The present work is a teaching proposal about the theme of Geometric Loci, aimed at Basic Education teachers and developed with the assistance of the software GeoGebra and the online platform GeoGebraBook. Contextualized and interactive, this proposal seeks, through Mathematical Investigation and Dynamic Geometry resources, to explore the theme in question gradually and softly, without losing sight of mathematical rigor, and placing the reader (teacher/student) as an active agent in the learning process. It was divided into two parts: one addressing Elementary Education, composed of basic
geometric loci (circle, perpendicular bisector, angle bisector, pair of parallel lines, and arc capable), as well as the method of geometric loci and the notable points of a triangle (circumcenter, incenter, barycenter, and orthocenter); and the other addressing High School, related to the study of conics (ellipse, hyperbola, and parabola), exploring their respective definitions, elements, eccentricities, as well as construction methods, and also the method of geometric loci. It is worth noting that the work was substantially developed in the field of Synthetic Geometry, where, through the properties of geometric figures and the relationships between their elements, the beauty of Geometry is highlighted.

The present work presents a didactic sequence elaborated and applied in a second year of high school and uses the Newton-Raphson Method to obtain the approximation of roots of polynomial functions of different degrees. As tools to assist in this endeavor, some Digital Technologies in Education were used, through the Geogebra software and Microsoft Excel spreadsheets, as well as their respective applications for the construction of graphs and spreadsheets (GEOGebra and Excel). Thus, it can be seen that the use of Didactic Sequences in mathematics classes, in this work specifically in the study of the roots of polynomial functions and Newton's Method, is an enriching and satisfying teaching possibility. It is also noticed that the use of educational technologies is a strong ally in the resolution of several mathematical problems, enabling studies of contents a little more advanced than those regularly presented in High School, as in the present work.

This dissertation presents a possibility for teaching and learning geometry through the Project-Based Learning (PBL) approach. The study is characterized by research of an applied nature, permeated by a descriptive approach and content analysis, with the adoption of qualitative methods. These methods were employed to investigate the implementation of an activity conducted with 9th-grade students in elementary school, in a public school, during which they developed a project for the creation of a playground in the school’s leisure area, aiming to benefit the entire local community. As they embarked on this mission, students applied their mathematical knowledge, particularly geometric, both those already acquired and those developed during the project’s elaboration process. In addition to the meticulous observation of the entire study, discussion, and production process, evaluative questionnaires were administered to allow students to express their perceptions and experiences throughout the project. These questionnaires were fundamental for data analysis, revealing that PBL is a methodology that can enrich the teaching and learning of geometry, promoting student engagement, collaborative work, and the acquisition of knowledge to deal with everyday issues beyond the school environment.

Mathematics is often feared and stigmatized by students, making the search for more effective strategies to approach it crucial. In this context, the use of games and gamification emerges as a teaching strategy in education, aiming to understand its effectiveness and pedagogical application. It is believed that games have a significant potential to engage and motivate students, providing a more attractive and dynamic learning environment.

In this work we will present the relationship between the decimal representation of a rational number with group 

theory, mainly groups, subgroups, side classes, order of a group and Lagrange theory. 

We will present a teaching proposal relating abstract subjects to the transformation of rational numbers into decimals.

In this work we begin by studying triangles with integer sides whose area and perimeter
are related. We also show that starting from any given rational-sided, right triangle, for
example the (3,4,5)-triangle with area 6, we use Euclidean geometry to show that there
are infinitely many other rational-sided, right triangles of the same area. We show further
that the set of all such triangles of a given area is finitely generated under our geometric
construction. Such areas are known as “congruent numbers” and have a rich history

This work deals with the study of mathematics applied in the investigation at the scene of a traffic accident, aiming at the inclusion of Traffic Education in the curricular components of basic education, in favor of traffic safety for all. The work is divided as follows: the first chapter deals with the importance of safe traffic on our roads and the social role of each individual in this context, the role of traffic forensics, which carries out investigative analyzes of the technical elements found and uses mathematical calculations involving kinematic parameters aiming at the materialization of the proofs, and traffic statistics, which point to the man as the causative agent in most accidents on brazilian roads, which justifies the need for Traffic Education actions. In the second chapter, we work on the mathematical modeling of some types of accidents, specifically those that can be treated with high school physics and mathematics. The third chapter proposes activities to be developed with GeoGebra applications, where it is expected that cognitive development will occur that establishes relationships between the physical-mathematical contents covered, so that students become protagonists of their own learning, by placing themselves in the role of traffic accident experts.

This dissertation aim introduce and anslyze like a pedagogical product that consists of an investigative activity for sixth year studentes of elementary school, associated with the use of etymology, can provide the (re)construction and compremension of angle concept and some your particularities. This work is composed for introduction, four chapters, final considerations and an appendix. In the introduction , are apresented the personal, professional and academic trajectories and the motivations for the choice of theme and how do they connect untill culminsting in the dissertation, as well a sumary of the structure. In the first chapter ais introduce theoretical, pedagogical and mathematical foundation that support the educational product developmant. Then, start a soon discussion about of the concepts of math investigation and investigative activities, your stages and particulaties, allies there a contributions broughts by etymology for the comprehension of terms and concepts matematical. Finishing this chapter, it is made an exposure of matematical content addressed in the educational product. The second chapter is dedicated at educational product description. In the your first part, it is explaned te structure of the investigative activity built, with your stages and objectives. In the second part, are detailed the profiles of the classes in wich the educational product was applied and the context of the application. In the third and last part, it is made a description of how the activity was carried out with the students. The third chapter is dedicated to methodological aspects. The elements of Content Analysis, the data analysis methodology used in the research, are presented, with the adoption of steps according to those proposed by Bardin (1977). The fourth chapter is dedicated at data analysis, treatment, inference and interpretation of results, according to the theoretical foundation and aligned with the research objective. In the fifth and last chapter, the final considerations are presented. After the references, there is an appendix that brings, in full, the structure of the Investigative Activity developed and applied. The data obtained and analyzed made it possible to infer that the Investigative Activities, associated with the etymological approach, provided students with the re(construction) and understanding of the concept of angle and its particularities. Throughout the application of activities, there was a progressive increase in students’ interest and understanding of the mathematical concepts addressed, as they were challenged by the proposed tasks, supported by the teacher’s mediation. Due to its objectives, proposed activities and results obtained, this research, in addition to being able to contribute to the Teaching of Mathematics, also has the potential to

Mathematics is an important area of human knowledge, and although students recognize
its value and the need to learn its concepts and properties, many students think of learning
mathematics as tedious, difficult and often menaingless. One of the reasons that support
these beliefs is related to the fact that the mathematics normally taught in the classroom
is very abstract and has no relationship with everyday life. In order to help students
overcome these difficulties, see the relationship between what they learn in class and its
applications, eliminate negative conceptions and develop pleasure in learning mathematics,
the present work presents a teaching and learning proposal of mathematical content based
on a context in which information and communication technologies are naturally part of
the lives of these students. The proposal uses the SketchUp software and has five activities
produced in the Google Forms search App. Each activity has a theme and a specific
number of exercises that has to de done students in a computer lab. The themes are
related to the basic use of the SketchUp program, orthographic projections, elaborations of
construction projects and reformations of spaces based on models produced in the drawing
app. The exercises include research activities, text production, creation of animations
and 3D models, in addition, they present problem situations whose contexts are aligned
with the activity’s theme. In the field of mathematical knowledge, it is hoped that this
experience will provide students with an opportunity to expand their visuospatial skills
and improve their capacity for logical, mathematical and geometric thinking.

This dissertation aims to present an educational product as a proposal for teaching polygonal functions via teaching-learning-assessment through Problem Solving methodology as pedagogical approach. The mentioned product, which can be applied in High School groups, consists of developing a water bill simulator in a spreadsheet software. This work is composed of an Introduction, two chapters and Final Considerations. In the Introduction, I present my academic trajectory, my motivations for choosing the theme and how they were articulated until they culminated in this dissertation, as well as a summary of its structure. In the first chapter, a literature review about problem conceptions and Problem Solving was done, followed by a brief discussion about new technologies – in particular simulations and the use of electronic spreadsheets – and their importance in the educational context. At the end of this chapter, polygonal functions, examples, propositions and theorems are presented, which can be used to help simulate water bills. The educational product is characterized in the second chapter, in which technical and legal information about the billing system and the tariff structure of water bills in the State of Bahia are displayed, so that we are able to present the proposed activity. The educational product is structured in three stages. The first step of the activity is to understand and discuss general aspects and characteristics of the water bills brought by students. The second part of the activity intends, based on the teaching-learning-assessment through Problem Solving methodology, to prompt students to think about functional relationships associated with the context of the water bills, by seeking to relate the volume of water consumed and the amount paid for each range of consumption to piecewise functions. The third, and last, stage of the activity consists of building a water bill simulator in an electronic spreadsheet program, thus resuming the analyzes carried out in previous activities. In the last chapter of this dissertation, final remarks were made, followed by an appendix containing a brief tutorial on how to use some features of a spreadsheet program.

The current learning scenario in Mathematics in Basic Education evidenced by education indicators such as the National Secondary Education Examination and the Basic Education Assessment System increasingly brings the necessity of a transformation in the way of approach the Math in the classroom. It is important to point out the importance of the teacher's role in this transformation process, adopting pedagogical practices that contribute to the improvement of Mathematics teaching. In this context, manipulable materials can help in the learning process, because they can facilitate the visualization of objects, and contribute to more dynamic, fun and interactive classes, helping students to develop their reasoning and association with everyday objects. This work presents a proposal for a didactic sequence on remarkable quadrilaterals based on the use of folding techniques as a learning tool on Mathematics. The activity starts with a proposal for diagnostic assessment in order to help in the detection of difficulties related to the content, going through the organization of resources, the step-by-step material that can be manipulated with students and ending with a suggestion for learning assessment.  
 

This dissertation features a proposal for the use of animations in the teaching of
equations. We will address relevant facts about its importance for teaching and highlight
two ways to create equation animations, the first through animations in Stop Motion and,
later, through an LDE (Language for Specific Domain) that was developed for the work,
called AnimaTEX. During the research and its application, we observed that animations
can be a mainstay for teachers because they can build materials with di↵erentiated quality
and, mainly, for students who will be an important part in the process, since, in addition
to classes, a priori, more “interesting” by the use of animations, will also be creators of
theirs through the first method informed above

The present study sought to develop a pedagogical model to assist teachers and students, starting from the 6o Year of Elementary School to the 2o Year of High School, capable of placing the student as the protagonist from the creation to the edition and presentation of video lessons which can be shared, related and directed to the most varied themes.The project proposes the effective participation of students using a young and more attractive language for those who perform and those who assist, making use of active teaching methodologies in mathematics classes.

The project seeks, in addition to strengthening the syllabus, raising the student's self-esteem, motivating, socializing, disinhibiting, creating him an agent of his own learning and responsible for the execution of the whole process.

In the 17th century, John Napier developed a method for performing multiplication and division operations using rectangular bars containing inscriptions of numbers, called Napier Bars. In this work, Napier Bars will be presented, including some examples of their operation, and some activities will be proposed that can assist the teaching and learning process of multiplication and division operations in the classroom. In addition, the activity developed in a high school class will be reported, as well as the conclusions about this experience.

We present a proposed solution to problems articulated by the mathematician Josephus in the 1st century. Legend has it that his guerrilla colleagues, preferring suicide to capture, decided, in a circle, to kill every third person remaining in the group. Disagreeing with the attitude of his colleagues, Josef, along with his friend, put himself in a position to survive. In search of an answer of the position taken by him and his friend, we constructed classes with the use of active methodology, for students of High School with the purpose of solving such problem, through investigation, using mathematical concepts such as arithmetic, geometric and notions of recurrence.

aguradando

Simple Machines are basic tools used both to increase or reduce the amplitude of a Forca, and to change the direction of a force or movement. They are basically the basic models that base the mechanical operation of most of the machines used since the beginnings of mankind, both the most complex ones such as cars, cranes and elevators, as simple as bolts, axes, pliers and scissors. All of them have in common a mathematical foundation that justifies their correct functioning.

 In this work we approach the mathematical fundamentals of simple machines, in particular, we discuss the basic mathematical concepts that allow in a general perspective the efficient functioning of these machines, presenting them in an interdisciplinary language that can be used by elementary and middle school teachers.