https://repositorio.ufu.br/handle/123456789/5155 2026-08-22T15:47:59Z 2026-08-22T15:47:59Z https://repositorio.ufu.br/handle/123456789/49625 2026-08-19T06:23:12Z 2026-03-26T00:00:00Z

Title: Fatoração de expressões polinomiais e decomposição em frações parciais Abstract: This dissertation investigates the factorization of polynomials and the decomposition into partial fractions within the context of Basic and Higher Education, articulating algebraic foundations with proposals aimed at teaching practice. The study begins with the extension of number systems, emphasizing the introduction of complex numbers as a natural extension of R, preserving its algebraic properties while enlarging the set in which solutions exist. It is shown that the solution of the quadratic equation ax^2+bx+c = 0, with real coefficients, maintains the same structure expressed by Bhaskara’s formula, the essential difference lying in the numerical set in which the discriminant is interpreted. In C, regardless of the sign of Δ = b^2 − 4ac, the square root of Δ always exists, ensuring the existence of solutions. It is further emphasized that algebraic properties valid in R, such as special products and completing the square, remain valid in C, helping to clarify frequent difficulties both in the factorization process and in solving polynomial equations. Classical methods are presented, including Euclidean Division for polynomials, the Briot-Ruffini algorithm, and the Rational Root Theorem, highlighting that the factorization of a polynomial depends on the coefficient ring. The case of x^2 + 1 in R[x] and C[x] is discussed, showing that in C[x] every polynomial can be factored into linear factors, according to the Fundamental Theorem of Algebra. This fact structurally simplifies the partial fraction decomposition of rational functions with real coefficients when analyzed in the complex setting. As an educational product, a Workbook of Commented Activities is presented, in which these structural observations are explored didactically through examples and proposed activities. The material is intended for high school students, early undergraduate students, and mathematics teachers, contributing to a more structured understanding of Algebra and its articulation with Calculus.

2026-03-26T00:00:00Z https://repositorio.ufu.br/handle/123456789/49389 2026-08-17T18:58:09Z 2026-02-25T00:00:00Z

Title: Modelos de inteligência artificial para predição de indicação e do risco de lesões em atletas de futebol feminino Abstract: Physical training plays a key role in enhancing athletes’ performance in the pursuit of high-level results; however, this context can trigger adverse effects that harm both these professionals and sports organizations. Sports injuries emerge from a complex network of factors, however, their occurrence is strongly associated with inadequate training load volumes. The aim of this work is to predict the indication and risk of injuries in professional female soccer athletes, where the injury indication is a binary value (0 or 1) and the risk is a value between 0 and 1. In this study, 11,612 daily records from athletes of two professional female soccer clubs in Norway were used, collected via the Player Monitoring System (pmSys) application during the 2020 and 2021 seasons. The database used includes variables related to training load, well-being, and injury occurrence. Training load variables were collected using the Rating of Perceived Exertion (RPE) scale, a tool that quantifies exercise intensity based on the athlete’s perception. In the dataset, injuries were recorded on the day they occurred, serving as the model’s output variable. Injury indication prediction models were developed using Decision Tree and Random Forest machine learning methods. The metrics used to evaluate model performance were sensitivity (success rate of positive predictions) and accuracy (success rate of all predictions). Random Forest outperformed Decision Tree, presenting a sensitivity rate of 64.52% and an accuracy rate of 98.71%. To predict injury risk, neuro-fuzzy methods were applied: the Dynamic Evolving Neural Fuzzy Inference System (DENFIS) and the Subtractive Clustering Method with Fuzzy C-Means (SBC/FCM). Each model employs four training and well-being–related input variables to generate a Fuzzy Rule-Based System (FRBS) aimed at predicting the athlete’s injury risk. In the test set, the DENFIS model presented a sensitivity rate of 75% and an accuracy rate of 85.38%, while the SBC/FCM model obtained a sensitivity of 75% and an accuracy of 91.70%. Using k-fold cross-validation with k=5, the DENFIS model achieved higher percentages across the folds in the sensitivity metric. In the injury risk models, to address the imbalance of the “injury” attribute, since its occurrence is generally of low frequency, the Synthetic Minority Over-sampling Technique (SMOTE) was applied to generate synthetic data for the minority class (injury). This study also developed a computational interface using R software that calculates the user’s injury risk based on physical training and well-being data, utilizing the model obtained by DENFIS.

2026-02-25T00:00:00Z https://repositorio.ufu.br/handle/123456789/49264 2026-08-05T06:21:27Z 2026-03-18T00:00:00Z

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 2026-08-01T06:28:09Z 2026-03-20T00:00:00Z

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