IME - Trabalhos de Conclusão de Curso

URI Permanente para esta coleçãohttp://200.137.215.59//handle/ri/1343

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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.
Entre o planejar e o fazer: construindo saberes sobre a prática de ensino de matemática em uma turma do terceiro ano dos anos iniciais
(Universidade Federal de Goiás, 2025-12-16) Araújo, Jade Faria de; Baia, Thifany Rodrigues Moreira Feitosa; Faria, Elisabeth Cristina de; Faria, Elisabeth Cristina de; Gonçalves Júnior, Marcos Antônio; Moraes, Moema Gomes; Castro, Karina de Oliveira
This study presents an investigation into the teaching practice of pre-service teacher-researchers, focusing on the movement between lesson planning and its materialization in pedagogical action during mathematical problem-solving classes with third-grade students in the early years of elementary education. The research is justified by the need to understand the relationship between intention and practice, especially in teaching contexts in which classroom heterogeneity poses significant challenges for teachers. The general objective was to analyze how the planned practice was implemented in the classroom. The study was conducted during Supervised Internship IV of the Mathematics Teacher Education program at the Federal University of Goiás, which enabled direct engagement with the investigated situations in the school context. The theoretical framework was grounded in Alarcão (2011) and Schön (2000), who conceive the teacher as a reflective practitioner capable of interpreting and re-signifying their practice, as well as in Ponte (2004), who addresses research on one’s own practice. Adopting a qualitative approach, the study used the narrative perspective of Clandinin and Connelly (2011), and the analysis of the experiences lived by the teacher-researchers was based on Fiorentini and Lorenzato (2006). The theoretical assumptions underlying the work developed with students were based on Polya (1995) and Smole and Muniz (2013) regarding problem solving; Libâneo (2013) on planning; and Nacarato, Mengali, and Passos (2011), who address teaching in early childhood education. The qualitative analysis identified three a priori categories: Category I – Planning: assumptions and intentionalities; Category II – Practice in action: teaching decisions during the lesson; and Category III – Teaching reflections and meanings constructed by the teacher-researchers. Among the main constraints faced were limited time for activities and gaps in planning related to anticipating students’ difficulties. On several occasions, at the beginning of the lesson, the teachers realized that students did not master essential prerequisites for the proposed tasks, which required revisiting content before moving forward. Although necessary, this process compromised the planned time and made the development of activities more challenging. Additionally, challenges related to initial teacher education were encountered, as such training does not sufficiently prepare future teachers to work with students who have not yet mastered elementary knowledge, such as reading, numerical recognition, or quantity comparison. The results revealed discrepancies between what was planned and what was implemented, highlighting the dynamic, uncertain, and adaptive nature of teaching work. Throughout this process, fundamental teaching knowledge was constructed, such as the ability to manage classroom conflicts, diagnose students’ real difficulties, adjust pedagogical mediation to ensure content comprehension, and balance instructional support with the development of student autonomy. This trajectory showed that teaching practice is constituted precisely in this ongoing movement between anticipation and adjustment, between intention and action. It is concluded that, although lesson plans signal powerful intentionalities, their effective implementation depends on pedagogical, formative, and organizational conditions that must be considered at the planning stage.
Acompanhamento pedagógico e mediação: uma narrativa com a matemática no ensino médio à luz da teoria da aprendizagem significativa de Ausubel
(Universidade Federal de Goiás, 2025-12-09) Alves, Isac Augusto Tristão; Silva, Jhone Caldeira; Lima, Aline de Souza; Vaz, Pedro Ítallo; Silva, Jhone Caldeira
This undergraduate thesis investigates the role of pedagogical support in the use of mandatory exercise lists as an instrument for meaningful learning of Basic Mathematics in High School. The research, of qualitative and narrative nature, was carried out in a private educational institution in Goiânia (GO), with a third-year class, during two academic terms in 2025. Grounded in David Ausubel’s Theory of Meaningful Learning (2003) and supported by authors such as Perrenoud (2000), and Libâneo (2013), the study analyzed how teacher mediation and continuous feedback can transform a traditional practice into a formative learning process. Field diary records and data from the seven exercise lists revealed that the teacher’s active presence through guidance, dialogue, and reflective feedback enhanced students’ conceptual understanding, intellectual autonomy, and engagement. The findings indicate that systematic pedagogical monitoring redefines the role of exercise lists, transforming them into tools for reflection and knowledge construction. It is concluded that intentional and dialogical pedagogical mediation is an essential factor for promoting meaningful learning, fostering not only mathematical competence but also critical thinking, responsibility, and the pleasure of learning.
Ações mentais matemáticas na resolução de problemas de limites sob a perspectiva das neurociências cognitivas
(Universidade Federal de Goiás, 2025-12-08) Damasceno, Isabela Batista de Sousa; Alvarenga, Karly Barbosa; Alvarenga, Karly Barbosa; Gonçalves, Dhiego Pereira; Rocha, Luciana Parente
This study aims to investigate the relationship between Mathematical Mental Actions (MMA) and Executive Functions (EF) in the resolution of a Limit problem by students enrolled in the Differential Calculus course of the Mathematics Teacher Education program at the Federal University of Goiás. The study adopts a mixed-methods approach, in line with the framework proposed by Creswell (2014) and is grounded in the Theoretical Model of Mathematical Mental Actions (MTAMM) developed by Alvarenga and Domingos (2020), as well as in Cognitive Neuroscience, specifically Executive Functions (EF). The corpus consists of 41 written solutions produced by students in an assessment task and semi-structured interviews conducted with three of them. Quantitative analysis involved descriptive statistics and the nonparametric Mann–Whitney U test, comparing the number of MMA mobilized by students who solved the problem correctly and those who did not. Qualitative analysis was based on key principles of Content Analysis, as proposed by Bardin (2016), and incorporated elements of Discursive Textual Analysis, following Moraes and Galiazzi (2016), allowing for greater flexibility in examining the cognitive strategies employed by students in their solutions. The results indicate that success in the task is associated with greater coordination among representations and metacognitive monitoring, suggesting that performance in this type of Limit problem is influenced by the integration of conceptual reasoning and executive function regulation. Accordingly, the study proposes the implementation of pedagogical practices that promote multiple representations, reflection on errors, and cognitive self-regulation, with the aim of enhancing the development of MMA and EF in the teaching and learning of Calculus.
Uma narrativa reflexiva de duas futuras professoras sobre a atividade orientadora de ensino e a formação na licenciatura em Matemática
(Universidade Federal de Goiás, 2025-12-12) Pereira, Gabriella Rosa; Moraes, Giovanna Lima Amancio; Cedro, Wellington Lima; Cedro, Wellington Lima; Silva, Jhone Caldeira; Silva, Mayline Regina
This Final Course Project focuses on the initial training process as mathematics teachers. The question that motivated this study was: How can the Teaching-Oriented Activity, as a theoretical-methodological principle, contribute to our training as mathematics teachers? To answer this question, the general objective is to analyze our initial training process as mathematics teachers based on the Teaching-Oriented Activity, and the specific objectives are to critically reflect on the aspects of the Teaching-Oriented Activity that influenced our training and to identify positive and negative aspects of our teaching practice based on the teaching experience carried out during the Supervised Internship. The methodology used is Narrative, as the work is structured in reflective narratives by two future teachers, authors of this study, about learning moments and experiences lived by us throughout the initial training process in the Mathematics Licentiate course. This entire process was marked by the assumptions of Historical-Cultural Theory, the theoretical-methodological principle called Teaching-Oriented Activity, and studies on the logical-historical movement of Algebra, specifically quadratic equations, content taught by both during their Supervised Internship. Evidence of the impacts and influences of these studies and reflections on formative spaces was identified, especially regarding the constitution of teaching identity and their awareness of their social functions. In short, immersing ourselves in the memories of our experiences proved to be an essential process for the completion of the course, as it allowed for reflections, analyses, and findings that impacted our academic, professional, and personal experiences.
Formulação e resolução de problemas: uma alternativa metodológica para o desenvolvimento do pensamento crítico
(Universidade Federal de Goiás, 2025-12-08) Lourenço, Arthur Alexandre Ramos; Lopes, Janice Pereira; Lopes, Janice Pereira; Santos, Maria Bethânia Sardeiro dos; Costa, Maraiza Oliveira
This paper presents the trajectory and results of a bibliographic study whose objective was to identify and analyze academic productions in the context of Mathematics Education that address problem posing and problem solving, and their possible relationships with the development of students’ critical thinking. To this end, open-access institutional repositories were consulted, considering master’s theses published between 2020 and 2025. The study focused on the analysis of three works, selected based on inclusion and exclusion criteria established to delimit the research corpus. Among the analyzed works were: a master’s thesis that investigated problem posing and problem solving related to conscious water consumption at school; another that analyzed the creation of mathematical problems from flyers and advertisements in the teaching of Financial Mathematics; and a third that discussed contextualization in the teaching of Mathematics in a rural school. As a result of the investigation and systematic analysis of these studies, it was possible to map the thematic scenarios that supported the productions, highlighting aspects that indicate certain convergences among the analyzed works, including the presence of elements such as contextualization, the development of problem situations, an emphasis on activities aligned with students’ everyday contexts, as well as the analysis of social practices related to the teaching of Mathematics. Based on the data obtained, both from the individual analysis of each study and from the comparative analysis among them, a systematic overview of characteristics that seem to structure and guide reflections and practices of problem posing and problem solving in the mathematics classroom is presented. Moreover, the results show that the act of posing and solving problems tends to foster meaningful student engagement and to bring the teaching of Mathematics closer to the social aspects of students’ lived experiences, which, consequently, may contribute to the development of their critical thinking when facing situations, both inside and outside school, whose understanding depends on mathematical knowledge.
Role-Playing Game (RPG) no processo de ensino e aprendizagem de Matemática: uma análise de pesquisas acadêmicas produzidas entre os anos de 2020 e 2025
(Universidade Federal de Goiás, 2025-12-11) Dias, Thalles Fernandes; Silva, Thomas Candido Oliveira; Lopes, Janice Pereira; Moraes, Moema Gomes; Faria, Elisabeth Cristina de; Lopes, Janice Pereira
Mathematics has historically been a curricular component marked by learning difficulties among Basic Education students. In this context, it becomes essential to investigate alternative methodologies that contribute to making the teaching and learning process more meaningful and motivating. Games, particularly Role-Playing Games (RPGs), show potential for promoting engagement, collaboration, critical thinking, and problem-solving. Furthermore, it can be observed that games have been explored in the field of mathematics education through the work of Grando (1995, 2000, 2004) and Kishimoto (2010, 2017). Thus, this study aims to investigate how RPGs have been explored in research related to mathematics teaching and learning, identifying the contributions, limitations, and perspectives of this approach. To this end, a literature review was adopted as the methodology, based on the perspectives of Pizzani et al. (2012) and Gil (1999), with searches conducted in the Brazilian Digital Library of Theses and Dissertations (BDTD), considering publications between 2020 and 2025. After filtering and refining the selection criteria, and considering the relevance of the studies found, eight research works were selected and analyzed in depth. The results indicate that the use of RPGs proved to be a positive strategy at different educational levels, promoting motivation, social interaction, development of mathematical skills, and student agency. However, challenges such as the need for adequate pedagogical time, rigorous planning, and teacher proficiency in both mathematical content and game dynamics were highlighted. It is concluded that RPGs constitute a powerful didactic resource for Mathematics teaching, especially when contextualized, well-structured, and accompanied by intentional teacher mediation, emerging as a promising methodology for future research and practices in Mathematics Education.
Modelos de ponto de mudança em dados de vacinação: aplicação ao número de doses aplicadas em Goiânia, Estado de Goiás e Brasil
(Universidade Federal de Goiás, 2025-06-20) Torido, Fernando Nery; Costa, Marta Cristina Colozza Bianchi da; Costa, Marta Cristina Colozza Bianchi da; Vasconcelos, Renata Mendonça Rodrigues; Aquino, Érika Carvalho de
This study presents the application of changepoint models to analyze the number of vaccine doses administered in Goiânia, the state of Goiás, and Brazil, with the aim of identifying significant changes in time series related to immunization campaigns. Changepoints were detected as significant shifts in the behavior of the data over time, allowing the identification of patterns of increase, decrease, or stabilization in the number of doses applied. For this study, public data were used from the National Immunization Program Information System (SIPNI), under the Secretariat of Health and Environmental Surveillance (SVSA) / Ministry of Health (MS), obtained from the website of the Department of Informatics of the Unified Health System (DATASUS), which is part of the Secretariat for Digital Health and Information (SEIDIGI/MS). The data were extracted using the Tabnet tabulation tool, covering the BCG, Hepatitis B, and Polio vaccines, which are highly representative in terms of basic immunization and are part of the country’s national vaccination schedule. Initially, a preliminary analysis of the data was carried out to understand trends and variations. Then, the results were presented through graphs generated using different statistical packages in R software: changepoint, changepoint.np, bcp, and mcp, the latter two being based on Bayesian models. In addition to the statistical analysis, the identified changepoints were historically contextualized and linked to public health initiatives in Brazil, highlighting their impact on vaccination policies over the years 1994 to 2022. This study is highly relevant as it significantly contributes to the understanding of changes in the number of vaccine doses administered across different regions. It also provides a basis for analysis, enhancement of strategies, and improvement of public policies related to collective health.

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