In this dissertation we will present a didactic sequence for teaching polygon areas using the GeoGebra software. For this purpose, a bibliographical study was carried out. Some concepts of plane geometry were covered, especially such as polygon area formulas, making use of the area formula demonstrated in the Dissertation made by (Lima, 2014) [17], where demonstrating a formula through Determinants, using the coordinates of the points in a Cartesian graph, whose area is the sum of the halves of these determinants. Projections of area formulas using this method were shown. Polygon constructions were made in the GeoGebra Software, calculating the areas to check whether the results generated by the formula were correct. Finally, a didactic sequence was made to apply the concepts mentioned.

This work addresses the topic of empathy between educator and student. More
precisely, we will address the following investigative question: how do
mathematics teacher’s experiences of empathy experienced as students affect
their learning processes and how can teachers of this discipline have a more
empathetic position towards their students? To answer this question, descriptive
qualitative research was carried out based on the phenomenological method
according to the variant proposed by Sanders for empirical phenomenological
research. In this research it was observed that teachers recognize the importance
of empathy in learning mathematics, this recognition being based on the belief
that if they had had empathy from their teachers, that is, if teachers had paid more
attention, presented more openness to identify the learner’s difficulties and had
established more affective relationships with the students, the teachers could
have achieved better results in terms of the student’s learning processes

Mathematics education has been undergoing a process of change that has intensified mainly
during the COVID-19 pandemic, as today's society is immersed in what is called Education 5.0.
In this type of "education", the approach is more focused on the digital technologies used in the
educational process to guarantee a better socio-emotional development for the student. The
National Common Curriculum Base (BNCC), through its general competences, learning
objectives, in the competences and skills of various curricular components, recommends the
use of digital technologies aimed at the students' experiences. It is in this sense that the use of
GeoGebra, as a technological resource, can guarantee a better approach to mathematical
concepts, as it is a dynamic software and tends to help in understanding the contents. The choice
of the approach of using GeoGebra in the area of Geometry is due to its presence in everyday
life, but also in various mathematical or physical contents and in various professions. The main
objective of this work is to demonstrate Plane Geometry concepts using GeoGebra software for
high school students, in addition to analyzing its potentialities and limitations in exploring Plane
Geometry concepts and solving questions of the Brazilian Mathematics Olympiad of Public
Schools (OBMEP). For this, the methodology used is of a qualitative nature, bibliographic and
exploratory. Finally, the results obtained through the demonstrations of the theorems and the
solutions of OBMEP questions show that GeoGebra can be used as a methodological resource
in the teaching of Mathematics and mainly in the demonstration of Plane Geometry theorems.

Financial education is defined as a cross-cutting theme by the

National Common
Curricular Base (BNCC). Although it is addressed from different
perspectives in various
curriculum components, beyond Mathematics, there are some
gaps in the curriculum re-
garding current topics related to various types of credit
operations. Research indicates
that the majority of the Brazilian population has some type of
debt to pay. Therefore,
this work begins by collecting data on the indebtedness of the
Brazilian population. Ad-
ditionally, it emphasizes the importance of laws that define
strategies for preparing the
population for everyday consumer relations through education.
As a result, an alterna-
tive educational material will be proposed, covering the most
commonly used financial
instruments by the population: credit operations, credit cards,
financing, among other
modalities. Finally, the responses of 3rd-year high school
students to a survey focusing on
their knowledge of financial topics and their ability to manage
household finances will be
highlighted

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