https://repositorio.ufu.br/handle/123456789/5473 2026-06-16T15:40:31Z https://repositorio.ufu.br/handle/123456789/48747 Title: Jogando e aprendendo matemática: o uso do material dourado no atendimento educacional especializado Abstract: This research aimed to investigate how the use of base-ten blocks (or golden material) can contribute to the teaching of mathematics to students with intellectual disabilities in the 3rd grade of elementary school. It stemmed from a problem experienced by the author of this work while working with students with disabilities as a Special Education teacher. In seeking teaching strategies, possibilities arose for using educational games as a tool in mathematics classes, which motivated this study. The guiding question was: how can the use of base-ten blocks contribute to the mathematical learning process of students with intellectual disabilities in the 3rd grade of elementary school? To this end, it was assumed that the use of concrete and playful resources, when integrated into inclusive pedagogical practices, can favor the understanding of numerical and operational concepts, can increase the active participation of students, and promotes the development of autonomy and logical reasoning. This qualitative and descriptive research was conducted in a municipal public elementary school located in the city of Ituiutaba, in the state of Minas Gerais. Four students with intellectual disabilities from the 3rd grade participated in the development of the game "Never Ten with Golden Material". Data was collected through observations, field diary entries, photographs, and notes on the interactions between the teacher and students during the game's stages. The analysis of the results indicated that the use of golden material contributed to the learning of the concepts of unit, tens, and hundreds, as well as to the understanding of addition and subtraction operations. It was found that the playful activities stimulated interest, concentration, and cooperation among the students, enabling cognitive and social advances, and that the teacher's mediation played a central role in consolidating knowledge, favoring the development of mathematical language and strengthening the self-esteem of the participants. The Educational Product, part of the Professional Master's program, was developed from the game "Never Ten," using Golden Beads (or Base Material) as a learning tool. The proposal aims to contribute to teaching practice by presenting didactic strategies that favor the learning of mathematical concepts through the use of Golden Beads, promoting a more playful, concrete, and accessible approach for students. It concludes that Golden Beads, associated with playfulness and pedagogical intentionality, is an inclusive resource for teaching mathematics in the early years, promoting learning and valuing the potential of each student. 2026-02-26T00:00:00Z https://repositorio.ufu.br/handle/123456789/48576 Title: A fatoração de xⁿ-1 em binômios e trinômios irredutíveis sobre os corpos com 2 e 4 elementos Abstract: Let q be a prime power and Fq the finite field with q elements. The factorization of polynomials over finite fields plays a fundamental role in several areas, such as error-correcting coding theory and cryptography. A particularly important polynomial is xⁿ-1, since, for example, each of its irreducible factors corresponds to a cyclic code. Under certain conditions, the polynomial xⁿ-1 factors exclusively into irreducible binomials and trinomials over Fq. In this case, we say that the pair (n, q) is 3-sparse. The aim of this work is to give a complete classification of the pairs (n, 2) and (n, 4) that are 3-sparse. 2026-02-19T00:00:00Z https://repositorio.ufu.br/handle/123456789/46700 Title: Alguns critérios de caoticidade de operadores em espaços de Fréchet Abstract: In this work, we study some dynamical properties of continuous linear operators on Fréchet spaces, focusing on the concepts of hypercyclicity, chaoticity, and frequent hypercyclicity. We study important conditions and results that characterize hypercyclic operators, chaotic operators, and frequently hypercyclic operators, and we explore the Hypercyclicity Criterion, Kitai Criterion, Gethner–Shapiro Criterion, Chaoticity Criterion, and the Frequent Hypercyclicity Criterion. We study the relationship that these criteria have with other notions of chaos, especially topological transitivity, as well as the notions of mixing and weakly mixing. Furthermore, we present examples, in each one of these cases, to show that such criteria provide sufficient, but not necessary, conditions for determining each of these notions. 2025-07-30T00:00:00Z https://repositorio.ufu.br/handle/123456789/46683 Title: Uma introdução aos polinômios sobre corpos finitos Abstract: In this work, we study topics in finite field theory. Initially, we explore the structure of finite fields, covering from basic properties to representations of their elements, such as polynomial, cyclotomic, and matrix representations. Next, we focus on the study of polynomials over finite fields, highlighting: the order-defined polynomials, linked to the structure of multiplicative groups; the primitive polynomials; and the irreducible polynomials, fundamental for factorization and construction of field extensions. Finally, we examine q-polynomials, which generalize classical polynomial structures. 2025-07-24T00:00:00Z