IME - Trabalhos de Conclusão de Curso

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Fatores associados à presença de triatomíneos em comunidades rurais de Goiás: uma abordagem com modelagem estatística
(Universidade Federal de Goiás, 2025-11-26) Silva, Larissa Carvalho Solino; Baumann, Luis Rodrigo Fernandes; Baumann, Luis Rodrigo Fernandes; Cardial, Marcílio Ramos Pereira; Matta, David Henriques da
Chagas disease remains a significant challenge in rural Brazil, particularly in traditional communities. This study investigated social and housing factors associated with the presence of triatomine bugs in households in Goiás, based on data from the SanRural project, encompassing quilombola communities, settlements, and riverside communities. Variable factors included community type, wall material, age structure of residents, use of water tanks or asbestos, and raising domestic animals. The statistical approach included logistic regression and generalized additive models - logistic regression (GAM-LR). Logistic regression allowed the identification of direct associations between the evaluated factors and infestation; GAM-LR showed non-linear effects related to the age of the head of household and the residents/rooms ratio. The results revealed a higher proportion of infested houses among quilombola communities (14.3%), in addition to the influence of the presence of young children and a positive history for Chagas disease among residents. The models performed well (86.1% accuracy and 97.3% city specification), reinforcing that the risk of infestation is closely related to the social and structural conditions of the dwellings.
Avaliação de testes de hipóteses assintóticos no modelo de regressão Lindley-unitária: um estudo de simulação e aplicação
(Universidade Federal de Goiás, 2025-11-28) Santana, Vinicius Ferreira Amorim; Silva, Tatiane Ferreira do Nascimento Melo da; Silva, Tatiane Ferreira do Nascimento Melo da; Milani, Amanda Buosi Gazon; Vasconcelos, Renata Mendonça Rodrigues
Inference in regression models can be compromised in small or moderate samples, since classical tests such as the likelihood ratio, Wald, score, and gradient tests tend to exhibit size distortions, leading to incorrect statistical decisions. This study aims to evaluate and compare the performance of these four tests, as well as a corrected version of the Wald test with second-order refinements, within the Unit-Lindley regression model, which is suitable for continuous variables restricted to the interval (0,1). For this purpose, a Monte Carlo simulation study was conducted, varying the sample size, the number of model parameters, and the length of the parameter vector under test. The results indicate that the performance of the asymptotic tests deteriorates as model complexity increases, especially in small samples. In general, the traditional Wald test was systematically liberal, increasing the risk of type I errors, whereas the score test showed markedly conservative behavior, implying a loss of statistical power. The corrected version of the Wald test presented significant improvements, but the gradient test stood out for its superior robustness and consistency. It maintained rejection rates very close to nominal levels, even in the most demanding scenarios, and benefits from greater computational simplicity, as it does not require the computation of the information matrix. It is concluded that the gradient test represents the most advisable alternative for practical analyses in this context, offering a combination of accuracy and efficiency.
Transmissão de rumores em redes
(Universidade Federal de Goiás, 2025-11-27) Quintanilha, Elis Regina Venancio; Vargas Junior, Valdivino; Vargas Junior, Valdivino; Silva, Tatiane Ferreira do Nascimento Melo da; Matta, David Henriques da
With the advancement of communication technologies, it has become easy to pass on information, whether true or not. This brings enormous challenges to ensuring that only correct information remains in circulation. This work studies how information spreads using four probabilistic models proposed in this study. More specifically, branching processes are used, which help to understand how a news item can grow or disappear over time. The idea is as follows: each person who receives the information can pass it on to others, and this dynamic follows a random pattern. Several important characteristics of the process are analyzed. For example, the number of people who receive the news from a single individual, the height of the cascade (i.e., how far the information reaches), the total size of the cascade, and the probability of the information ceasing to spread. These models help to identify patterns that can be useful for developing strategies to control the dissemination of false information.
Análise da estabilidade do processo de vacinação no Brasil usando CEP sobre os resíduos ARIMA
(Universidade Federal de Goiás, 2025-11-27) Carvalho, Matheus Henrique de Souza; Vasconcelos, Renata Mendonça Rodrigues; Vasconcelos, Renata Mendonça Rodrigues; Silva, Tatiane Ferreira Nascimento Melo da; Menezes, José Elmo de
This study aimed to analyze the stability of the vaccination coverage process for poliomyelitis and yellow fever in Brazil, from 1994 to 2022, using historical vaccination coverage series. The methodology of Statistical Process Control (SPC), adapted for autocorrelated data, was employed. The statistical diagnosis of the original series confirmed the presence of autocorrelation and the lack of adherence to normality. The series were treated through the adjustment of Autoregressive Integrated Moving Average (ARIMA) models, following the Box–Jenkins methodology. The application of individual control charts and EWMA charts to the residuals indicated that, after the removal of autocorrelation, both vaccines exhibited processes under statistical control, with no points outside the control limits, demonstrating the adequacy of this approach for monitoring vaccination coverage.
Simulação do campeonato brasileiro de 2013 e estimativa de lucros em um sistema de apostas hipotético
(Universidade Federal de Goiás, 2025-11-27) Correia, Letycia Milene Neves; Vargas Junior, Valdivino; Vargas Junior, Valdivino; Saraiva, Marley Apolinário; Feliciano, Joelmir Divino Carlos
The study develops a probabilistic model for the 2013 Brazilian Championship, using exponential smoothing to update the probabilities of each team winning, drawing, or losing. The smoothing parameter h was estimated by comparing the model’s probabilities with those implied by Bet365’s opening odds, resulting in h = 0.9. With the model trained up to the 28th round, one million Monte Carlo simulations were performed to estimate title probabilities, relegation risks, and the teams’ expected final points. Cruzeiro showed approximately a 90% chance of winning the championship, and the average difference between actual and estimated points was 2.7 points. In the second stage, the model was used to simulate the profit of a betting house through inflated probabilities. The results showed that as the inflation rate increases, the ratio between actual and expected profit decreases.
Passeios aleatórios: teoria, propriedades e aplicações
(Universidade Federal de Goiás, 2025-11-28) Campos, Nilo Célio Elias; Vargas Junior, Valdivino; Vargas Junior, Valdivino; Silva, Tallyta Carolyne Martins da; Baumann, Luis Rodrigo Fernandes
The present Undergraduate Thesis focuses on the study of the random walk, a fundamental probabilistic model in the theory of stochastic processes and applied statistics. The study adopts a theoretical approach with illustrative examples, exploring the properties, classifications, and applications of random walks in different contexts, ranging from the simple one-dimensional case to versions with barriers and bidimensional and tridimensional generalizations. Based on an axiomatic construction, the work presents theorems and propositions that formalize the behavior of the process, with emphasis on classic results such as the Law of Large Numbers and the Central Limit Theorem. These theoretical foundations are illustrated through computational simulations carried out in the RStudio environment, which allow for the visualization of trajectory evolution and for understanding the role of randomness and variance in the walker’s behavior over time. The work also presents applications of random walks in gambling problems, queueing processes, and birth–death models, highlighting their practical relevance. From an applied perspective, we emphasize the importance of this topic as an essential tool in statistics, since simulation and graphical visualization enhance the development of probabilistic reasoning and conceptual understanding. We aim to convey the view that the random walk constitutes a scientific model of great value, as it combines mathematical rigor, computational experimentation, and practical applicability, serving as a point of convergence between theory, practice, and statistical training.
Inferência via bootstrap no modelo de regressão gama unitária: desenvolvimento e aplicação do pacote UnitGammaReg em R
(Universidade Federal de Goiás, 2025-11-28) Pereira, Vitor Hugo Floriano; Silva, Tatiane Ferreira Nascimento Melo da; Silva, Tatiane Ferreira Nascimento Melo da; Milani, Amanda Buosi Gazon; Vasconcelos, Renata Mendonça Rodrigues
The unit gamma regression model is an alternative to the beta regression model, which is used for modeling data restricted to the unit interval (0,1). There are several practical situations in which these models can be applied, such as: modeling interest rates; discount rates; the proportion of individuals who survive a given period of time with a certain disease; the incidence rate of respiratory diseases in a given population; proportions of responses in a survey; student pass or fail rates in exams; teams’ win rates in sports, among others. In this study, we use a real dataset referring to the Índice de Desenvolvimento Humano Municipal (IDHM) of Brazilian states in the year 2021, obtained from the Pesquisa Nacional por Amostra de Domicílios Continua (PNAD Continua), to illustrate the applicability of the unit gamma regression model with bootstrap-based inference. We also propose an R package that allows users to implement this methodology and perform hypothesis testing for the model coefficients.
Técnicas de aprendizado de máquina aplicadas na predição da produtividade de soja no estado do Tocantins
(Universidade Federal de Goiás, 2025-11-26) Viotto, Gabriel Senosien; Matta, David Henriques da; Matta, David Henriques da; Vargas Junior, Valdivino; Feliciano, Joelmir Divino Carlos; Campos, Leonardo José Motta
This study applies and compares machine learning techniques for predicting soybean yield in the state of Tocantins, using categorized variables via k-means derived from climate data from the NASA POWER platform and soybean yield data obtained from experiments conducted in several municipalities of Tocantins from 2013 to 2023. Five algorithms were implemented: Random Forest, Decision Tree, XGBoost, Support Vector Machine, and Bagging. The models were trained using yield data from municipalities and evaluated through cross-validation using the metrics RMSE, MAE, and R2. The results demonstrated the superiority of ensemble methods, with Bagging showing the best performance (RMSE = 498.64 kg/ha, MAE = 380.07 kg/ha, R2 = 0.724). XGBoost and Random Forest also achieved very similar results. The variable importance analysis revealed that climatic factors—especially precipitation during the reproductive period and solar radiation during the vegetative period—are crucial determinants of productivity. The study concludes that machine learning techniques, particularly ensemble methods, are promising tools for predicting soybean yield and can support agricultural planning and decision-making in the sector, contributing to reducing the high inherent risk of this activity.
Criação de painel com dados da FOSP: uma abordagem com análise de sobrevivência
(Universidade Federal de Goiás, 2025-11-28) Gonçalves, Igor de Sousa; Milani, Eder Angelo; Milani, Eder Angelo; Santos, Fabiano Fortunato Teixeira dos; Cardial, Marcilio Ramos Pereira
The Fundação Oncocentro de São Paulo publicly provides several datasets related to cancer; however, these datasets are not presented in an easily interpretable format, requiring preprocessing and organization for better understanding. An elegant and intuitive way to display this information is through interactive panels, or dashboards. This study extracted data from FOSP and integrated them into an interactive dashboard to provide users with a clearer and more dynamic visualization of the information. The dashboard was developed using the Shiny package in the RStudio software. The current version contains 3 main tabs: Dashboard, Análise de Sobrevivência and Sobre. In the Dashboard tab, users can select variables such as escolaridade, idade, sexo, UF de residência, categoria de atendimento, radioterapia, quimioterapia, cirurgia e idade mediana, and the software displays descriptive statistics for the chosen variable. In the Análise de Sobrevivência tab, the survival function is estimated using the Kaplan-Meier method, allowing the selection of International Classification of Diseases (ICD) and filtering by variables such as sexo, idade mediana, categoria de atendimento, radioterapia, quimioterapia e cirurgia. Additionally, Cox and Weibull regression models were implemented to assess the impact of covariates on the risk of death and to understand the behavior of the hazard function over time. The Cox model, of semiparametric nature, allows the study of covariate effects without specifying the baseline hazard function, while the Weibull model, of parametric nature, enables explicit modeling of the risk variation over time. Finally, the Sobre tab provides a brief explanation of the software and details regarding the time period used in the analyses.
Ajuste de análise fatorial exploratória com método dos mínimos resíduos a dados de testes neurocognitivos
(Universidade Federal de Goiás, 2025-11-28) Cardoso, Inácio Torres; Silva, Renato Rodrigues; Silva, Renato Rodrigues; Feliciano, Joelmir Divino Carlos; Silva, Tallyta Carolyne Martins da
In this study, an exploratory factor analysis (EFA) was applied using the minimum residuals method (Minres) to data from the NeuroCognitive Performance Test (NCPT), a battery of neurocognitive tests. The central objective of the study was to investigate the applicability of the Minres method as a robust alternative to traditional extraction methods, such as principal components and maximum likelihood. The research used data from the NCPT battery 26, comprising 11 subtests that assess different cognitive processes. The analytical procedure began by verifying the suitability of the data for EFA using the Kaiser-Meyer-Olkin (KMO) index, which indicated good suitability (0.82). The determination of the number of factors to retain was conducted through parallel analysis, which indicated the existence of three factors. The extraction of factor loadings was then performed using the Minres algorithm, followed by an orthogonal varimax rotation to facilitate the interpretation of the factors. The results revealed a three-factor structure. Factor 1 showed a contrast between working memory and fluid intelligence subtests, Factor 2 was predominantly loaded by verbal memory subtests, and Factor 3 was dominated by the arithmetic reasoning subtest. The model’s fit quality was confirmed by the Root Mean Square Error of Approximation, or RMSEA (0.037), and the Tucker-Lewis Index, or TLI (0.969), indices. Despite the successful application of the method, the study has some limitations, such as the low communalities found in some subtests and the possible influence of the type of rotation used. It is concluded that the minimum residuals method proved to be fully applicable and viable for exploratory factor analysis of neurocognitive data.
Inflação de zeros nas notas da redação do ENEM: comparação entre o modelo beta inflacionado em zero e o modelo de barreira
(Universidade Federal de Goiás, 2025-11-25) Lima, João Marcos Ribeiro; Andrade, Ana Carolina do Couto; Andrade, Ana Carolina do Couto; Silva, Tatiane Ferreira do Nascimento Melo da; Tojeiro, Cynthia Arantes Vieira
The essay score of the National High School Exam (ENEM), bounded to the interval [0, 1000], presents a considerable proportion of zero scores, a phenomenon known as zero inflation. This structural characteristic of the data requires the use of specialized statistical models capable of handling the hybrid nature of the distribution, which consists of a point mass at zero and a continuous component. The primary objective of this work is to identify the factors impacting the distribution of essay scores for students from public and private schools. As a secondary objective, of a methodological nature, this study seeks to compare the adequacy and robustness of two modeling strategies: the Zero-Inflated Beta model (BEINF0) and the Hurdle Model. For this purpose, ENEM microdata made available by the Anísio Teixeira National Institute of Educational Studies and Research (INEP) were utilized. The analysis was conducted on two distinct populations: one restricted to Goiânia (2023) and a broader one covering the state of Goiás (2021-2023). The models were implemented within the GAMLSS framework in the R statistical software, where the Hurdle Model was specified with a binary component (Logistic) and a continuous intensity component (modeled with the Box-Cox t distribution). Descriptive analysis results indicate significant disparities in performance and socioeconomic profiles between students from public and private schools. Although both modeling approaches identified objective scores and socioeconomic variables as relevant predictors, diagnostic analysis (such as worm plots and residual statistics) demonstrated that the Hurdle Model, despite remaining inadequacies, is methodologically more robust and conceptually more aligned with the exam's evaluation structure. Both models struggled to capture the shape of the data distribution, although the hurdle approach showed superior performance.
Calibração do modelo de simulação de cultura DSSAT: uma abordagem através do otimizador bayesiano
(Universidade Federal de Goiás, 2025-11-26) Carvalho, Wanessa Bastos de Oliveira; Matta, David Henriques da; Matta, David Henriques da; Silva, Renato Rodrigues; Justino, Ludmilla Ferreira; Rodrigues, Marcio Augusto Ferreira
The present work sought to show that, through the application of the Bayesian Optimization (BO) technique, it was possible to efficiently and computationally calibrate the parameters of a crop simulation model such as DSSAT (Decision Support System for Agrotechnology Transfer), with BO being a statistical and Machine Learning technique that robustly identified DSSAT parameters through optimization. In this study, the calibration was focused on parameters of the phenological submodel CROPGRO-Drybean for the common bean BRS Esplendor cultivar, in order to evaluate and demonstrate the effectiveness of the technique in isolation, keeping all other parameters constant and applying BO only to the phenological parameters of DSSAT. The use of the BO technique was carried out in the R software through the ParBayesianOptimization (PBO) function, which sought to estimate a set of parameters whose objective was to minimize the Objective Function, which, in this study, was given by the MAPE (Mean Absolute Percentage Error). It was an appropriate technique when optimization was computationally expensive and, moreover, it stood out for its intelligent way of selecting candidate points that composed the optimization result, using an Acquisition Function, which was the subject of analysis in this work. The results therefore aimed to show the efficiency of BO-based calibration when compared with manual calibration performed by an agronomic expert and with the separate and simultaneous estimation approaches proposed in the Calibration Protocol for Soil-Crop Models. The results examined the boxplots of the outputs obtained by each methodology in order to identify the efficiency of the calibrations, and, in this way, Bayesian Optimization proved to be an adequate technique for estimating the phenological hyperparameters of the BRS Esplendor cultivar when compared with agronomic protocols and manual calibration, as the results were able to optimize the hyperparameter values by reducing the MAPE (Mean Absolute Percentage Error). This showed that the technique could be expanded to other groups beyond the phenology of common bean.
Comparação de modelos preditivos para campeonatos de futebol: uma análise de seis ligas mundiais (2003-2023)
(Universidade Federal de Goiás, 2025-11-25) Oliveira, Danilo Silva Carvalho de; Vargas Junior, Valdivino; Vargas Junior, Valdivino; Matta, David Henriques da; Piscoya Diaz, Mario Ernesto
This study systematically compares three predictive modeling approaches for football championships: (i) a purely quantitative model based on Poisson distribution, (ii) a purely categorical model based on performance profiles, and (iii) a hybrid model combining both approaches. The analysis was applied to six major world leagues (Brazil, England, Spain, Italy, Germany, and France) over 21 seasons (2003 to 2023), totaling 126 season-championships and 46,503 matches. Using temporal cross-validation with 5 folds, the memory parameter $h$ was optimized independently for each model, league, and season. The results revealed better performance of the Pure Poisson model for the analyzed dataset, which presented the best metrics across all six leagues (global MAE: 3.37 versus 3.43 for categorical models) and higher categorical accuracy (82.5% champion prediction versus 79.4%), empirically validating the adequacy of the Poisson distribution for modeling goals in football within the scope of this research. All combinations showed high performance inertia (h > 0.75), indicating that accumulated history is more informative than recent form. Systematic differences between leagues were identified: Germany more predictable (MAE = 2.96), England less predictable (MAE = 3.71). Hierarchical clustering analysis identified three distinct groups of leagues with similar dynamics, demonstrating that inertia and predictability are partially independent dimensions. As a practical application, although the Pure Poisson model presented superior metrics, the Hybrid model was used to generate predictions for the 2025 Brazilian Championships Series A and B due to its methodological completeness in generating realistic scores while capturing match outcome dynamics (W/D/L). The application indicated a balanced title dispute in Series A between Flamengo (46%) and Palmeiras (43%) and Coritiba's favoritism in Series B (72% title probability), in addition to detailing the 35 possible promotion combinations in the latter.
Análise dos efeitos do ENOS sobre o clima e a produção agrícola no Brasil: um estudo de caso dos estados de Goiás e Rio Grande do Sul
(Universidade Federal de Goiás, 2025-11-26) Santos, Marcos Vinício Cesario dos; Matta, David Henriques da; Matta, David Henriques da; Baumann, Luis Rodrigo Fernandes; Justino, Ludmilla Ferreira; Diaz, Mario Ernesto Piscoya
Understanding the effects of the El Niño-Southern Oscillation (ENSO) is crucial for Brazilian agriculture, given its influence on production risks. This study aimed to evaluate the individual importance of climatic variables and municipalities in model performance, establishing evidence of the phenomenon’s effect on the high-yield class based on SHAP values. Fixed agricultural production cycles were analyzed, covering the period between planting and harvesting, lasting ten months in the state of Rio Grande do Sul and eight months in Goiás, for rice, bean, and soybean crops. Cycles from 1961 to 2019 were grouped according to El Niño, La Niña, and Neutral phases using the functional k-means method. The study focused on the period from 1990 to 2019, totaling 29 agricultural cycles, and tested the hypothesis that the three phases of the phenomenon produce similar effects through Functional Analysis of Variance (FANOVA) at a 5% significance level. This analysis considered the variables of maximum temperature, minimum temperature, and accumulated weekly precipitation. The results showed significant evidence of climatic influence only in Rio Grande do Sul, which motivated the performance of multiple tests to identify which phases differ from each other. The impact of the phenomenon on crop productivity was also evaluated using the Random Forest algorithm, applying yield classification categorized by classical k-means. The main results indicate that in Rio Grande do Sul, the influence of the El Niño-Southern Oscillation on climatic variables is marked, reflecting differences among the analyzed phases. SHAP values showed that municipal factors predominate in model performance, while climatic variables have lesser but still relevant contribution. It is concluded that the phenomenon exerts significant climatic and productive impacts in Rio Grande do Sul and that, despite its complexity, municipal regional aspects play a fundamental role in forecasting agricultural yield. These results contribute to the development of adaptive strategies in response to climate variability associated with the El Niño-Southern Oscillation.
Materiais concretos no ensino fundamental: uma análise teórica em Vygotsky
(Universidade Federal de Goiás, 2025-12-10) Marques, Erick Vinicíus de Freitas; Brito, Leandra Gonçalves Pinheiro de; Santos, Maria Bethânia Sardeiro dos; Castro, Karina Oliveira de; Moraes, Moema Gomes; Santos, Maria Bethânia Sardeiro dos
This study aimed to reflect on the role of concrete materials in the teaching of subtraction in the 3rd year of elementary education, based on Vygotsky’s historical-cultural theory. The research emerged from experiences during Supervised Teaching Practice III, in which the use of different manipulatives—such as student-made counters and base-ten blocks—produced distinct learning outcomes. While the counters supported an intuitive understanding of simple subtraction, the base-ten blocks did not meet expectations regarding the teaching of regrouping, leading to the need to investigate how teacher mediation influences the use of these resources. Methodologically, this is a qualitative, bibliographic, and participant study, grounded in the articulation between theory and practice. The theoretical review encompasses conceptions of concreteness proposed by authors such as Montessori, Piaget, Dienes, Lorenzato, and Soares, highlighting that concreteness is not limited to the materiality of objects but is related to the cognitive meaning constructed by the learner. From a Vygotskian perspective, it was understood that concrete materials become pedagogical instruments only when integrated into activities mediated by language, social interaction, and intentional teaching, enabling the transition from empirical understanding to abstraction. The results indicate that the effectiveness of concrete materials does not depend on their physical structure or pedagogical tradition, but on the quality of the mediation guiding their use. It is concluded that, in order to contribute meaningfully to mathematics learning, concrete materials must be embedded in practices that articulate action, reflection, and meaning-making, fostering the construction of scientific concepts in a contextualized and socially mediated manner.
Introdução a sistemas suaves por partes com duas ou três zonas no plano
(Universidade Federal de Goiás, 2025-12-03) Artuzi, Luís Fernando Pereira; Gonçalves, Luiz Fernando; Gonçalves, Luiz Fernando; Gomes, Alacyr José; Cunha, Gregory Duran
This work had as its objective the introduction to the Qualitative Theory of Differential Equations and Discontinuous Systems. Firstly, contact with the basic definitions and principal theorems of the theory is necessary. Subsequently, the study of piecewise smooth systems begins, in particular, in the search for limit cycles in piecewise linear systems. Traditional techniques of mathematical research were used, consisting of the focused study of the proposed bibliographical references and follow-up meetings with the development of the problems suggested through analyses and discussions of the main definitions and proofs of theorems that encompass the theme, through the study of the article [12], we investigate the existence of limit cycles in piecewise differential systems formed by linear centers and Hamiltonian saddles. Initially, continuous or discontinuous systems divided by a single line are considered, where the non-existence of limit cycles is proven. Next, the study proceeds to continuous and discontinuous systems with three zones, separated by two parallel lines. In this context, it is observed that in the continuous cases there are no limit cycles, contrary to the discontinuous cases, which present at most one limit cycle. In this way, this research plan provided contact and theoretical deepening regarding the content of dynamic systems, in addition to the introduction to the scientific research environment, working on critical study and the capacity for investigation.
A socilização e o conceito de número: relações entre o jogo Mitch and Titch e o cotidiano da sala de aula no 1º ano dos anos iniciais
(Universidade Federal de Goiás, 2025-11-28) Santos, Ana Vitória Alves dos; Nogueira, Raynara Martins; Faria, Elisabeth Cristina de; Faria, Elisabeth Cristina de; Godoy, João Paulo Machado; Santos, Maria Bethânia Sardeiro dos
The use of games in early childhood education allows students to experience the learning process in a playful way and promotes their social integration. Considering the current generation, which is in frequent contact with technology and uses it as part of their daily routine, it is important to investigate how digital games can contribute to learning the concept of numbers. In this context, this research aims to analyze teaching activities and the use of digital games in early childhood education as a pedagogical resource for mathematical learning and for the construction of socialization rules. We developed a qualitative, participatory research study, using field diaries, class recording, and student records as data collection instruments. All stages were initiated only after approval by the Research Ethics Committee and the legal consent of the children and their guardians. The subjects involved are first-year students in the early years of the Center for Teaching and Applied Research in Education. The analysis of the data obtained in the field was conducted based on the categorization process and cross-sectional content analysis. The participants built relationships between the digital game, the concept of numbers, and factors relevant to living well in society. Thus, by questioning the activities developed, it was possible to identify how these relationships emerge and the importance of this teaching resource in the development of mathematical activities. The research was extremely important in valuing the work of teachers and the need for mediation in learning the concept of numbers at this stage of education, as it provides a better understanding of the content and opportunities for socialization among these children.
A evasão dos cursos de licenciatura em Matemática: uma pesquisa bibliográfica sobre os motivos apontados em produções acadêmicas no Brasil no período de 2016 a 2023
(Universidade Federal de Goiás, 2025-12-16) Santos, Alexsander Gomes Pereira dos; Faria, Elisabeth Cristina de; Faria, Elisabeth Cristina de; Moraes, Moema Gomes; Rocha, Luciana Parente
Dropout is defined as the definitive withdrawal of a student from their course before its completion. This study is initially motivated by the relationships established by the author with other students in the on campus Mathematics Teacher Education program. The problem arises due to the high rate of enrollment withdrawals, as evidenced by data from the Analisa UFG Platform (2025), which indicate that between 2014 and 2024, out of 1,03 4 enrolled students, 473 suspended their enrollment and 8 requested transfer. According to the literature on mathematics teacher education programs, factors leading to dropout include the need to work, difficulties in balancing study and work, teacher stud ent relationships, dissatisfaction, among other factors. This is a bibliographic study that uses theses and dissertations from the Brazilian Digital Library of Theses and Dissertations (BDTD) as its source. Eight studies were selected and analyzed as the c orpus of the research based on the following criteria: time frame; titles and abstracts that mentioned dropout factors; and on campus teacher education programs, covering the period from 2014 to 2024, with the aim of answering the question of what the main factors that may lead to dropout in mathematics teacher education programs are, according to research conducted in Brazil. Based on the inclusion and exclusion criteria, eight studies published between 2016 and 2023 were selected, with the objective of id entifying and analyzing the reasons presented in these academic productions from Brazilian institutions. Based on the methodological proposal of Marconi and Lakatos (2003), the selected material was examined through critical reading and note taking. After analyzing the selected studies, the dropout factors discussed in these academic works were identified and grouped into four thematic categories: factors related to the Mathematics Teacher Education program; factors related to difficulties stemming from pri or basic education; factors related to the institution; and personal factors. Grounded in studies by Silva et al. (2021), Cruz (2017), Masola and Allevato (2021), among other authors, it was found that many students drop out of Mathematics Teacher Educatio n programs due to factors such as the specific demands of the course; difficulties generated by content centered pedagogical practices; insufficient basic education; lack of institutional support and welcoming practices by the institution and faculty; the need to work and the inability to dedicate sufficient time to studies; as well as family and personal reasons. It is concluded that dropout is a complex and multifactorial phenomenon arising from both objective and subjective issues, and that students do n ot drop out simply “because they want to”; rather, real conditions of access and retention are required in order to ensure more accessible, fair, and equitable education.
Tendências das pesquisas acadêmicas no Brasil sobre o uso da estratégia da investigação matemática em sala de aula, no ensino fundamental
(Universidade Federal de Goiás, 2025-12-02) Aguiar, Daniel Leão; Gonçalves Júnior, Marcos Antonio; Gonçalves Júnior, Marcos Antonio; Rocha, Luciana Parente; Moraes, Moema Gomes
Mathematics is almost always seen by students as a set of rules, algorithms, and unquestionable formulas, reduced to a school subject focused on the memorization of procedures dictated by the teacher. Currently, mathematics trains students who are excellent at executing procedures but are unable to think mathematically. In contrast, Mathematical Investigation (MI) in the classroom emerges as a methodological approach that places the student as the protagonist in the construction of knowledge, developing their mathematical thinking, contrary to the content-focused and rule-based thinking learned in schools. The general objective of this work was to map, describe, and analyze the characteristics and trends of academic research in Brazil on the use of mathematical investigation in Elementary Education (Ensino Fundamental), published in the Catalog of Theses and Dissertations of the Coordination for the Improvement of Higher Education Personnel (CAPES) during the period of three CAPES evaluation quadrennials (2013-2024). For this purpose, a bibliographic review was conducted on ten dissertations that applied investigative tasks in the classroom. Data analysis was grounded in the theoretical frameworks of Fiorentini (2009) for research modalities, Skovsmose (2000) for investigation scenarios, and Butts (1997) for types of problems. The results indicate a concentration of research in the 7th and 8th years of Elementary Education and a predominance of algebra content. Finally, it was concluded that the research exclusively adopts exploratory or descriptive modalities and that, although the investigation scenarios are diverse, the problems are always structured as open research problems, problem-situations, or application problems, avoiding traditional algorithmic exercises, in order to seek the best application and utilization of what a mathematical investigation activity can extract from the student.
Entre o solo e o gráfico: a horta escolar como espaço de modelagem matemática no ensino de funções para o 9° ano
(Universidade Federal de Goiás, 2025-12-05) Silva, Vinícius Arrais Leite; Propheta, Welber Gonçalves; Lourenço, Kélem Gomes; Lourenço, Kélem Gomes; Santos, Ronaldo Antônio dos; Santos, Maria Bethânia Sardeiro dos
This academic work proposes a pedagogical activity that integrates the study of functions – specifically linear and quadratic functions, as covered in the 9th grade of Brazilian Elementary Education – with Mathematical Modeling, utilizing the school vegetable garden as a contextual framework. This approach is aligned with the directives of the Brazilian National Common Curricular Base (BNCC). As a qualitative, bibliographical, and documentary study, this research examined theoretical references that interconnect Mathematical Modeling, the teaching of functions, and vegetable gardens in educational settings. The investigation sought to comprehend how the vegetable garden environment can benefit the teaching of Mathematics, particularly the concepts of linear and quadratic functions, through activities that connect formal knowledge with students' daily experiences. The theoretical analysis underscored the potential of Mathematical Modeling as a pedagogical strategy to foster meaningful learning, encourage student agency, and integrate different fields of knowledge. Following the framework proposed by Biembengut and Bassanezi, a theoretical-methodological path was developed, outlining the application of Modeling within the specific context of a school vegetable garden, thereby promoting the understanding of dependency relationships between variables. It is recognized, however, that Mathematical Modeling is not confined to a rigid didactic sequence, as its implementation is contingent upon the concrete conditions of each school's reality, student profiles, and available resources. Consequently, rather than presenting a definitive proposal, this study offers a guiding framework for educators interested in incorporating Modeling into the teaching of functions within contextualized environments. Although empirical application was not conducted, the theoretical findings suggest that the integration of Mathematical Modeling, school vegetable gardens, and the BNCC constitutes a promising approach to Mathematics education, with the potential to support future research and pedagogical practices involving other content areas and grade levels, thereby promoving interdisciplinarity, by using Mathematical Modeling, in the school context.

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