https://repositorio.ufu.br/handle/123456789/19678 2026-09-03T12:15:08Z https://repositorio.ufu.br/handle/123456789/49996 Title: “E agora, cinco?”: uma história virtual do conceito para o ensino da tangente no ensino médio Abstract: This study aims to analyze the potential contributions of an intentional organization of teaching and the development of a pedagogical proposal on the concept of tangent, grounded in the perspective of the Logical-Historical Movement of the Concept and the assumptions of the Guiding Teaching Activity (GTA). It is based on the understanding that mathematics teaching should enable students to access the historical conditions that gave rise to mathematical concepts, fostering the development of theoretical thinking. The research is characterized as qualitative and was developed through the elaboration and implementation of a Learning Triggering Situation (LTS) that addressed historical elements related to the emergence of the concept of tangent. The activity was organized to engage students through a Virtual History of the Concept, designed to highlight the need for the concept of tangent and enable the investigation of its conceptual connections. For the analysis of the empirical material, two analytical axes were established: the understanding of the historical need for the concept of tangent and the identification of its conceptual connections and students’ appropriation of the concept. The results of this research indicate that articulating the study of the Logical-Historical Movement of concepts with the organization of teaching through the Guiding Teaching Activity constitutes a promising approach to teaching trigonometry in the school context, as it enables students to understand the conditions that gave rise to mathematical concepts and fosters an understanding of the conceptual relationships that structure them. 2026-03-20T00:00:00Z https://repositorio.ufu.br/handle/123456789/49994 Title: Construção de bases de Gröbner para ideais polinomiais sobre um corpo K Abstract: This work presents an introduction to the theory of Gröbner bases for polynomial ideals in the ring K[x1,...,xn] over an arbitrary field K. The aim of this work is to develop the main foundations of this theory, establishing the results necessary for the construction and characterization of Gröbner bases. To this end, it adopts a theoretical approach, in which the concepts, definitions, and proofs are developed progressively. Initially, it presents fundamental results on ring theory, monomial orderings, and the division algorithm in several indeterminates, extending to the multivariate case tools previously available only for polynomials in one indeterminate. Next, it characterizes monomial ideals and proves Dickson's Lemma and Hilbert's Basis Theorem, from which the existence of Gröbner bases for every polynomial ideal follows. Subsequently, it establishes Buchberger's Criterion and Buchberger's Algorithm, culminating in the characterization of minimal and reduced Gröbner bases. The results developed make it evident that Gröbner bases provide effective methods for solving problems involving polynomial ideals and can serve as a foundation for the future study of applications of the theory. 2026-08-04T00:00:00Z https://repositorio.ufu.br/handle/123456789/49264 Title: Tecendo histórias: narrativas e marcos legais no cenário da educação matemática inclusiva mineira Abstract: This work seeks to understand how the movement of implementation of Inclusive Education in Brazil has taken place. The research is guided by the following question: what can be said about the movement to implement Inclusive Education in schools, especially in the context of Mathematics Education? To achieve the objective, a study of national and international legal frameworks that underlie Inclusive Education was initially carried out, as well as theoretical references in the area of Mathematics Education that discuss inclusion and diversity in school. The research adopts a qualitative approach, based on the methodology of Oral History, as practiced by the Oral History and Mathematics Education Group (Ghoem). As methodological procedures, interviews were conducted with educators who work or research inclusive practices in the school context. The participants were invited virtually and, after signing the Informed Consent Form, they previously received a set of guiding questions. The interviews took place in person or virtually, were recorded in audio and later submitted to the processes of transcription and textualization, according to the assumptions of Oral History. The analytical movement was developed from the narrative analysis of narratives, articulating the narratives of the participants to the theoretical references and documents analyzed throughout the research. The results indicate that, despite important advances in the legislative field, the effectiveness of Inclusive Education in schools still faces significant challenges. Among the main obstacles identified are the insufficiency of initial and continuing training of teachers to deal with the diversity present in the classrooms, the permanence of structural prejudices in the school environment and the lack of investment in public policies that sustain inclusive pedagogical practices. The narratives also show that the construction of a more inclusive education involves the recognition of the singularities of students, the appreciation of differences and the need for a more sensitive and humanized teaching attitude. Thus, it is concluded that the implementation of Inclusive Education does not occur in a linear way, but constitutes a process in constant construction, marked by tensions, advances and challenges. In this scenario, Mathematics Education can play an important role in promoting pedagogical practices committed to social justice, contributing to the construction of a more equitable and welcoming school. 2026-03-18T00:00:00Z https://repositorio.ufu.br/handle/123456789/49214 Title: Entre arquivos e relatos: o laboratório de ensino de matemática do Instituto de Matemática e Estatística da Universidade Federal de Uberlândia enquanto território vivo de formação Abstract: This work aims to perform a historiographical exercise on a possible movement of constitution of the Mathematics Teaching Laboratory (LEM) of the Institute of Mathematics and Statistics of the Federal University of Uberlândia (IME/UFU). It is based on the understanding that the constitution of a teaching laboratory does not occur in a linear or homogeneous way, but as a historical process marked by collective actions, institutional disputes, educational policies and different conceptions of teacher training. The research is based on the perspective of Oral History, as developed by the Oral History and Mathematics Education Group (GHOEM), and dialogues with historiographical assumptions that understand History as a situated and interpretative narrative. Methodologically, interviews were conducted with professors who participated, at different times, in the trajectory of the LEM, in addition to the analysis of institutional documents, minutes and records located in the UFU Archive of Dead. The interviews were transcribed and textualized, assuming the interpretative character of this process. The analysis of the narratives and documents allowed us to understand that the LEM was constituted as a space in permanent (re)configuration, crossed by different pedagogical conceptions, by moments of institutional strengthening and fragility, and by extension initiatives, initial and continuing training of teachers. It is concluded that the LEM/IME/UFU cannot be understood only as a physical space or storage of materials, but as a formative and political environment, whose history reveals movements of resistance, reinvention and commitment to teacher training in Mathematics. 2026-03-20T00:00:00Z