assimilation by the students at the final years of middle schools since they only need basic knowledge of mathematics. In addition, it is intended to lead the student to realize that mathematics is important so that he understands and knows how to solve problem situations experienced in his daily life.

We live in a society where young people are increasingly influenced by technology. The evidence of this fact is when we observe the behavior of students in the classroom. Indeed, despite the restriction of use, they never cease to interact with their cell phones, tablets or other electronic devices. Thus, it seems reasonable to think about a pedagogical practice of teaching mathematics that allows students to use electronic equipment for another purpose, in this specific case, educational. Thus, the objective of the present work was to create a digital plataform trying to keep students motivated with the teaching-learning process of mathematics, as well as to test, in practice, the influence thais paradidatic tool in the school performance of students. In fact, we created the SIGA Web application that has the differential of allowing users to connect from any technological devices that have access to the internet. In addition, the activities proposed in the SIGA Web application are punctuated and each task accomplished the student accumulates points, initially by accessing the platform and confirming the receipt of the activity and later by the correction note. In this way, the application generates a healthy competition among the students, as it provides the ranking of the best students scored by the class. Thus, the first part of the work was created by the Web application SIGA and the second part the accomplishment of a research of data collection, using the hypothetic-deductive method, with Quanti-Quali approach, applied to students of schools of the municipality of Rio de Janeiro, in particular, the second elementary school segment of a School Unit of the 10th CRE, whose purpose was to measure the motivation and level of influence of the SIGA Web application on the student achievement index in the bimonthly tests.

This work presents, through a case study, the analysis of an experience involving problems of Paths in Graphs in two classes of a school of the Municipal Network of Education of Rio de Janeiro located in Curicica, Jacarepaguá. The classes, one of the seventh year and another of the eighth year, had approximately 60 students participating in the experiment in the months of November and December of 2017. To carry out the experiment, four mathematics classes were used, each composed of two times of fifty minutes. In order to observe the effect of the introduction of simple and versatile graphical path techniques in solving some problems familiar to the students, the experience was as follows: in the first class, a motivational questionnaire adapted from the questionnaire Gontijo, for the collection of information about the relationship between students and mathematics. A test  with questions involving topics familiar to the students was also carried out and can be solved with mathematical techniques already known to them. In fact, such questions are more easily solved by techniques of Paths in Graphs. Such techniques are taught in the second and third classes. In the last class, the test was applied again, and this time they can already use the new techniques learned. A final questionnaire was also applied to assess what the students felt about the process. An analysis of the results is carried out at the end, leading to conclusions about a positive impact of the experience on the group studied.

The objective of this work is to construct a material destined to the classes of the final years of high school, presenting mathematics in a more interesting way from the basic concepts of game theory. Understanding these concepts, the student can solve problem situations using mathematical instruments, seeking the best choice in certain interactions and not making decisions instinctively. After studying the research, the reader will have to understand that mathematics can be more attractive and useful in the decisions to be taken in their daily life and broaden their critical view on current issues such as the application and importance of "awarding" in judicial processes that constantly happen in Brazil. It will be approached a theoretical basis with the resolution of some activities presented to the students, using the strategies that will be worked on in the text. In the end, two activities are proposed so that the students can apply the knowledge acquired in the development of all the presented work, with its due solutions.