The university extension program is important both for student education, combining theory with practice in academic learning, and for society, which now has access to different products and services that contribute to building citizenship. In this paper, we first present a brief history of the evolution of university extension in universities, as well as the legislation and guidelines that govern its actions. Next, we present the extension project awarded one of the highlights at the XX SEMEX (2023) of the Federal University of São João del-Rei, entitled "Connection: PROFMAT-UFSJ and Basic Education" and its contributions to preparing public school students for the Enem exam. Motivated by this project, we sought to analyze the Enem Mathematics exams from the last five years, classifying their questions by content and checking the frequency with which these contents were covered in this exam. Finally, we chose two oft the main contents most often covered (percentages and functions) and built two didactic sequences using a more dynamic and dialogical teaching approach, using active methodologies. The main aim of creating these teaching sequences is to contribute to the above-mentioned project in preparing the students taking part in its Enem preparation tutoring.

This paper brings the elaboration and application of a teaching proposal in the field of Statistics for students in the first year of High School, using the Project Based Learning methodology, and the LibreOffice Calc software. Thus, we first present the main facts and changes that have happened in basic education since the implantation of the National Curriculum Parameters (PCNs), and the consequences that were reflected in Brazil’s basic education up until the implantation of the New High School. The teaching proposal is performed in three steps, the first one is a conceptual view of descriptive Statistics’ topics, the second one aims to teach the LibreOffice Calc software, and the last one is practical, where students will apply their acquired knowledge and then elaborate and present a handwritten report on the developed projects. As a result of this teaching experience, and based on the performed tasks, we could find that the learning of descriptive Statistics’ concepts was effective in all of the three steps. In conclusion, the students understood the importance of transferring theoretical concepts into practical situations, making learning more significant, strongly contributing to consolidate their understanding of the statistical concepts that were taught.

The Hardy-Littlewood F Conjecture, proposed in 1922, states that certain quadratic functions generate infinitely many prime numbers, and provides an asymptotic relationship for the counting function of prime numbers. The present work exposes Conjecture 41, which states that the function count of primes−41, generated by the 2nd degree polynomial v41(x) = x^2 + 81x + 41^2, obtained through the n-square Zeta, is asymptotically equal to x/(A ln x+B) and verifies that if the conjecture were true, the polynomial would generate infinitely many prime numbers.

The present work presents some considerations about the active methodologies and their modalities, in the teaching of Mathematics in the final years of elementary school. Active methodologies are presented as pedagogical strategies, aiming at a challenging, transformative and meaningful education, in which the student occupies the center of the teaching process as the main agent responsible and committed to the construction of knowledge. The great challenge of teaching Mathematics has been to insert the student as a protagonist in the learning process, in this sense, a proposal is presented to introduce the content of Similarity of Triangles using the active methodologies of the inverted classroom, through a collaboration tool and a problem-based learning.

This work is composed of a bibliographical research of how the pandemic caused by the COVID-19 virus started and the way in which it affected education in Brazil, in particular in the state of Minas Gerais, making a bibliographic survey of the years 2020 and 2021 and pointing out the main resolutions that regulated remote teaching, such as the analysis of results already published on the subject in question. The second part of the work is of an investigative nature, where through the application of a questionnaire it is intended to probe whether mathematics teachers were prepared for this teaching model, what were their difficulties and limitations, whether physical, emotional, financial, cognitive or social. We also tried to find out how they adapted to this new educational system, if something had changed after more than a year working remotely, how and if it was possible to overcome the different obstacles that arose over time. In addition, we asked about the role of state and federal education agencies in the face of these challenges and whether they gave due support to mathematics teachers.

In this work we will present a mathematical model that describes the temporal dynamics of SARS-CoV-2 infection in humans. WANG et al. (2020) elaborate a mathematical model for SARS-CoV-2 infection, where the target cells are type 2 pneumocytes (primary target) and lymphocytes (secondary target). In our model, we added a new variable, Interleukin 6 (IL-6), which is a pro-inflammatory cytokine and plays a key role in the evolution of the inflammatory immune response, the “cytokine storm”, which causes Discomfort Syndrome. Acute Respiratory Syndrome (ARDS). In addition, it is associated with a severe clinical condition of COVID-19. The problem is modeled through a system of nonlinear first order ordinary differential equations, which is numerically solved as an initial value problem. To obtain the parameters involved in the model, we used information on the viral load of the lower respiratory tract of patients who acquired COVID-19 in Germany (WANG et al., 2020) and those available in other literature. It is observed that the solution numerical model of the mathematical model is consistent with the clinical data available, in part, from some patients. The importance of understanding these mechanisms of action of the virus, as well as the action of the immune system, brings us evidence of how to develop treatment strategies to combat the disease COVID-19.

This paper aims to establish a connection between the Insertion on Computational Thinking in elementary school and the teaching of Mathematics and focuses on answering the following question: how can Computational Thinking, through the construction of algorithms/flowcharts and creation of digital systems, contribute to the teaching of Mathematics, enabling the development of skills and abilities provided for the National Curriculum Common Base? For this, a didactic sequence, consisted of seven classes, was conceived and applied in a class of the 6th of elementary school II of a public school of the state school system of the city of Divinópolis in the state of Minas Gerais. On the other hand, interviews were carried out with Mathematics teachers from the public school system on the topic addressed by this dissertation. The didactic sequence proposes to take specific knowledge of Mathematics as well as insert in an introductory way constructions of algorithms and flowcharts, which serve as a basis for the construction and compilation of a computer program involving a mathematical theme. According to the results of the proposed activities, the authors were able to verify that the students were interested in the new mathematical and computational knowledge and did not offer resistance in the assimilation of the contents taught, through which it was possible to answer the question raised assertively. However, through the teachers' answers, it was noted that it is still necessary to narrow the distance between the proposals related to Computational Thinking, which brought the BNCC, and the teaching practice. In this sense, it is noteworthy that, for its implementation in a planned and isonomic way, in which students and teachers can properly appropriate this new knowledge, it is necessary to invest increasingly in teachers training the reformulation of the vocational training curricula and raising awareness of the institutional counterpart.

This dissertation aims to highlight the importance of Financial Mathematics in the basic formation of a student, working necessary skills to make decisions in purchase and sale operations and investment analysis. We seek to show that some skills developed in basic education serve as a theoretical basis for a more investigative vision, which provides the construction of models and problem solving, providing conditions for the approach to Financial Mathematics contents that, generally, are worked only in higher education. The development of the work led us to the study of two of the main mathematical methods used in the “Investment Analysis” (Net Present Value Method - NPV and Internal Rate of Return Method - TIR), providing to the basic education teachers necessary subsidies for initial teaching of this important branch of Financial Mathematics. The work was accomplished through the description and mathematical analysis of each of the two investment analysis techniques, and later study of some applications (worked algebraically and with the HP-12C financial calculator). It is important to stand out that the whole mathematical theory involved in the work is based on capital equivalence where, through the displacement of capital over time, we developed both methods of investment analysis.

The main objective of this work is to reflect on the use of mathematical modeling as a didactic tool. We present it as an alternative active methodology for teaching mathematics in basic education, seeking to place the student as a protagonist in the construction of their knowledge. Through the mathematical interpretation of real problems, we try to support the teaching-learning process. The mathematics teacher is invited to verify how the construction of a mathematical model can be done during his teaching practice, in view of two examples for secondary education: the modeling of mobile phone rates and the modeling of the propagation of COVID-19 cases in the Brazil.

Differential and Integral Calculus is a discipline present in several undergraduate courses, not only in the areas of Exact Sciences. Specific contents of this discipline are applied in several areas of knowledge, providing relevant scientific contributions to society. In Mathematics teacher education courses, this subject is mandatory. Given this fact, we intend to analyze in this work the Differential and Integral Calculus in the formation of the Mathematics teacher. For this, we carried out a study of the official documents that guide the implementation of these courses, as well as works that deal with Calculus in undergraduate courses, in particular, in Mathematics licentiate courses. The Calculus and Professional Masters Program in Mathematics in a National Network (PROFMAT) was also the object of investigation in this work. Through the dissertation list, we selected conclusion papers that deal with topics in this discipline and made a survey of the main characteristics of these papers. Finally, this work proposes didactic material and didactic sequences on Limit, Derivative and Integral, which can support the Mathematics teacher in the elaboration of a teaching project for the last years of basic education. The idea is that this project involves students who wants to enroll in undergraduate courses of exact sciences or other courses that include the Differential and Integral Calculus discipline.

This study verifies the general performance of high school graduates in 2019 from schools in the State of  Minas Gerais in the Exame Nacional do Ensino Médio, the ENEM. Through data provided by the Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira - INEP, descriptive statistics were used considering the following variables: school administrative dependence, gender, race, income, parents' education, grades in order to relate them to the performance of these students according to their socioeconomic profile. Altogether, the grades of 91540 students from private, federal, state and municipal schools and from the Military Police Tiradentes Schools (CTPM) are counted. The data show that, although most students who took the ENEM 2019 and who completed high school in the same year are enrolled in state schools, these institutions had the lowest averages in all areas of knowledge of the test. The average of the grades of private schools, in turn, was superior to all other institutions in all areas and follows a national standard. The investigation shows how socioeconomic variations contribute to a broader framework through which inequalities constitute barriers to improving school performance and to the democratization of education in Brazil.

Only with the emergence of the National Curriculum Parameters in 1997, the contents of Statistics, Probability and Combinatorics were included in the Basic Education curriculum, initially only for the early years of Elementary School, in 1998 for the final years of Education Elementary and in 1999 for High School. However, it is observed that there is still a gap in probabilistic and statistical education, more specifically in the first two grades of high school, which has a direct impact on the results of the National High School Exam (ENEM). This study aimed to quantitatively analyze the issues related to probability and statistics involved in the ENEM Mathematics test and its technologies, from 2009 to 2019, according to the skills and competences approach. A questionnaire was also applied to high school mathematics teachers in order to help them understand how teaching practices have been organized in relation to the teaching of issues associated with Probability, Statistics and Combinatorial Calculus. Throughout the study, it can be understood that it is essential that schools should train basic education students to take this exam, creating new teaching strategies that can favor the development of probability and statistics skills. In view of the results presented in this work, there is a considerable amount of issues of Statistics, Probability in ENEM tests, and with it the importance that such matters are dealt with even more carefully in basic education, especially throughout the high school.

In view of the serious problems faced in the teaching of mathematics and its consequences, there is a need for the search for updating, innovation and the study of procedures aimed at teaching tools. In this scenario, investigations related to new pedagogical practices have conceptualized active methodologies as a viable proposal in the search for better results. Therefore, this study aims to discuss the importance of active methodologies. Therefore, it is essential to discuss the need to update and complement current practices, describe the benefits derived from active practices, identify which factors linked to the methods contribute to the process, carry out a study of actions that are being addressed and finally propose possibilities for implementation in the high school, especially in the subject of mathematics. Thus, a bibliographic research was used as a method of collecting information, using materials developed by scholars in the area. From the analysis of the studies carried out, it appears that the implementation of active practices in the teaching and learning process, contributes positively to the social and professional training of the student, increases the representativeness of the school as a space for training, raises the levels of consolidation of content and promote better working conditions. Such results impose the observation that the adoption of active methodologies can favor the achievement of better results, as well as promoting greater satisfaction for those involved in the educational environment.

This work approaches a perspective for solving linear systems and its applicability in high school, where emphasis is given to the study of the existence and uniqueness of solutions of linear systems as well as analytical and numerical techniques to find solutions, if any, through methods such as: Gaussian elimination, LU factorization, Jacobi method, Gauss-Seidel method. It will also analyze the most common techniques for solving linear systems in high schools. Thus, this work aims to point out the importance of teaching linear systems in high school and to contribute towards making this mathematical content more meaningful to students. The main idea defended in this paper is that when exposed to challenging situations, students feel the need to learn new mathematical techniques and tools, which provide the mastery of skills and competencies that can be applied to everyday situations. The need to learn a new content should come from the students themselves, as soon as they are faced with a situation that challenges and motivates them. Thus, this is a proposal for the teaching of systems of linear equations in which topics contemplated in the Common National Curricular Base (BNCC) of high school are presented as well as complement this subject with other analytical and numerical methods, so that the student has a broader view of the range of methods and problems that can be contemplated. For this, a lesson plan is proposed in which the main theoretical tools are presented, as well as the solution of contextualized problems through different analytical and numerical techniques.

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The aim of this study is to present chess as an effective tool for Mathematics classes, being an educational tool capable of assisting learning. This popular hobby found space between all levels of education and age. Thus, over the last decade, the international `` school chess '' movement emerged.

It is now seen not only as a competitive board game: it is a domain in which the interaction of pieces, movements and rules, with subsets and variants, provides the environment for intricate challenges and problem solving. With this, it can be inserted in the scope of the mathematics class, as a strategy to increase the students involvement.

The aim of this study is to present chess in mathematics classes in the year of 2018 as a pedagogical tool for learning. From there, to demonstrate that children who play improve their abstract thinking, planning and problem-solving skills, as well as overall academic performance. The research methodology is bibliographic through the collection of data in books and articles, as well as field research, when applying problems proposed to a specific group of individuals, and quantitative research when presenting numerical data after the application of field research.

The present research, which focuses on the area of research in Mathematics' teaching, had, as main goal, to show tha the Geometrical Constructions act as a relevant practicalmethodologicol tool for teaching Geometry. In the context, a study was made as a theoretical contribution and, besides that, it was essential to discuss its teaching throughout
the ages until contemporary times grounded on the normative base, which is currently guiding teaching and learning today. According to that, the Common National Curricular Base (BNCC), which is the normative document that defines the learnings that have to be acquired throughout Basic Education, and the carrier of skills of Geometric Constructions
that must be developed, as well as consolidated in the final years of elementar school. Hence, the present investigation is justified for discussing this pertinente and relevant question. Likewise, for the realization of the undertaken goal, it was proposed to produce didactic material, aiming to consultations and, having as target audience, the teachers of
Basic Education in order to deepen their knowledge for teaching such constructions, mainly in classrooms.

Games are part of our cultural context. In the scope of this research, the interest turns to the pedagogical game, more specifically, to the game in the teaching of Mathematics. The research environment is the classroom, the instrument is the game and the investigation arises from the need to understand the cognitive aspects involved in the use of this instrument in mathematical learning. The processes triggered in the construction and / or rescue of concepts and mathematical skills from the pedagogical intervention with games of rules are investigated.

For the theoretical foundation it was based on the historical-cultural perspective based on Vigotski (2009), aiming at a discussion about mathematical literacy and the insertion of digital technologies and other media in Mathematical Education for the development of algebraic thinking.

As results, two categories were obtained that discuss the senses and meanings produced in the development of the student's thought and the mediating role of digital technology and other media in the development of probabilistic thinking.

The presence of incomplete data or censorship in the sample dataset requires the use of specialized statistical techniques to include the information contained in such observations, such as Survival Analysis. The purpose of this study was to evaluate two sets of data containing censuses, one in the area of education and another in health. In the first study, the analysis refers to the time of completion of the Professional Master's Degree in Mathematics from the USFJ in which quantitative surveys to record the completion dates of entering students between the years 2011 and 2016. In the second study, the waiting time until primary surgery in patients with Orofacial Fissure was evaluated, in which quantitative and qualitative registration of dates of birth and primary surgery in addition to variables associated with gestation and the anomaly itself. We performed a descriptive statistical analysis of the results and the Survival Analysis with the application of the non-parametric technique with Kaplan-Meier estimation and Log-Rank test in order to compare the obtained curves. For the data of the Profmat, it was presented the relation of enrolled and disconnected and graphs of numbers of defenses occurred. In addition, statistics of the average completion time were calculated based on the year and the National Qualification Examination in which approval was given, and the event of interest was the "defense of TCC". It was found that 81.76 % did not complete the course at the regular time of 24 months. Disregarding the censors, which correspond to students turned off or evaded, the average time was 798 days. By posting them, this value increases to 1232 days. By the Log-Rank test, when comparing the curves obtained by the analysis of the date of entry into the course and approval in the ENQ with the date of defense of the CBT, the significant difference between the time of conclusion for students with approval in the first application of the ENQ and in the second, being higher for the latter. For health data, percentages of variables associated with gestation were initially presented: age, diagnosis, information on anomaly and type of delivery. In addition, statistics of variables associated with the anomaly were calculated, presenting a table by type of fissure, lactation and hospital. It was concluded that, by disregarding the censors, which correspond to the patients who did not perform the surgery until the end of the research, the mean time was 246.12 days. By posting them, this value increases to 289.91 days. When comparing the survival curves we obtained a significant difference between the time to the primary surgery of patients with fissure of the post-foramen type when compared to the others.

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This work consists of a study on the incidence of road traffic accidents from 2013 to2018 on the BR 265 highway between the junction with BR 040 (Barbacena) and the junctionwith BR 381 (Lavras) , totaling 169km of highway. The number of accidents per highwaysegment was verified and proposals for reducing the number of accidents or the severity of thevictims in the accidents were analysed. What encouraged us to do this work was the fact thatwe could propose real improvements for the preservation of human lives and the reduction inthe severity of injuries of those involved in accidents. This research is qualitative and quantita-tive, using the database of accidents in the section analysed from 2013 to 2018. After severalanalyses it was shown that the duplication of the highway would be a viable way to reduce thenumber of deaths and the severity of accidents. A projection was made in relation to the costsof highway duplication in relation to the benefits it would bring not only in reducing deaths andserious casualties, but also in improving users’ quality of life, such as reduced travel time, eco-nomy fuel consumption and reduction in pollutant emissions. Thus, it has been shown that theduplication of the highway is a viable project and that the investment would be fully returnedto benefits for society over a period of 17 to 22 years.

The present research is an analysis of the possibility of teaching Differential and Integral Calculus concepts in high school. The introduction of these concepts aims to develop a previous knowledge of the content, facilitating the learning in the higher courses, beyond the importance of its applicability in the resolution of several problems A bibliographical survey was carried out on the history of the teaching of calculus in Brazil and the reasons for this content no longer compose the curricular programs of this teaching stage.In addition, activities related to the derived content, which could be used in high school classes, were elaborated.