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In this dissertation, we will discuss the work of Bautista Vidal, who dedicated his career to the study of biomass energy, with a special focus on his efforts and the implementation of the Pro-Alcohol program. At the end, we will present a comparison between the productivity of sugarcane and corn in ethanol production. This will be done by using concepts such as the rule of three, percentage, proportionality, tables, and graphs, which allows us to integrate the discussion of Brazilian energy autonomy within the context of basic mathematics education.

This work aims to verify the results obtained by the participants in relation to the mathematical problems corresponding to the Mathematics Olympiad exams at Unemat, Barra do Bugres Campus - MT. In this sense, it also aims to observe which skills in the areas of numbers and algebra, as listed in the National Common Curricular Base for Mathematics, were fully developed by the participating students during the exams under analysis, and which are still in the process of development. Initially, a bibliographic research was conducted through the websites of the main mathematics Olympiads, such as the International Mathematical Olympiad (IMO), Brazilian Mathematics Olympiad (OBM), and Brazilian Mathematics Olympiad for Public Schools (OBMEP), as well as the National Common Curricular Base (BNCC), providing relevant information for the research objective. To support the analyses, we relied on the results obtained by students who participated in the High School stage and took the exams in the 2nd and 3rd phases of the competition in the editions of 2017, 2018, 2019, and 2022, analyzing their average performance. It is important to emphasize that all problems were classified by units and skills. The average performance per unit was described considering the three units of the BNCC for high school: Numbers and Algebra, Geometry and Measures, and Probability and Statistics, highlighting the average percentage of correct answers, and subsequently, the skills within the numbers and algebra unit. At the end of the analysis, it was observed that in most of the skills related to the mathematical problems, the average performance of the students fell short of the expected results for this stage of education.

In view of the great expansion of technologies, it is essential that the teacher uses these resources in the teaching and learning process in order to arouse students' attention and interest. The main objective of this study is to use the GeoGebra software to enhance teaching and learning in mathematics, in a meaningful and fun way for the student. It will talk about the application of the software in the teaching of Matrices and their applications, allowing the study of simple geometric transformations (rotations, translations, re ections, enlargements and reductions) that can be worked on in the 2nd year of High School, enabling the exploration of the notion of matrices and its operations. At first, there will be a brief history of the emergence and teaching of matrices and geometric transformations, the importance of using digital resources in the classroom, as well as the guidelines of official documents on such subjects. Then, it will present a synthesis of the works already carried out on the theme, highlighting the diffeerential of this work. Soon after, the mathematical definitions of matrices and geometric transformations necessary for understanding and carrying out the proposed activities. Finally, a presentation of the Geogebra software and its functionalities and some activities to be worked on in the classroom. In addition to this text, an online book was also created with all the constructions suggested in the activities. The end result is an interesting visual material for the application of geometric transformations in the teaching of matrices using the Geogebra software. This proposal, for all the above considerations, can enrich the teaching and learning process and contribute to the development of students' autonomy and creativity, contemplating the studied themes.

This research aims to develop a game-like digital learning object to contribute to the teaching and learning of addition and subtraction operations with whole numbers. In this sense, we approach the concept of digital learning object and its technical and pedagogical characteristics, as well as the properties that characterize the set of whole numbers. It is noteworthy that every digital resource that can be reused for learning is considered a learning object. To achieve the objective used the INTERA methodology which consists of a framework of processes for the development of digital content used for learning. The digital learning object developed in this work is called “Labyrinth of Integers” and is intended for students in the 7th year of elementary school. This object is a game inspired by Pac-Man, where the puppet (Minecraft) aims to catch the fruit that contains a correct answer to the operation with whole numbers, while avoiding the ghosts that appear over time, as if the ghosts touch it the game is over. This type of object awakens internal motivation and, consequently, the active participation of students and habits of persistence in advancing challenges. Thus, the student learns by himself, through interaction with the game, and it is up to the teacher to mediate the process, providing guidance so that the student's attention is not only destined for competition and emphasizing the concepts to be developed.

The general objective of the educational product communicated in this dissertation is to offer a proposal for digital, interactive and customizable material about Round Bodies, through a GeogebraBook, with the purpose of contributing to mathematics teachers. The activities developed include BNCC skills correlated to the theme of this study.

This work presents a differentiated methodological proposal based on meaningful learning, defended by David Ausubel to work skill 23 of the BNCC (Common National Curriculum Base), from the 9th year of elementary school, also contemplating some specific skills, so that the student is able to assimilate and understand mathematical and statistical concepts, through everyday problem situations, in our specific case the discussions will be based on the food management of a fish farmer, using statistics as a tool, so that you can help them, in decision-making and who are able to read and interpret statistical data and results, whether presented in tables or graphs, in which an Excel approach is also made, as a tool for teaching the contents taught, in order to insert the active methodologies in the teaching-learning process. At the end of this work, it is expected that a pedagogical proposal will be built that can help teachers to teach these contents to students.

This work presents an educational proposal that considers the teaching and learning process of algebra, in particular, arithmetic progressions, through a perspective of sensory influence. To this end, we use Geogebra software to create a set of learning objects (applets) that, based on the principle of dynamics, allow us to establish a cognitive structure that can lead to the understanding of algebraic patterns linked to numerical sequences in arithmetic progression. These patterns are expressed as figurative/geometric elements, dynamized by movement and visual elements of didactic persuasion. Digital objects created in Geogebra constitute educational products that are presented as results of this work.