https://repositorio.ufu.br/handle/123456789/19678 Tue, 14 Apr 2026 15:41:03 GMT 2026-04-14T15:41:03Z https://repositorio.ufu.br/handle/123456789/48020 Title: O conceito de mediação em pesquisas no campo da Educação Matemática Abstract: This study was motivated by the question "How has the concept of mediation, from Vygotsky's perspective, contributed to research in Mathematics Education?" and aimed to analyze the contributions of the concept of mediation, from Vygotsky's perspective, to research in Mathematics Education from 2019 to 2023. A qualitative, explanatory-descriptive approach was adopted, and the research is configured as bibliographic, assuming as methodology a systematic literature review, through searches in the CAPES Theses and Dissertations Database from 2019 to 2023. Among the results, we noticed that some works found use the term mediation in their arguments in the lexicographic sense, the one that is equivalent to intervention, and, in general, the term is used in the sense that approaches common sense, which is that of the dictionary. This meaning refers to the word's origin in Latin, mediatio, which refers to the act of intervening or placing oneself between two parties, and is related to the Latin root medius, meaning "in the middle" or "between two." In this study, we do not exclude this meaning but rather propose the perspective of Vygotsky's Historical-Cultural Theory, which expands on it. We hope to contribute to investigations on how the concept of mediation has been used in Mathematics Education research and how it differs from and/or approaches the concept grounded in Historical-Cultural Theory. We also propose reflections and provocations on how the term can contribute to Mathematics Education when treated from Vygotsky's perspective, considering the concept's depth in theory. Wed, 24 Sep 2025 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/48020 2025-09-24T00:00:00Z https://repositorio.ufu.br/handle/123456789/47801 Title: O conceito de mediação em pesquisas no campo da Educação Matemática Abstract: This study was motivated by the question "How has the concept of mediation, from Vygotsky's perspective, contributed to research in Mathematics Education?" and aimed to analyze the contributions of the concept of mediation, from Vygotsky's perspective, to research in Mathematics Education from 2019 to 2023. A qualitative, explanatory-descriptive approach was adopted, and the research is configured as bibliographic, assuming as methodology a systematic literature review, through searches in the CAPES Theses and Dissertations Database from 2019 to 2023. Among the results, we noticed that some works found use the term mediation in their arguments in the lexicographic sense, the one that is equivalent to intervention, and, in general, the term is used in the sense that approaches common sense, which is that of the dictionary. This meaning refers to the word's origin in Latin, mediatio, which refers to the act of intervening or placing oneself between two parties, and is related to the Latin root medius, meaning "in the middle" or "between two." In this study, we do not exclude this meaning but rather propose the perspective of Vygotsky's Historical-Cultural Theory, which expands on it. We hope to contribute to investigations on how the concept of mediation has been used in Mathematics Education research and how it differs from and/or approaches the concept grounded in Historical-Cultural Theory. We also propose reflections and provocations on how the term can contribute to Mathematics Education when treated from Vygotsky's perspective, considering the concept's depth in theory. Wed, 24 Sep 2025 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/47801 2025-09-24T00:00:00Z https://repositorio.ufu.br/handle/123456789/47549 Title: Semigrupos numéricos e equações diofantinas: uma relação entre elementos gerados e quantidade de soluções Abstract: This work presents an introduction to Number Theory from the perspective of Diophantine Equations and, subsequently, to the study of Numerical Semigroups associated with these equations. Initially, we develop fundamental results on Diophantine equations and numerical semigroups, allowing the characterization of some Numerical Semigroups, in particular, those with maximal embedding dimension, with the Arf property, saturated, and irreducible. These results may be relevant in a future attempt to solve the problem of finding the Frobenius number for semigroups generated by three elements and, in particular, to formalize a counting principle for the number of solutions of equations with three variables. Furthermore, an original result will be developed that counts the number of solutions of an equation with two variables, which will be compared with other known results, and its extension to three variables is suggested, optimizing existing algorithms in particular cases. Wed, 17 Sep 2025 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/47549 2025-09-17T00:00:00Z https://repositorio.ufu.br/handle/123456789/47475 Title: Introdução à teoria dos reticulados de banach e operadores regulares Abstract: The work presents a systematic introduction to the Theory of Banach lattices and to the study of Regular Operators defined on these spaces. Initially, the theoretical foundations are developed, focusing on Riesz spaces, Banach lattices, and the fundamental properties that connect the order structure with the normed space structure. The discussion then turns to operator theory, emphasizing positive operators and, in particular, regular ones. The investigation shows how the notion of regular operators is deeply connected to that of order-bounded operators, highlighting the importance of the Riesz–Kantorovich Theorem in establishing conditions of equivalence between these classes. Continuity and decomposition properties are also explored, as well as the construction of the so-called r-norm, which endows the space of regular operators with the structure of a Banach lattice under appropriate conditions. Fri, 19 Sep 2025 00:00:00 GMT https://repositorio.ufu.br/handle/123456789/47475 2025-09-19T00:00:00Z