When discussing the teaching, learning and assessment of mathematics,
educators and education professionals are placing an important focus on the
quality of education provided to students. This suggests a commitment to ensuring
that students acquire solid and meaningful knowledge in mathematics. Educators
can implement strategies such as differentiated instruction, contextualization of
mathematical concepts, use of diverse educational resources, collaborative
teaching practices, and providing emotional and motivational support to students.
These approaches can help promote more meaningful learning and overcome
barriers students face in mathematics, with an emphasis on external assessments
as well. In this context, this research seeks to answer the following question: how
can problem situations involving digital technologies contribute to student learning
in SAEB mathematics assessments? The general objective was to investigate the
mathematical learning obtained when using activities that relate problem situations
and digital technologies to solve SAEB mathematics items in elementary school.
The present work developed didactic sequences for teaching mathematics
focusing on the difficulties of students in the 9th year of elementary school, based
on the results of the SAEB with a qualitative approach, based on field research.
The data collection instruments were the school documents that guide the learning
assessment; and our diary of observations of the activities that will be carried out.
With this, it is concluded that there are dualities in the teaching of mathematics
between traditional and innovative methods, what we noticed is that based on the
study, students felt more motivated with technological resources and that there is
always a need to have reflections on praxis teacher's pedagogical skills and that
this can lead to better performance in external assessments, in addition to setting
an example for other schools.

This paper presents a proposal for teaching spatial geometry using Geogebra software. Spatial
geometry is an area of Mathematics with a wide range of applications, and its teaching is a
challenge due to the difficulties in representing geometric solids in planar media, such as
whiteboards and books. Thus, the use of Digital Information and Communication Technologies
(DICT) demonstrates great potential in facilitating the teaching of spatial geometry and
promoting critical and meaningful learning, taking advantage of the growing evolution of these
tools, which has driven their integration into the educational scene. In this context, Geogebra
emerges as a powerful tool, having a variety of resources that can be applied in various areas
of Mathematics. Aiming to evaluate the use of Geogebra as a pedagogical tool in the teaching
of spatial geometry, this research has a qualitative character, and the methodology used was
field research, supported by bibliographic research. To collect the data, a pedagogical
intervention was carried out, composed of a diagnosis to verify the students' prior knowledge,
a pedagogical workshop, and questionnaires. A high acceptance rate of Geogebra was observed
among the students, who found it easy to use and helpful in visualizing and understanding the
elements and measures of a spatial figure. Geogebra also helped the students to understand a
proposed problem situation. Based on the results obtained, it was concluded that Geogebra is a
facilitating tool in the process of learning spatial geometry, promoting dynamic, interactive,
and collaborative teaching and contributing to the development of critical thinking, motivation,
and student interest.

Este trabalho apresenta uma proposta de utilização do software GeoGebra como uma ferramenta facilitadora da interdisciplinaridade entre a Matemáticas e a Física no ensino fundamental e médio nos assuntos relativos `as funções afim e quadrática. O estudo foi realizado com alunos da primeira série do ensino médio de uma escola pública militar em São Jose de Ribamar, Maranhão. A pesquisa envolveu atividades práticas e exercícios específicos utilizando o GeoGebra, e os resultados mostraram que os alunos conseguiram utilizar o software adequadamente, indicando que seu uso teve um impacto positivo no processo de ensino e aprendizagem.

A dissertação tem como objetivo geral apresentar diferentes demonstrações do Teorema de Pitágoras generalizado por triedro tri-retangular. Para isso, será realizado um breve contexto histórico sobre Pitágoras, Teorema de Pitágoras e sua recíproca, bem como algumas de suas demonstrações incluindo abordagens geométricas, algébricas e vetoriais. Além disso, será apresentado o triedro tri-retangular e sua relação com o teorema, assim como as generalizações e aplicações do teorema de acordo com alguns autores. Também serão apresentadas algumas generalização no espaço. É discutida a inserção da generalização do Teorema de Pitágoras na educação básica e seus benefícios para o estudante. Será apresentada a proposta da pesquisa, ou seja, será apresentada as demonstrações do Teorema de Pitágoras generalizado por triedro tri-retangular de diferentes formas. A dissertação concluirá destacando a relevância de cada uma das generalizações do teorema de Pitágoras generalizado por triedro tri-retangular, sugerindo qual é mais adequada para se trabalhar no ensino médio e qual a mais indicada para o ensino superior. As referências bibliográficas utilizadas ao longo do trabalho são apresentadas no final.

The research addresses a current and interdisciplinary theme, with great
repercussions in the educational field. It is a fact, at the present time, that the
teaching of mathematics is undergoing reformulation in its methodologies, with the
insertion of teaching methods that propose the active participation of students, as in
mathematical modeling. A teaching trend that leads to the elaboration of strategies
that make the curricular component more attractive. From this perspective, the
research sought to identify whether the teaching-learning process of Spatial
Geometry through the teaching methodology of Mathematical Modeling contributes to
the scientific and technological training of students, as well as to their citizenship.
The study contemplated spatial geometry with emphasis on convex polyhedra. The
method applied to carry out this study was a qualitative research, in which the author
applied questionnaires and sought elements to answer the problem question in the
analysis of the collected data. The results are consistent with the concern about the
knowledge of second-year high school students at the research field College. It is
concluded that the use of mathematical modeling can be an opportunity for the
development of autonomy, critical thinking, the ability to live with and learn from
others.

The use of technological resources in the teaching of mathematics is a widely discussed topic and is seen by many as inevitable, given the justification that their use enhances teaching and learning. It has been observed that a significant proportion of students lack interest in learning mathematics because they find it difficult, challenging teachers to try all possible technologies and develop new teaching proposals to make this part of the curriculum more appealing to students. The use of software, whether in computers or in mobile devices such as smartphones and tablets, can be considered as one of these 'new' teaching proposals. This paper presents the results of a study whose objective was to investigate the contributions of the GeoGebra application on mobile devices to the process of understanding the graphical content of quadratic functions in a first year high school class at the Centro de Ensino Professor Robson Campos Martins, in Paço do Lumiar - MA, with the aim of verifying if there is a greater learning outcome with the use of this software. Using a research-action methodology and a qualitative-quantitative method, data were collected and analysed. The instruments used for data collection were questionnaires and activities using GeoGebra on mobile devices. At the end of the research, students indicated that the use of the GeoGebra app on their smartphones greatly facilitated their understanding of the study of quadratic function graphs, suggesting that its use had a positive impact on the teaching-learning process.

The objective by objective is the application of a teaching strategy whose main focus
is the teaching contents presented among the mathematical contents that are
consistent in the middle grades of the analyzed elementary level and of higher
elementary education and teaching. The strategy proposes an existing
interrelationship between some contents that appear in the two levels of education, in
order to teach and review the contents of fundamental level, to present a medium of
introduction of level contents, and consequently to help the transition process of
students from the 9th year of elementary school to the 1st year of high school. In
order to validate the use of the proposed strategy, methodology chosen to carry out a
survey with 9th grade students, the interventionist and mathematics teachers who
teach or have taught for this series. At the end of further analyses, a definition of its
use and future actions was chosen among the results of the strategy model
operation.

Quando observamos os documentos oficiais que norteiam a educação nacional, no que diz respeito aos conteúdos, percebemos que há um consenso no objetivo: formar cidadãos. O ensino de Matemática com abordagem CTS visa, sobretudo, o fomento da criticidade do aluno perante os prós e contras do desenvolvimento referente à tecnociência, verificando assim, seus benefícios e custos. Partindo desse ponto, o presente estudo de caráter quanti-qualitativo, objetivou-se discutir a origem e a utilização da abordagem CTS no ensino de Matemática bem como identificar as concepções e práticas dos professores sobre essa abordagem em suas práxis, especificamente, apresentando o olhar dos professores de Matemática no que concerne essa abordagem de ensino e ainda descrevendo suas práticas. Focalizando a aprendizagem baseada em contextos sociais, uma vez que a contextualização dos conteúdos, voltado para além dos métodos, fornece novos significados no contexto ensino de Matemática, pelo sentido transformador da realidade, para tanto como aporte da pesquisa apresentamos como referencial teórico Bazzo, Auller e Santos, autores de renome quando se trata em tecnociência. Ressalta-se como problemática central desta pesquisa a seguinte questão: Como os professores de Matemática veem o ensino de Matemática com abordagem/enfoque CTS/CTSA? Os professores partícipes da pesquisa são professores de Matemática da educação básica (Ensino fundamental/anos finais e Ensino Médio) da cidade de Codó-MA. Durante todo o processo de coleta dos dados, o professor partícipe foi estimulado a refletir e compartilhar suas experiências de ensino com o intuito de colocar o professor no centro da discursão. Assim, para o tratamento dos dados foi utilizado análise dos questionários semiestruturados dos participantes previamente elaborados. Em caráter conclusivo, as respostas permitiram investigar a concepção dos professores, onde ficou evidente que grande parte dos professores de Matemática partícipes, até mesmo pela falta de formação continuada no seguimento, desconhecem a abordagem CTS/CTSA bem como suas potencialidades no ensino-aprendizagem dos conteúdos matemáticos.

A Matemática é, por vezes, entendida como uma ciência muito complexa, a qual só pode ser aprendida por aqueles que possuem uma suposta pré-disposição a seu entendimento. Além disso, o ensino de Matemática pode se tornar consideravelmente teórico e enveredar para objetos de profunda abstração, sem conexões claras com a realidade do estudante, propondo-se a resolução de problemas puramente matemáticos. Porém, o “[...] ensino-aprendizagem de Matemática inicia a partir da intuição e progressivamente aproxima-se da dedução.” (HUETE E BRAVO, 2003, p 23). Assim, o caminho do aprendizado desse componente curricular pode ser percorrido por qualquer indivíduo. Além disso, entende-se que o aprendizado em Matemática “[...] precisa voltar-se para a promoção do conhecimento matemático e da habilidade de utilizá-lo. [...] significa ir além das simples resoluções de questões matemáticas, muitas vezes sem significado para o aluno [...].” (BIEMBENGUT e HEIN, 2018, p 18). Diante desses entendimentos, este trabalho foi pensado no intuito de expor a Modelagem Matemática, Tendência de Ensino da Educação Matemática, a qual se propõe, segundo Meyer, Caldeira e Malheiros (2011), confrontar o mundo real com o universo da Matemática, como a alternativa mais adequada para tornar mais eficaz e proveitoso o ensino dessa ciência na Educação Básica. Para tanto, além do estudo de escritos já mencionados, lançou-se mão da pesquisa qualitativa por meio de formulários, com profissionais da área de Matemática, sobre seu conhecimento sobre essa tendência, assim como o rendimento de seus alunos no processo de ensino-aprendizagem de Matemática, em particular com as Funções Elementares, Afim e Quadrática. Tais funções foram os objetos de conhecimento escolhidos, pelo fato de serem entendidos como ótimos temas matemáticos para serem percebidos na realidade dos indivíduos. Foi proporcionada aos pesquisados uma oportunidade de conhecer e/ou aprofundar os conhecimentos sobre a Modelagem, em um minicurso de Formação Continuada, voltado para a Tendência de Ensino em questão. Um dos produtos desse processo seria a construção de Sequências Didáticas com fulcro em Modelagem Matemática, para o Ensino das Funções Elementares já citadas. As Sequências Didáticas são, “[...] um conjunto de atividades ordenadas, estruturadas e articuladas para a realização de certos objetivos educacionais, que têm um princípio e um fim conhecidos [...].” (ZABALA,1998 P.18). Essa estrutura de planejamento agrega bastante valor ao ensino de Matemática ao ser aliada a Modelagem Matemática, pois as duas ferramentas se ajustam, por terem estruturas semelhantes. Os resultados da pesquisa, aliados aos estudos e a interação didática com os professores, permitiu a inferência que afirma que a Modelagem Matemática é uma ferramenta de ensino com substancial efeito positivo no processo de ensino- aprendizagem de Matemática. Mostrando-se sempre passiva de inovação e capaz de acompanhar as mudanças na sociedade, por trabalhar com situações cotidianas.

O ensino de matemática e física requer do professor conhecimento científico e uma boa didática, com alternativas para despertar interesse no aprendizado. A Geometria é de grande utilidade neste sentido, já que possui diversas aplicações na vida do aluno. Este trabalho tem como objetivo geral ajudar os alunos da educação básica a compreender os fenômenos ópticos de reflexão e refração através da homotetia. Os objetivos específicos são investigar como ocorrem as práticas de ensino dos fenômenos ópticos, utilizar a homotetia para o estudo da propagação da luz, propor o uso de aplicativo de geometria para o ensino de fenômenos ópticos, discutir as aplicações de óptica no cotidiano. Para isto, foi realizado levantamento em livros de matemática sobre a abordagem sobre homotetia e em livros de física sobre como é sugerido o ensino de óptica geométrica. Em seguida, foi realizado pesquisa com professores das duas disciplinas sobre o ensino de homotetia e óptica geométrica. Podemos concluir que a maioria dos professores não ensina homotetia, parte por não conhecer e outra por não ser um assunto abordado na maioria dos livros didáticos. Na formação inicial, a maioria dos professores não estudaram o assunto. A pesquisa com os alunos relaciona o interesse do aluno por matemática e física, a familiaridade deste com os assuntos propostos e a sua visão em relação a situações cotidianas. A maioria relatou dificuldade com o assunto. O aluno teve contato com uma breve explicação de cinco minutos sobre o que é homotetia e foi convidado a responder três questões. A maioria conseguiu acertar pelo menos duas questões, apesar da dificuldade inicial.

A presente pesquisa tem como objetivo analisar os erros cometidos por estudantes do
Primeiro ano do Ensino Médio na resolução de questões de Função Afim. Os objetivos
específicos são: a) analisar as estratégias de resolução de problemas envolvendo Função
Afim; b) classificar os erros cometidos pelos alunos na resolução dos problemas; c)
compreender dificuldades que os alunos apresentam no estudo de Função Afim; d)
analisar opiniões de professores acerca dos erros cometidos pelos alunos; e) verificar se
a análise de erros oferece ferramentas para a melhoria da aprendizagem da Função
Afim. A investigação tem caráter qualitativo e realizou-se em uma escola Pública
Estadual da cidade de São Luís- MA, com 64 estudantes de três turmas do Primeiro
Ano. A primeira etapa do estudo, desenvolveu-se a partir de aplicação de questionários
direcionados aos alunos e professores das turmas pesquisadas, sobre a percepção que
eles têm a respeito da Matemática e a avaliação nessa disciplina. Na segunda, foi
aplicado teste com questões sobre Função Afim com os estudantes da etapa anterior. Na
terceira etapa, ocorreu a análise das respostas dos testes aplicados e a categorização dos
erros verificados. Foi utilizado como referencial teórico, os trabalhos de Cury (2019),
Escobar (2020), Hoffmann (2019), Luckesi (2018) e Zabala (1998). Pelos dados
coletados, verificou-se que tanto professores quanto alunos ainda têm arraigadas
concepções tradicionais de avaliação, influenciando no modo como percebem o erro.
Porém, a partir da Análise de Erros nas respostas obtidas nos testes, pôde-se conferir as
dificuldades sentidas pelos estudantes no domínio de conceitos e procedimentos
associados à Função Afim, por conseguinte, percebe-se que esta é uma estratégia que
pode fundamentar ações com vistas a favorecer uma melhor construção do saber
Matemático.

A pesquisa objeto deste trabalho enfatiza a teoria de Congruências Modulares, expondo seus fundamentos e diversidade de aplicações no cotidiano e propondo o ensino desse conteúdo nas séries finais do ensino fundamental por sua relevância teórico-prática para o desenvolvimento do ensino de matemática. Utiliza-se a pesquisa bilbiográfica para abor- dar tópicos necessários à teoria de congruências como o conjunto dos Números Inteiros e o conteúdo de Divisibilidade. Além disso, são apresentadas aplicações de Congruências modulares em calendários, sistemas de identificação e criptografia bem como as propriedades que auxiliam na resolução mais célere de problemas. E realiza-se aplicação com alunos da rede pública de São Luís para verificar as hipóteses acerca das contribuições dateoria de congruências para essa etapa do ensino.

O trabalho desenvolve uma pesquisa de aplicação do software Calques 3D no ensino de Matemática.  A ferramenta Calques 3D é aplicado como uma ferramenta didática, possibilitando a compreensão e visualização das figuras geométricas, contribuindo para no desempenho dos alunos, mostrando a importância da tecnologia para o ensino e Aprendizagem de Matemática. O software educacional Calques 3D é utilizado no trabalho como um recurso metodológico para analisar e auxiliar no processo de ensino e aprendizagem do conteúdo de Geometria e Álgebra no Ensino Básico.

Education and technology currently go together, however, uniting them is a task that requires preparation by the teacher inside and outside the school. At the same time that it offers challenges and opportunities, the digital environment can become an obstacle for learning, leaving the educator, the mission to make its relationship with the objects of knowledge taught in the classroom. In this sense, it is up to the teacher to use resources that allow the student to know something abstract and relate it to the real. In view of the above, this work proposed methodologies for teaching Flat Geometry and Spatial Geometry to conceive such a link. For this, two computer programs that constitute technological devices used by man in the construction industry were used, Autocad and 3Ds Max. Initially, research was carried out on articles, monographs, dissertations and theses that dealt with the generations of individuals who how they conceived and conceive the reality that surrounds them. The purpose of this search was to understand how the current generation acts and learns, called “generation Z”. It was found that digital natives do not want to learn and then practice, they use the trial and error method for learning, since they are not afraid of making mistakes and therefore learn more easily. Subsequently, writings were sought that dealt with the importance of technology for education. It was observed that technologies, as educational technological resources, express benefits that go beyond the academic competences linked to cognition, allowing the development of autonomy in the intellectual and behavioral spheres, considering that the students themselves go in search of the solution of the challenges found in their daily. After expressing the link between technology and education in today's society, the presentation of a brief history of geometric knowledge and its importance for students was carried out. This part dealt with the emergence of Geometry, its importance in Institutional documents such as the PCNS (National Curriculum Parameters) and the BNCC (National Common Curricular Base). It was noted that geometry seems to be, within school mathematics, an area particularly conducive to carrying out activities of an exploratory and investigative nature, especially through the use of technological resources. Through the presentation of proposals for the use of software, in the process of teaching and learning geometry the ability to visualize can be developed, as the student is provided with didactic support materials based on concrete elements representative of the geometric object under study.

São várias as dificuldades encontradas no ensino e na aprendizagem de Matemática no Ensino Fundamental. É comum encontrarmos em nossas salas de aula, alunos que não gostam ou, até mesmo, temem a disciplina considerada extremamente difícil e árida. É preciso despertar desde cedo nos discentes a ideia de que a Matemática é compreensível para todos,  mesmo que, em níveis diferentes de complexidade. Nesse sentido, os professores, são desafiados a todo o momento em investir na busca de procedimentos e recursos metodológicos que os auxiliem na mediação entre o saber matemático e o aluno. Por isso, a pesquisa indica os paradidáticos como uma opção a ser utilizada nessa mediação. O estudo realizado partiu de um estudo bibliográfico para a experimentação. A atividade foi desenvolvida  em uma turma de oitavo ano de uma escola municipal de São José de Ribamar no Estado do Maranhão. A pesquisa permitiu verificar a relevância que tem a leitura e a escrita em Matemática e que a relação entre esta e a língua materna precisa ser mais evidenciada nas aulas. Entender conceitos, interpretar corretamente os problemas matemáticos, expressar oralmente ou escrever seu pensamento matemático perpassa por momentos de leitura e escrita dentro da disciplina em questão.

This work shows the use of Maxima software as a tool to perform matrix operations and
solve linear systems. Therefore, before using the software, a brief approach on matrix
operations is presented, as well as the inverse determination of a matrix, calculation of
determinant of 2 and 3 order matrices and resolution of linear systems through scaling
and the Gauss-method Jordan. Then, it shows some Maxima functions that are necessary
to perform these operations. Then, the software is used to perform the operations with
matrices, determine the transpose and inverse of a matrix of order 3, calculate the
determinants of matrices of order 3 and 4 and still solve possible and determined systems.
Finally, graphical representations of linear systems of two and three equations are made
and some applications involving matrices and linear systems are presented.

Digital Information and Communication Technologies have made significant advances in recent years, the emergence of faster internet, modern computers and state-of-the-art cell phones have decentralized access to information, challenging the school community to include such technologies in teaching, adding value and knowledge to the teaching-learning process. With this, the teacher was challenged to innovate and work these tools in classes, focusing on mathematics, which theoretically is a discipline rated as plastered and exact, to introduce audiovisual resources, videos, games, it required the teacher's availability and willingness to transform mathematics into an attractive and better-understood discipline. The challenge of this work is to identify how Digital Information and Communication Technologies can be inserted in classrooms, contributing mainly to better student learning, through the Khan Academy platform, in order to investigate how the platform works. it can streamline the classroom space and the teaching and learning process, thus offering possibilities for teachers to teach content in an innovative way and for students to learn at their own pace, building knowledge through gamification and videos. To this end, the work was developed with 16 students from the 9th year of elementary school, from Colégio Militar Tiradentes VI, we verified with this study that the use of the adaptive Khan Academy platform in the classroom, provided it is done correctly, with planning and adequate study, becomes beneficial for the teaching-learning process of mathematics, leading the student to become interested in the discipline, making him an active subject in this process, thus being the author of his own knowledge.

Esta investigação teve o propósito de analisar as contribuições da régua compasso e transferidor no ensino introdutório da geometria. Para o estudo, valeu-se de uma abordagem qualitativa, com pesquisa de campo. O surgimento da geometria remonta a períodos anteriores ao nascimento de Cristo e as necessidades do homem desde o seu surgimento, contribuíram para a origem e evolução deste campo do saber matemático. Realizou-se uma oficina com alunos do 9º do ensino fundamental, no colégio onde foi realizado a pesquisa na escola. Durante a oficina, os alunos realizam construções geométrica com ouso da régua e do compasso. Durante o estudo, constatou-se certas dificuldades da aprendizagem de geometria usando estes instrumentos.

In this work we present the results of the research on the Simplex Method applied in a Technical Course in Administration and we emphasize the importance of this knowledge for a Technical in Administration. GeoGebra, OR Simplex and Solver, an Excel tool, were used to speed up and facilitate the resolution of applied problems. The first method presented was the graphical method used only when the problem involves two decision variables. The second is the analytical method (Simplex Primal Method) using the Simplex tableau, that is, a table to organize the calculations and the main steps to solve a problem involving three or more decision variables. Next, we present OR Simplex a proprietary cell phone application to solve Linear Programming Problems (PPL) that can be used in problems involving up to thirty decision variables (this was the method that students liked the most because of the simplicity in solving PPL). And finally we used Solve from Excel to solve some problems in the list of exercises that students had to put the problem in its standard form and check if there is a relationship between the problems that are already in the standard form.

The present work is related to a brief analysis of the changes arising from technological developments and how they directly influence the school environment. Thus, it was decided to investigate and the use of the Inverted Classroom as a hybrid teaching modality in which the student learns in different environments, in person and virtual, and how this methodology, added to technological elements, can contribute to the improvement of the teaching mathematics by optimizing time in the classroom and allowing students to be able to experience learning experiences different from those traditionally offered. Therefore, we sought to achieve the objectives of identifying the elements that distinguish the traditional teaching-learning process from hybrid teaching, showing how it can be adopted to improve teaching practice, in addition, it was possible to study the characteristics of the classroom methodology inverted class and how practices based on this methodology can promote the engagement of 9th grade students and optimize the teaching-learning process. It is also necessary to say that to support the present study, the ideas and theories defended by Bacich (2015), Bergann (2018) and Camargo (2018), among others, were used as the basis for this study, making it possible to achieve the results desired, showing the compatibility of the inverted classroom methodology to the teaching of mathematics in the 9th grade of elementary school.

In view of the importance of trigonometric functions and their applicability in solving problems involving other sciences, including Physics, this work presents a study on the teaching of trigonometry in problem solving, through everyday applications and in solving problems of simple harmonic movement using geogebra dynamic software, in order to highlight the importance of interdisciplinarity in the disciplines Physics and Mathematics. Therefore, it is necessary to develop trigonometry with applications in Physics in High School, from problem solving, apply a didactic sequence involving simple harmonic movement and trigonometry in solving Physics problems, using a simulator in the geogerbra software, discuss alternatives overcoming difficulties in teaching trigonometry through interdisciplinarity. Thus, a research is carried out, using the exploratory method, with a bibliographic review addressing the analysis of behavior and its relationship with teaching. Therefore, it is expected that students know how to use mathematics to solve practical problems and the use of information and communication technologies together with the application in physics, to facilitate the teaching-learning process, which requires the verification that this work serves to help teachers who face difficulties in working trigonometry applied to physics in a dynamic way and linked to the students’ daily lives.

It is believed that the teaching process should always be carried out in a way that promotes learning. With this conception, the present work was thought and structured, considering that in the particular case of teaching mathematics, the object of study of this investigation aims to investigate in textbooks of basic education if the treatment of the angle concept provides the Didactic Transposition approach a, based on Yves Chevallard (1991), considering it a teaching strategy that, being adopted by the teacher in his pedagogical practice, can favor the learning of mathematical concepts. according to the ideas of mathematics education. An investigative analysis was carried out on a set of books belonging to the National Book and Didactic Material Program - PNLD, currently adopted in public schools, aiming to identify how the angle concept is treated, if it favors the application of didactic transposition, which aims at transposition of scientific knowledge into school knowledge For the observation of Didactic Transposition Theory and its applicability in the chosen works, we use the concept of angles studied in the thematic unit Geometry because it is a knowledge that favors contextualization for the elaboration of problem situations. To this end, we sought a basis on the National Common Curricular Base -BNCC, regarding the skills and competences that the process of learning mathematics must develop in students. The writing of the research report was based on content analysis, which according to the conception of Laurence Bardin (2011), develops in chronological and systematized, complementary and well-defined phases.

Algebra allows us to find solutions to certain problem situations in our daily lives. Thus, this work that addresses semiotic representation records in algebra teaching, through problem solving, aims to discuss the contributions of semiotic representation records in the ninth grade of elementaryschool in algebra learning, by solving problems. It highlights the importance of the way that the initial concepts of Algebra have been constructed and the need to promote reflections in teachers on the teaching methodology through Problem Solving to achieve relevant results in their classrooms, as well as the development of ability to understand future mathematical concepts. The research has a qualitative nature with intervention, was carried out in a state public school in the city of São Miguel, state of Tocantins, with the aim of investigating the students' learning in the didactic use of the conversion and treatment of records. The study made it possible to verify the students' difficulties in learning algebra and its representations, as well as their difficulties in applying it daily. In addition, algebra is a branch of mathematics intrinsically linked to geometry, as it is necessary in demonstrations and technologies. Thus, it is possible to carry on the reflection on the methodologies used by the teachers, contributing to a creative dialogue, which allows the progress towards the objectives proposed by the teaching of algebra. The data were analyzed by statistical treatment and with the help of Microsoft Excel.

The present work presents relevant details about the numerical sets that go from the set of natural numbers to the complexes, showing historical parts and a dynamic context of each set, substantiating these arguments with the speech of some mathematicians about the numerical sets. The dissertation aims to investigate the organization of numerical sets and their elements, from the set theory, showing their importance in mathematics and its application in Basic Education. The sets have the elements perfectly characterized and, among them, were studied in this research the sets of Natural (N), Integer (Z), Rational (Q), Irrational (I), Real (R) and Complexes (C). Finally, a field research was carried out with students of the third year of high school of a public school in Teresina - Piauí, aiming to verify if the students of the last year of Basic Education present the knowledge of numerical sets considered essential to give continuity learning mathematics without many disabilities; whereas numeric sets are one of the key prerequisites for a good understanding of math contents. The research was conducted by applying a questionnaire to the students. The answers were tabulated and analyzed from the theoretical framework and the results indicate that there are knowledge gaps that may hinder the formative path of the respondents.

The main focus of the work is the Chinese Theorem of Remnants, presented the fundamentals and elementary applications, showing the utilities of the Theorem, prioritizing the application in Basic Education and the theoretical and practical importance for students and teachers who are interested in learning more of Number Theory. To present a better understanding of the theorem Chinese of the Remains are covered preliminary topics of the Whole Numbers, necessary for the construction of Theorem. Diophantine Equations and Divisibility criteria are shown and solved by applications. optimized congruence properties and results. The theorem is used for OBMEP, OBM proof testing and selection processes. The work is a support for teachers and students who use improve their studies
and research on integer numbers and their basic applications.

The purpose of this study was to propose an alternative method of teaching that could facilitate the teaching-learning of the Quadratic Function. The research deals with the application of the quadratic function modeling the phenomena of nature in experiments with students in rocket launching competitions. The research regarding its approach is qualitative in nature because it has the natural environment as a source of data, because it has a concern in the researcher to know how phenomena manifest themselves and to be aware of their role in data collection. The methodology used was the mathematical modeling, because they are considered an active methodology where the student participates directly in the process, bringing everyday situations from the student to the classroom. The question of guiding research of this study was the modeling of the phenomena of nature, the trajectory described by pet bottle rocket facilitates the learning of Quadratic Function? A workshop was held with the purpose of developing techniques, skills and knowledge with the students participating in the research, allowing them to review contents and have motivation to study the mathematical object under study. During the preparation for the launch it was observed a lot of students enthusiasm and great motivation. After the experiment it was observed that the level of understanding of the concept of function by the students had a scientific character.

With the systematization of student incomes in universities through ENEM, many schools seek to work the student's time spent in solving questions. And, why not use the calculation? Do educators, in general, have difficulties in dealing with calculus, and its various applications? With this, the Differential and Integral Calculus, is a very important tool for some resolutions of exercises in the scope of Mathematics and Physics. This work consists in the use of Differential and Integral Calculus to show to the students that it is an optimized tool in some cases and essential for life as a student as a secondary school student or as a university student. We used the federal Institute of Maranhão Santa Ines campus, as the center of the research, in which it was made an explanation of the definition of limits, derived and integral with their respective properties. We believe it is possible to propose improvements on the benefits of inserting the calculation already in high school. It is hoped that this work will stimulate educators and learners, the challenges of teaching in a more meaningful way, and new approaches in the daily classroom.          

This study aimed to contribute to the teaching practice of the mathematics teacher in the classroom through the active methodology: The Inverted Classroom. Using videoconference as a pedagogical tool we seek to apply the use of information and communication technologies (ICTs) in learning in mathematics in Basic Education. We seek to analyze the teacher training public policies for the use of ICTs; to oppose the guidelines provided in the continuing education courses with the teaching practice and to see how the mathematics teacher can organize a teaching practice with the use of the video lesson. We also try to answer the following research question: what are the possibilities of the Basic Education teacher to use the video lesson as a didactic instrument in the organization of the pedagogical practice for the teaching of mathematics? The research has a qualitative approach with intervention, with the use of active descriptive and interpretive methodologies.

The one of the challenges of the basic education math teacher is transmit financial knowledge with the aid of financial mathematics, transforming classroom content into something experienced by the student in the

day by day. This paper proposes to present the financial mathematics not punctually, but transversally with the most common themes of the high school, as the study of the functions and progressions that are inputs

essential in mathematical modeling in the financial area, as suggested by the National Curriculum (BNCC). In addition to this proposal will be exposed as the Financial mathematics contributes to financial literacy for building of the most financially conscious citizen, and for that, was listed ENEM problems with alternative solutions and use of digital technologies. In this learning process financial mathematics is part of the

Financial Education, that is, it alone does not form the student with the ability assertive financial decision-making, but it enables you to have a more critical view on the evolution of money over time and alternatives on

finance problem solving for financial management. To learn more about how financial mathematics is experienced by teacher and student, a research was developed involving the teachers participating in or participating in the PROFMAT program and its students primarily to map the financial math domain of the student.

One of the several challenges of the contemporary educator is to provide a meaningful education to the student and in this sense the methodology used by the teacher is of fundamental importance for the achievement of the objectives. Thus, the present work aims to show the various benefits proposed by the methodology of problem solving through the m and quadratic function. The research still uses the connection between mathematics and physics, as an important factor in understanding some movements, and has this relation as motivation for the student to continue with the study of mathematics. The research was carried out at the state school C. E. Nina Rodrigues in the municipality of Anajatuba-MA with students from the 1st and 3rd year of high school. Through problem solving, research showed how methodology is beneficial to education when it could achieve a variety of objectives such as: connection between mathematics and physics, better interpretation of texts, connecting mathematics to the real world, to motivate the study of mathematics, to associate the content in situations contextualized problems.

Bicudo (1999), Boyer (2012), Eves (2004), Fossa (2001), Maranhão (2019), Lorenzato (2006) and Monteiro and Junior (2001). Methodologically, the research is inserted in a qualitative perspective. The methodological option adopted as a data collection instrument was the application of questionnaires to teachers and students. Regarding the research results, it is understood that teachers and students consider the history of mathematics important for the construction of knowledge, highlighting it as a facilitating element of mathematical learning, because it is through it that it is possible to make a rescue. from the origins of the first ideas of mathematical construction to current mathematics, besides knowing the cultures of the peoples who developed such science and that this are important factors for the construction of citizenship of primary school students, focusing on students from 6th to 9th grade. .

Os indicadores de qualidade do ensino, como o Índice de Desenvolvimento da Educação. Básica (IDEB), por exemplo, mostram que os resultados na disciplina de Matemática, noBrasil, estão abaixo do esperado. Os resultados insatisfatórios, segundo alguns teóricos,estão relacionados com o fato de profissionais da ´área de educação apresentarem a Matemática de forma não contextualizada e com fórmulas e m´métodos mecanizados de resolução de problemas. Por outro lado, tem-se verificado também que o aprendizado dafísica também deixa a desejar sobretudo pela falta de conhecimento sobre como aplicaros fundamentos da Matemática na resolução de problemas físicos. Nesse sentido, pretende-se apresentar uma proposta para que temas específicos de Matemática sejam abordados de modo aplicado e com explicações baseadas na física. Pretende-se fazer com que nossos discentes percebam que ´e necessário, de forma sucinta, conhecer as mais variadas aplicações de equações, função afim, função quadráticas e razões trigonométricas para que possam ter um melhor entendimento de demonstração e aplicação das fórmulas á Física. A ideia principal e mostrar que é possível solucionar questões de Física dos mais variados conteúdos, usando somente os conceitos físicos e os conhecimentos Matemáticos.

Esta investigação teve como objetivo discutir o contexto da formação dos pedagogos para o ensino da matemática nas series do ensino fundamental, bem como pensar as metodologias educacionais e os espaços pedagógicos, considerando as demandas contemporâneas, um percurso que questiona os significados construídos pelo professor pedagogo, enquanto mediador do conhecimento matemático.  O estudo teve uma abordagem  de  natureza qualitativa, com embasamento metodológico da engenharia didática. No quadro teórico analisou-se documentos oficiais, resultados de avaliações em larga escala voltadas para os anos iniciais do ensino fundamental e autores que discorrem sobre a formação matemática do pedagogo no ensino dos anos iniciais. O estudo foi norteado pelas questões de pesquisa: Qual a percepção dos estudantes de pedagogia sobre sua formação, para o exercício da docência da Matemática nos anos iniciais do ensino fundamental? Quais seriam os conhecimentos matemáticos necessários a formação do pedagogo, para ensinar Matemática nos anos iniciais do ensino fundamental? Os Fundamentos Teóricos- Metodológico da Matemática abordados no curso de pedagogia contribuem para uma formação do pedagogo com conhecimentos sólidos voltados para a futura pratica docente? A pesquisa mostrou que: Menos de 30% dos discentes têm plena convicção de estarem aptos a lecionar a disciplina nas séries iniciais; Os discentes de pedagogia não tinham dificuldades de realizarem soma de números naturais de até três algarismos, mas apresentaram certa dificuldade com divisão por números de até dois d´dígitos, e uma dificuldade mais acentuada quando envolvia mais de duas operações no mesmo problema; E que e generalizada nas instituições de ensino superior, responsáveis pelaa  formação  do  profissional  de  pedagogia,  a  disponibilização  de  um  currículo  com pouca ênfase no ensino da Matemática. 

This work aims to present a proposal of teaching equations and quadratic functions through the Olympic sport of archery, in a class of elementary school of a public school in the city of São José de Ribamar, Maranhão. Based on the National Curriculum Parameters, the project will present a sequential lesson plan, and the formal explanation of the subjects will be presented, ending with a contextualized class using a craft bow.

The work presents an analysis of the use of Cryptography in the teaching of Mathematics, with the student becoming more interested in the discipline through the realization of practical activities, developed within a project entitled "Unraveling Secrets", and making use of of some of the best known cryptographic figures associated with mathematical contents that are addressed in primary and secondary education. The research was developed on the main concepts applied in cryptography, relevant historical facts that contributed to the development of cryptography and some cryptographic ciphers used to encrypt and decrypt a message. The method motivates the students in the learning of mathematics and in the deepening of the contents applied in the classroom.

This paper, whose theme is Concrete Materials: a strategy for the teaching of Geometry in School and Space in High School, presents considerations about the teaching of Mathematics in high school, through a brief analysis of the traditional teaching of Mathematics, pointing out the necessity of its readjustment to the current context and highlighting the role of the teacher and his teaching methodologies. It addresses the use of concrete materials, especially in the teaching of Geometry. Data analyzed by the More IDEB Plan are analyzed through the so-called More IDEB Simulations. The stages of the mini-course on Plane and Spatial Geometry are described in the CE Professor Barjonas Lobão, a research school. We discuss the results of the research carried out, whose main objective was to verify the influence of the use of concrete materials as a strategy for
the teaching of Flat and Space Geometry in the first year of high school.

Representa-se aqui uma investigação, que tem como objetivo avaliar as contribuições dos registros de representação semiótica no processo de ensino e aprendizagem da função afim aos alunos do 1ª ano do Ensino Médio da Instituto Federal do Maranhão no Campus Avançado da Cidade de Rosário - Ma. Utilizou-se uma abordagem qualitativa por se caracterizar pela utilização do ambiente natural como fonte direta de coleta de dados e ter o pesquisador como instrumento fundamental para esta coleta, além de utilizar a indução como na análise dos dados. Para realização dos estudos utilizou-se Teoria dos Registros de Representação Semiótica de Raymond Duval. O problema que norteou o estudo foi se os registros de representação semiótica contribuiriam no ensino e aprendizagem da função afim para alunos do primeiro ano do Ensino Médio do IFMA Campus Avançado Rosário. Justifica-se a escolha do tema “função afim”, dentre outros tipos de função matemática estudados no 1º ano do Ensino Médio, por ser esta a primeira a ser trabalhada com os alunos, possibilitam dose observar mais claramente as dificuldades de ensino e aprendizagem deste assunto. Verificou-se na realização deste trabalho que, inicialmente, um número expressivo dos pesquisados não tinham domínio sobre os tratamentos e representações semióticas do objeto matemático estudado, não conseguindo transitar entre as várias formas de representação da função afim, o que levou às intervenções a didáticas na pesquisa para se alcançar os resultados esperados. A pesquisa foi desenvolvida, por meio de aplicação de atividades, junto a alunos de três turmas de ensino técnico integrado da qual o pesquisador foi o professor, num total de vinte alunos participantes efetivos. Foram realizadas duas baterias de atividades, em algumas delas com intervenção, perfazendo um total de quinze itens. Na execução, tomou-se o cuidado de se realizar avaliações diagnósticas e uma consequente intervenção para, a partir da análise destas estabelecer uma sequência didática. Ao fim da pesquisa conclui-se sobre as contribuições dos Registros de Representações Semióticas no ensino e compreensão da função afim