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The central theme of this study arose from reflection on the importance of developing
differentiated methodologies in the classroom when addressing the concept of pi and valuing
the cultural knowledge carried by our students. Based on this reflection, the following
question was formulated: how to explore mathematics in the typical Northeastern Brazilian
dish of couscous through the application of a didactic sequence in a seventh-grade class of
elementary school? To answer this question, the research had as its general objective the
exploration of the mathematics present in the Northeastern Brazilian dish of couscous through
the application of a didactic sequence, guided by specific objectives that included research
into the theoretical foundation, elaboration and application of a test didactic sequence
(addressing Geometry, Quantities, Measurements and Numbers), where the latter underwent
the necessary adjustments after the collection and verification of the application data,
culminating in an educational product. The methodology used was action research with a
mixed approach (qualitative and quantitative) and applied nature, using the inductive method.
The sample consisted of all students in a seventh-grade class at the Escola Estadual Professor
Benedito Moraes in Maceió/AL. The research and data collection instruments included
written questionnaires (an entry questionnaire about local culture and an exit questionnaire
about impressions from the classes), students' completion of mathematical activities, and
photographic and audio recordings. The data analysis method was quantitative (to assess
mathematical reasoning in the activities) and qualitative (to analyze the questionnaires about
culture and impressions). After completing each of the above steps, it can be concluded, based
on the students' accounts, that they understood the number pi in a contextualized and
exploratory way, going beyond the memorization of formulas, as well as valuing cultural
knowledge and strengthening the culture of Northeastern Brazil. Thus, it is also hoped that the
educational product presented will be a new tool to assist other elementary school
mathematics teachers in Northeastern Brazil in addressing the concept of the number pi in a
contextualized manner and valuing local culture.

The purpose of this study is to conduct a literature review on the fundamental principle
of counting and its applicability in the school setting through the problems presented in the
Brazilian Public School Mathematics Olympiad (OBMEP). Thus, for a comprehensive
investigation, we based our analysis on teaching through problem-solving from the book
Programa de Iniciação Científica Jr. (PIC), with discussions regarding methodological
applicability and the presentation of a Teaching Sequence (TS) related to the fundamental
principle of counting. This serves as a suggestion for counting problems inspired by the
OBMEP and the PIC book for public school teachers. In this sense, we seek answers to the
following questions: How are issues related to the fundamental principle of counting presented
in the PIC book and their applicability in OBMEP, and what strategies can teachers use to
enhance understanding of the topic? Furthermore, the research is guided by the specific
objectives of reflecting on teaching strategies through the resolution of counting-related
problems, enabling students to construct their own knowledge through problem-solving,
understanding the interpretive context of the questions presented in the book/workbook used in
the PIC program and the paths to their solutions, and creating a teaching sequence to serve as a
reference for teachers in the future. To achieve this objective, we will conduct a literature review
and an in-depth study of the PIC textbooks and problem-solving, engaging with various authors
who research the subject, such as: Paulo Cezar Pinto Carvalho (PIC textbook: Methods of
Counting and Probability, 2017). The research was developed based on a literature review of
the content, leading to the creation of a suggested teaching sequence for teachers of grades 6
through 9 who wish to use the problem-solving method when addressing concepts and questions
as preparation for the OBMEP. Thus, with successful reports of application, we recognize the
contribution of the PIC books/workbooks to students’ learning in the logical mathematical
understanding of the solved problems.

This dissertation presents the development of a pedagogical proposal based on mathematical modeling, aiming to integrate concepts of financial mathematics and entrepreneurial education into public high school education. Given the alarming scenario of learning gaps in mathematics in Brazil, where only 5% of students finish high school with adequate proficiency (QEdu, 2023), and considering the gap between curricular content and the sociocultural reality of young people, this study proposes a systematic articulation between mathematical modeling (Biembengut; Hein, 2016; Bassanezi, 2014), entrepreneurial education (Dolabela, 2008), and financial mathematics as a strategy to promote student protagonism and life projects. The research, of a theoretical descriptive nature with a qualitative approach, resulted in the development of a didactic sequence structured in 16 class hours, organized into five stages: diagnosis and sensitization, content leveling in blocks (ratio and proportion, percentages and interest, equations, functions), organi zation of students into interdependent departments (costs, pricing, revenue, taxes, and profit), the mathematical modeling cycle, and validation through an entrepreneurship fair. The proposal uses the simulated production and commercialization of cookies as a case study, incorporating real elements such as price research, tax calculation (MEI– Individual Microentrepreneur), and break-even and maximum profit analysis through linear and quadratic functions. Expected outcomes include student engagement in mathematical learning, the development of financial autonomy, and the construction of a life project based on critical and conscious decision-making. It is concluded that the integration of modeling, entrepreneurship, and financial mathematics constitutes a viable and replicable path to transform the classroom into an environment of inves tigation, social innovation, and preparation for the world of work, in accordance with the general and specific competencies of the Brazilian National Common Curricular Base (Brasil, 2018).

The proper location of emergency service facilities is a relevant problem from both operational and urban planning perspectives. In urban environments, where movement occurs mainly along orthogonal street grids, Euclidean distance may fail to accurately represent actual travel times. In this context, Taxicab Geometry, associated with the L1 metric, provides a more suitable framework for modeling urban displacements. This dissertation investigates the problem of optimally locating fire stations of the Fire Department of the State of Alagoas in the city of Macei´o, adopting the 1-center (minimax point) criterion under the taxicab metric, whose goal is to minimize the maximum response time to emergency calls. The study begins with a discussion of historical and mathematical foundations related to non-Euclidean geometries, Taxicab Geometry, and classical facility location models. Subsequently, a mathematical modeling of the problem is developed considering two and three high-demand neighborhoods, with an analysis of the structure and geometric interpretation of optimal solutions. For the case of two demand points, it is shown that the set of optimal solutions of the 1-center problem under the taxicab metric may take the form of a line segment, possibly degenerating into a single point in particular configurations. This behavior contrasts with the 1-median problem, whose solution set, when the two points differ in both coordinates, forms a two-dimensional region. For three demand points, the determination of the optimal solution through the intersection of coverage regions is discussed, showing that, under general conditions, the solution is a single point, which may degenerate into a line segment in particular geometric configurations. Extensions of the model, such as the introduction of weights associated with neighborhoods to represent different demand levels, are also addressed. As an educational product, a didactic manual for the Otimizador GeoTaxi application is proposed, articulated with a didactic sequence for the third year of high school, using the fire station location problem as a context for studying Taxicab Geometry, distance concepts, and optimization problems. The proposal integrates mathematical rigor, urban contextualization, and the use of visual and technological resources, contributing to the development of competencies outlined in the Brazilian National Common Core Curriculum and to the understanding of the social role of Mathematics in managing essential public services

This study investigates the greatest integer function as a relevant mathematical tool for teaching
and problem solving, proposing its inclusion in the high school curriculum starting from the
second year. Although widely used in several areas of Mathematics, especially in Number
Theory, this function still occupies limited space in basic education textbooks and is rarely
explored through practical or contextualized applications. In this context, the research discusses
the conceptual, historical, pedagogical, and curricular foundations related to the greatest integer

function, as well as its potential contribution to the development of logical-mathematical reaso-
ning and the modeling of both everyday and pure mathematical problems. The study includes a

bibliographic survey on the subject, addressing fundamental properties, graphical representations,
and applications of the greatest integer function in different mathematical contexts. Furthermore,
it is grounded in theoretical and pedagogical references aligned with the Brazilian National
Common Curricular Base (BNCC), which emphasizes meaningful and contextualized learning
aimed at fostering students’ intellectual autonomy. As a practical outcome of the research, a
didactic sequence was designed and implemented with second-year high school students in
order to introduce the greatest integer function through an accessible and investigative approach.
The results indicate that the inclusion of this content contributes to a deeper understanding of
functions and broadens the possibilities for solving mathematical problems, demonstrating the
pedagogical feasibility of incorporating the greatest integer function into basic education.

This dissertation presents a reflective account of my teaching practice in the
instruction of geometric transformations (isometries) for the 8th grade of Elementary
Education, developed from a decolonial, anti-racist, and ethnomathematical perspective. The
text begins with a critique of the Eurocentric narrative that traditionally structures the
Mathematics curriculum, highlighting the systematic erasure of mathematical knowledge of
African origin: a realization that emerged from my own trajectory as a teacher and the
concerns it raised.
In response to this exclusion perceived in my everyday practice, I began to use the
Adinkra symbols of the Akan people (present-day Ghana and Ivory Coast) as a didactic
resource in my isometry classes. In my experience, the Adinkras revealed themselves not as
mere ornaments, but as a sophisticated mathematical technology that expresses, through
geometric patterns, knowledge about axial symmetry, rotation, translation, fractals, and
symbolic logic, contents that naturally integrated my usual planning.
The reflection I now present articulates three theoretical axes that supported my
practice: Ubiratan D'Ambrósio's Ethnomathematics, which recognizes the diversity of
mathematical knowledge; the decolonial thought of authors such as Quijano and Mignolo,
which denaturalize the hierarchization of knowledge; and Laws 10.639/2003 and
11.645/2008, which establish the mandatory teaching of Afro-Brazilian and Indigenous
history and culture, guidelines that already guided my work in the classroom. The proposal
reflected here is also aligned with the Brazilian National Common Curricular Base (BNCC),
especially regarding the skills related to geometric transformations.
Methodologically, this work adopts a qualitative approach of inquiry into one's own
practice, drawing on my teaching experience at a public school in the Agreste region of
Pernambuco, Brazil. The account describes didactic sequences I developed over six classes,
mobilizing investigative activities with concrete materials, manual construction of patterns,
and digital modeling in GeoGebra software: resources that were already part of my didactic
repertoire. The reflection recorded here is not based on data collected specifically for this
research, but on observations and records of my everyday practice, kept in my class diary and
pedagogical planning.
The reflections arising from this experience indicate that the approach with Adinkras
contributed to meaningful learning of geometric concepts, while also promoting the
appreciation of African knowledge and the strengthening of the cultural identity of Black
students, aspects I observed in my daily interaction with the class. It is concluded, from this
experience, that it is possible and necessary to articulate mathematical rigor, digital
technology, and anti-racist education, reaffirming the school's commitment to cognitive and
social justice, a commitment that, in my practice, proved not only possible but urgently
necessary.

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