This work aimed to learn about play as a support for the teaching of Mathematics, with the aim of alleviating school dropout rates. It refers to a study that was developed in two moments: the first in the experience of a supervised internship in a school in the municipal network of Coruripe-Al, which caused the motivation for the study, and the second, based on research and bibliographical production on the topic. The exploratory study, with a qualitative approach, had students and a Mathematics teacher as collaborators. The investigation instruments were observations during the internship and a semi-structured interview with a conversation circle feature, as well as printed and online books, which deal with the subject in question. The information acquired during the experience with the class shows that evasion, among other reasons, can also be motivated by the cold way in which classes take place, as well as references such as Novaes (1987); Gadotti and Romão (2002); Brazil (2004), Libâneo (2004), Teixeira (2010); Huizinga (2010); Santos (2011), among others, who indicate that Playfulness can develop the learning of adult students, as long as games, toys and games bring the content closer to the experiences of life in society, so that teaching and playing do not invalidate each other in teaching and learning.

This dissertation aims to demonstrate how to calculate the volume of an elliptical
paraboloid, using as an example the calculation of the volume of objects in the shape
of elliptical paraboloids, such as pans or decorative household items. Thus, it highlights
the importance of studying Analytical Geometry and its applications in high school,
establishing a connection between the study of conics, especially the parabola, and its
generating quadratic surface, the paraboloid. To this end, we will address some historical
and analytical aspects of these conical surfaces and present basic and geometric elements
important for determining the volume of such objects. In this way, this dissertation seeks
to assist high school students in calculating, in a practical and precise manner, the volume
of solids in the shape of elliptical paraboloids, without the need for prior knowledge of
differential calculus

This paper addresses the teaching of Financial Education in the
context of EJA – Youth and Adult Education, considering the
various references that point to the contributions of Financial
Mathematics and its critical use for the development of individual
skills, offering the subject better conditions to make conscious
decisions in the financial field. Due to its relevance, this topic has
gained increasing recognition, especially in the school
environment, expanding its presence in different contexts in recent
years, which justifies the realization of this research within the
scope of the Professional Master's Degree in Mathematics in the
National Network (PROFMAT), of the Federal University of Alagoas
(UFAL). The study aims to study the theoretical basis and develop
a didactic sequence that incorporates everyday resources, such as
invoices, bills and investments, combined with technological tools,
such as the cell phone calculator, and based on the perspective of
Critical Mathematics Education. The research was qualitative in
nature and was based on the Problem-Solving Methodology as an
approach. The didactic sequence, applied in an EJA class, had its
main points recorded in this work, and reports obtained at the end
of its application indicate that its development provided discussions
on financial concepts and aspects, contributing to the promotion of
Financial Education among students. Reiterating the importance of
Financial Education in the context of EJA, the aim was for this work
and its results, together with the educational product generated, to
serve as inspiration and support for other teachers interested in
addressing this topic.

This paper has a narrative that dates back to the beginning of high school when it was still known as Secondary Education and which shared a great process with many reforms and new nomenclatures, we arrived at the current New High School, with all its novelties, increased workload, new subjects, new training itineraries, and the standards of BNCC, LDB and PNE were also worked on. And we continued with this narrative to where we wanted to go, which are the elective subjects that are also new to basic education in schools in Brazil. Among the most variable electives available for mathematics education in public schools in the state of Alagoas, more precisely in the city of Rio Largo, at the Francisco Leão State School, which is located in the Mata do Rolo region, Rio Largo - AL. It was at this school that in the current year of 2025, RPG Elective classes are being held, something new for students and teachers. It is with a focus on this elective that this TCC was developed, with Arithmetic Progression classes being learned through tabletop RPG. Classes from other RPG games were applied to increase students' knowledge, and finally the development of an RPG game as an educational product that allows students to delve deeper into the subject of P.A. through the practice of the game, which is make-believe stories.

This dissertation presents a pedagogical proposal that integrates Mathematical Modeling and
the Study and Research Pathway, based on the World Questioning Paradigm, as a teaching
strategy aimed at analyzing a real problem: the cost-benefit of installing photovoltaic solar
panels to generate electricity in homes. The approach seeks to promote student protagonism,
investigative autonomy, and the development of mathematical skills by contextualizing the
content in situations close to the students' reality. The activities were planned to stimulate the
formulation of hypotheses, the interpretation of data, and the construction of solutions based on
geometric, trigonometric, and financial concepts, articulating social, environmental, economic,
and scientific aspects. The work is based on authors such as D'Ambrosio, Chevallard, and
Bassanezi, who advocate a critical, contextualized, and meaningful mathematics education.
Although the proposal was not fully implemented due to limitations imposed by personal
factors, it was partially explored with teacher support and is structured for future
implementation. It is believed that this proposal can contribute to the advancement of innovative
pedagogical practices, expanding the possibilities of teaching Mathematics in an
interdisciplinary, investigative, and socially committed way.

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.

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

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.

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.

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.

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.

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.

In this work we present a didactic sequence that deals with the unfolding of geometric solids. With this
objective in mind, a survey on the subject was carried out based on Capes theses and dissertations, as
well as a reflection based on guiding and normative documents, namely: National Curricular Parameters
(PCN) and National Common Curricular Base (BNCC). We elaborated a didactic sequence formed by
five activities in this school, in a 3rd grade high school class, with thirty-three students. The didactic
sequence proved to be promising, as the planning activities provided a more effective understanding
of the topics covered in this teaching stage. In addition, we obtained elements that indicate that the
use of planning activities focused on the development of spatial visualization can contribute to the
recomposition of learning for students who still do not have the expected competences in mathematics
for this stage

Nowadays, mathematics is present directly and indirectly in our daily lives.
and even so, teaching mathematics is a challenge, as it is known that
Students have learning difficulties when it comes to this subject.
Therefore, working on mathematics through modeling would provide students with
students a better understanding of mathematical content, as we would be
showing these students that mathematics is in everything, as well as, we can
represent real problems through mathematical models leaving abstraction.
We believe that questions related to this topic are very relevant, as it is
necessary to analyze and reflect on the benefits that the incorporation of new
tools can bring to education, mainly considering the scenario
current situation and the educational needs brought about by the “technological age”. All these
changes in educational paradigms bring great challenges to our
educational system, as it requires individuals increasingly prepared to deal with
the problems of modern society. To meet the current need,
Firstly, we need to rethink our pedagogical practice and innovate
methodologies so that teaching has an educational process as a way of
bring the object of study closer to the students’ reality.
In this way, this project
aims to present high school students at the Federal Institute of
Santa Catarina (IFSC) - Câmpus Caçador the use of mathematical modeling
as a tool for teaching and learning this subject, which for many
is quite complex. We will represent some real problems in the area of activity
of the Production Engineer using mathematical models to control the
stock and optimize the process, generating more in less time. During the
During the development of this project, data was collected from some
companies in the city of Caçador where some higher education students from
Câmpus Caçador Production Engineering works, then we organize
these data and use mathematical models to represent them, then
These higher education student works were presented to students at the
high school through lectures, in addition to the application of two forms before and
after the presentations. During the presentations, the
definitions of mathematical modeling, its stages and the difficulties encountered
at the time of application, as a way of helping students in the development
of mathematical language, as well as awakening their curiosity, providing
self-confidence and initiative in the search for knowledge. Considering the
development of this project and the results obtained we have the objective of
study was achieved

Starting from the study of the National Common Curricular Base (BNCC), more specifically from the parts of Mathematics, the present work sought to understand this normative document and with that we find indicated ways to work the content of exponential function. Thus, after studying the BNCC, a search was made in books and academic papers about the content of exponential function that provided us with a theoretical foundation to apply in solving problems related to some skills listed in the BNCC. To conclude, we propose three playful activities to work exponential function with a focus on skills expressed at BNCC

This work aims to carry out an analysis on the importance of Problem Solving in Elementary Education. In the course of this study, strategies and paths emerged in which educators in the area of Mathematics can appropriate themselves to know and improve their views on the topic, as well as to become aware of how important it is to value the problem solving process. In the research carried out, other important factors in the process of knowledge and appropriation of the study were also described by the great scholars of the theme, such as George Polya (1995) and Dante (2010), who emphasize the teaching-learning process since the human being is challenged to solve problems constantly in his life. These facts can influence both math teachers and their students. We present a brief profile of teachers working in elementary school, pointing out the need for continued training in the area of Mathematics, especially for professionals working in the early years. We show concepts, types, goals and suggestions for how the teacher can use problem solving in the classroom. And, we also expose how students in the early years begin to perceive a mathematical problem.Finally, we suggest an Educational Product through continuous training, in order to assist and enrich the methods used by teachers in their daily school practices.

This work presents an introduction to the Logic used in the development of Axiomatic Theories associated with the Basic Education Mathematics Curriculum according to the Common National Curriculum Base. Emphasis is given to the discussion regarding the most used demonstration methods to justify the main mathematical results presented at this level. It highlights, among others, the Methods of Demonstration by Direct Proof, Reduction to Absurdity and Mathematical Induction, being that, unlike most of the literature, it presents the whole relation of these methods with Logic its principles, operations and rules of inference fundamental prerequisites justification for their use. In particular, it makes a more comprehensive discussion of the Mathematical Induction Method associating it both to the Induction Principle or Axiom and to the Induction Theorem, demonstrating it and presenting its various applications whether in the rigorous definition of mathematical objects or as a powerful instrument to demonstrate the most varied results involving natural numbers in basic education. In addition, it brings examples of Axiomatic Theories developed at this level and enunciates several Theorems making their respective demonstrations using one or more of the demonstration methods presented including the demonstration in standard argument notation thus explaining its direct relationship with logic and its algebra. The work can be used as a reference material for the teacher of basic education or graduating from a Bachelor's Degree in Mathematics who wants to deepen with respect to Theorem Demonstration Techniques and all the Logic behind this process.

This research presents a study on the use of Problem-Based Learning in mathematics, and more specifically, in Geometry classes among elementary school students, both in regular and youth and adult education, based on the observation that students, in general, have little identification with mathematics at this stage of their education. To this end, a historical and philosophical background that supports its use in several professional areas and its application in the field of mathematics was conducted. To support the formatting of a pedagogical proposal for each of the teaching modalities mentioned above, an analysis and evaluation of the documents that govern Brazilian education, of the textbooks currently adopted, and of the menus of the related disciplines in undergraduate mathematics courses was carried out, as well as a comparison between them. The work culminates with the presentation of the pedagogical sequences, which are presented in three stages, the first one explaining the use of the methodology in general and the two following stages with concrete, specific and detailed proposals, one for students in the seventh grade of elementary school, regular modality, and the other for students of youth and adult education, in the first cycle.

In the current stage of teaching in Brazil, the configuration of the school curriculum, the methodologies employed, the guiding principles of high school educational practices, are constant fields of intense debate, with the aim that the school can perform consistently and appropriately the its social and citizenship role. In this scenario, the teaching and learning of Mathematics, especially with regard to the curriculum and teaching methodologies, is routinely the subject of studies and investigations, in view of the problem that insistently plagues the processes of learning and teaching this science, namely: mathematics teaching cast in an algebraized practice. This apparent concern can be proven from the various events that include the teaching and learning of Mathematics as a subject of study, books dealing with the theme, varied publications and the recommendations of the country's normative documents, such as National Curriculum Parameters - PCN, PCN + , National Education Guidelines and Bases Law - LDBEN, and the National Curriculum Guidelines for Basic Education. In this scenario, mathematical visualization constitutes a means of developing relevant skills in subjects, not only for the broad and meaningful understanding of mathematical knowledge, but for life in society. In this context, this work aims to understand how teaching is taking place. and learning mathematics, through mathematical visualization related to problem solving, in the country. Thus, the intention to analyze the ENEM selections arose, focusing on the problems with the highest percentage of error and which demonstrate the lack of visualization for resolution. Problem solving is, in this universe, a method to be followed to assist in the resolution process. Still, as we solve the selected problems, we make available material that can be useful to anyone who is interested, especially to the Basic Education teacher. , as a means of helping and encouraging the use of visualization in the classroom.

The present work brings a proposal of Didactic Sequence (SD) that uses the resolution of problems related to the themes of Arithmetic of the Brazilian Public Schools Mathematics Olympiad (OBMEP), from its question bank, from the material of "Arithmetic Meetings"of the Scientific Initiation Program (PIC), with the aim of developing BNCC (Common National Curriculum Base) skills EF06MA05, EF06MA06, and EF07MA01. To analyze the effectiveness of DS, the proposal was applied to two first grade high school classes at a state school located in the city of Arapiraca-AL. In solving these problems, we sought to reflect on the procedures used in each question, motivating students’ critical thinking, seeking to motivate and instigate their participation in classes. Working with OBMEP’s problems is to bring mathematics in a different way, closer to everyday life and demystify the image of a rigid and purely calculating discipline.

Neste trabalho, vamos apresentar uma proposta de projeto de ensino de álgebra para o Instituto Federal de Alagoas, Campus Murici, que visa a resolução dos três famosos problemas dos gregos a partir dos conteúdos abordados no ensino médio integrado dos cursos de técnico em agroecologia e técnico em agroindústria. Esses problemas consistem sobre a possibilidade de construção de um quadrado de mesma área que um círculo dado, um ângulo com um terço da medida de outro ângulo dado e um cubo com o dobro do volume de um cubo dado, usando apenas uma régua sem marcações e um compasso.

Este trabalho apresenta uma proposta de abordagem da matemática financeira no ensino médio. Diversas pesquisas mostram que boa parte dos brasileiros estão endividados, um dos fatores que contribuem para isso é a falta de conhecimento para lidar com transações financeiras. Apesar de presente no currículo escolar, a matemática financeira vista na escola não é suficiente, exemplos improváveis no cotidiano e o afastamento dos termos ligados ao mercado financeiro contribuem pra isso. Com base nisso, este trabalho visa abordar a matemática financeira de maneira mais intuitiva, a partir de exemplos e situações problemas das quais os discentes irão se deparar no decorrer de suas vidas. Inicialmente serão propostas atividades que preencham lacunas referentes ao planejamento financeiro individual e familiar. Em seguida, a fim de atrair os discentes será apresentado alguns problemas iniciais, problemas estes que servirão para introduzir os conceitos básicos de matemática financeira, como por exempllo, juros simples e compostos, além de sistemas de amortização. Por fim, será apresentado tipos de investimentos que tem como objetivo enfatizar a importância de poupar e investir.

O presente trabalho abordaos métodos numéricos da Bissecção, Falsa Posição e de Newton para aproximação de zeros das funções polinomiaisde qualquer grau, dados os intervalos em que estasfunçõesse anulamou quando podemos deduzirou em cenários que tais intervalos possam ser inferidos.Ressalta-se que o texto compreende aelaboração dealgoritmose demandao pensamento computacional para resolução de problemas, em conformidade com os aspectos previstos na BNCC.A utilização dossoftwareseducacionaisVisual Cálculo Numéricoe o Excelfoi determinante para a eficiênciados algoritmosnos quesitos: velocidade e precisão.

Neste trabalho abordamos o simulador de investimento do tesouro direto, o qual encontra-se no site<https://www.tesourodireto.com.br/simulador/>, como recurso didático paraapresentar alguns conceitos de Matemática Financeira, visando aproximar tais conceitos à vida coti-diana dos discentes. Tal abordagem atende as competências e habilidades da área de Matemática esuas tecnologias que estão inseridas na Base Nacional Comum Curricular, quando estabeleceu que“no Ensino Médio o foco é a construção de uma visão integrada da Matemática, aplicada à realidade,em diferentes contextos”, ver [10, p.528]. Concluímos esse trabalho com uma proposta de sequênciadidática, bem como uma possível resolução dessa proposta