Revista de Investigação e Divulgação em Educação Matemática

A produção de vídeos de Matemática por estudantes: reflexões e desafios do Projeto Matflix

Leonardo Corrêa Sabbado — 2025-12-03

This article aims to present the Matflix project, developed under PIBID, and the perceptions of the participating students. Developed in the first semester of 2023 with final-year elementary school classes at a state school in Pelotas/RS, the project integrated mathematics and video production, using digital technologies as a pedagogical strategy. Structured in six stages, Matflix resulted in the creation of 19 videos, following specific quality criteria. Upon completion, students answered a questionnaire with open-ended questions, revealing that 95% had never produced videos before. Their perceptions highlighted the development of technological skills, teamwork, and a new way of understanding mathematics, while also pointing out challenges such as shyness in front of the camera and the complexity of video editing. The project underscores the role of PIBID in promoting innovative practices for mathematics education, aligned with the challenges of the 21st century.

Da sociedade à sala de aula: entre a evolução tecnológica e os desafios educacionais

Vanuza Camargo Durães — 2025-09-20

This article analyzes the historical trajectory of the insertion of technologies in mathematics teaching in Brazil, from the Cold War period to the actually days (1980-2000). It begins with the influence of the Modern Mathematics Movement and international exchanges that occurred even during the Military Dictatorship, such as visits by theorists to the country and projects supported by the MEC. The text highlights programs such as ProInfo, created with the aim of promoting the use of information technology in basic education, in addition to the importance of teacher training focused on the use of these tools. Even so, the results were not always positive, revealing challenges such as technocentrism and semiotic illiteracy, which compromise the understanding of mathematical content mediated by technology. The author argues that the presence of technology should not be restricted to instrumental use but requires critical training that considers the symbolic and cognitive aspects involved in digital learning. Based on authors such as Santaella, Vieira Pinto and Costa e Silva, the article analyzes the uncritical use of technologies and the need to overcome the idea that they alone solve educational problems. Finally, the article proposes a reflection on the urgency of rethinking teaching strategies, considering technological advances, but without disregarding the complexity of education and human development.

Mathematical literacy as a praxis in the transformation of self in education

Milagros Elena Rodriguez — 2025-11-18

We have successfully supported mathematical literacy as a praxis for self-transformation in education; we do so with complex decolonial transmethodologies, forming rhizomes with the complex transparadigm and the transmethod of rhizomatic deconstruction. In reconstructing the transmethod, we have gathered some shoots from the rhizomes we carry and further consubstantiated provocative conceptualizations: Mathematics: enlightenment and provocation of Sapere Aude: potential extracted from the being. Mathematics for awakening, illuminating minds, awakening the most sublime thoughts in hearts—a journey of self-knowledge, acceptance, and personal development. Mathematical literacy, as an ethical and subjectivation practice, is a praxis of the self that relates to autoethics and the self-politics of the self; service to the development of our own complex, grandiose being, in the image of Jesus Christ, with the power to understand and do. Mathematics in the deconstruction and detachment of an oppressed and denigrated self, convinced of its inability to learn deeply. Forming rhizomes with provocative shoots that unite with the expeditious art of poeticizing with mathematics as creation and life. Mathematical literacy as ethics, writing, care, and praxis of oneself, and of our fellow human beings, to demystify injustice toward oneself and mathematics as a science-art-language. As a need to be in one's own feeling in order to function efficiently and understand oneself in one's own constitution. Contributing to a well-grounded mind, to the reform of authentically Morinian thought, instead of a full mind. Mathematics - Language in the being that is intrinsic to the creation of its own biology; in an indescribably complex unity of high Celestial engineering. In the formation of the ethical, complex, decolonial, and problem-thinking citizen who does not remain superficial; he understands the roots of his origins.

A Geometria Analítica para o ensino superior: saberes profissionais em obras de autores brasileiros nas décadas de 1960 e 1970 utilizados na UFJF

Daniel José de Paula — 2025-07-01

This writing presents the results of a professional master's research that investigated the teaching of Analytical Geometry (AG) in higher education through the analysis of AG textbooks published in the 1960s and 1970s that circulated in the context of XXXX. Five works were analyzed to observe how AG teaching is systematized in each one and to identify the knowledge required to teach and for teaching. According to the analyses, we identified the following as indications of knowledge required to teach and for teaching AG in higher education: the use of set theory language, vector language in the plane and space, algebraic treatment, the use of trigonometric concepts, and Euclidean plane and spatial geometry, among others.

Contribuições de oficinas sobre Educação Financeira para Estudantes da Educação de Jovens e Adultos

Lucas Machado Garcia — 2025-04-09

The contemporary world has demanded economic literacy from citizens that is not restricted to knowledge of simple or compound interest, but rather the adoption of healthy and stable financial behavior. Financial Education, as it has direct applicability in everyday situations, can contribute to making quick and coherent decisions, whether in corporate business or in calculating the profitability of a cash or installment purchase. Adopting these assumptions and realizing, empirically, the difficulty of some people in managing their finances and being, consequently, in debt for not using the bank credit system properly, the intervention and research presented in this article have the problem: What is the contribution of a sequence of workshops for the financial education of students in an EJA class? Based on the principles of Andragogy and the Theory of Didactic Situations, the intervention and research were carried out in a municipal public school, which has the Youth and Adult Education - EJA modality. To this end, five workshops were held, one every week, in a class of Total 5, which corresponds to the 8th year of Elementary School. It is considered that the workshops helped students understand that adequate management of monetary resources promotes a more balanced financial life, as the concepts relevant to Financial Education make it possible to identify factors that generally go unnoticed in everyday life, but which have a great impact economic.

O raciocínio proporcional: a 'pedra de topo' na formação de professores dos anos iniciais

Silvia Rocha Falvo — 2025-04-09

This article is the result of an Academic Master’s research of a qualitative and descriptive nature, which aimed to investigate teachers' knowledge of proportional reasoning and the potential of the Teaching-Learning-Assessment Methodology of Mathematics through Problem Solving (MEAAMaRP) in the continuing education of teachers working in the early years of Elementary Education. The central question guiding the research was: “How do teachers engage in an investigation of proportional reasoning using MEAAMaRP, and what does this reveal about their knowledge and abilities?” As part of this study, the article seeks to verify whether these teachers were able to differentiate additive thinking from multiplicative thinking in a problem-solving situation that generated the concepts of ratio and proportion. This work proposes to: gather materials to construct, organize, raise, and build proportional reasoning through research, data collection, and analysis. More than constructing it, the goal is to reflect on it in the context of teacher education. Despite the challenges in distinguishing additive thinking from multiplicative thinking through a problem that generates the concept of proportional reasoning, the teachers engaged with the methodological teaching-learning model in the classroom using MEAAMaRP. They were inspired by the desire to use the problem as a starting point and to challenge their students in this work with Problem Solving.

Gênese documental de uma professora de matemática no contexto de uma formação continuada

Adriana de Oliveira Dias — 2025-04-18

O presente estudo analisa a gênese documental de uma professora de matemática em um contexto de uma formação continuada ocorrida de forma remota, durante a pandemia de COVID-19, utilizando a Abordagem Documental do Didático (ADD) com o objetivo de analisar como as ações ocorridas durante a formação continuada influenciaram sua construção documental. Foi utilizada a metodologia de investigação reflexiva na coleta dos dados durante a formação continuada aplicada com seis professores via plataforma Microsoft Teams, focando no uso de tecnologias como o GeoGebra. A fundamentação teórica baseia-se na ADD, que analisa a interação dos professores com seus recursos didáticos. Os resultados indicam que a professora ampliou seu repertório de recursos e desenvolveu novos esquemas de utilização, evidenciando uma evolução na organização e clareza de suas atividades pedagógicas. Conclui-se que a formação continuada e a adaptação às novas tecnologias foram cruciais para seu desenvolvimento profissional.

A Educação Estatística na BNCC E DCEPA no Ensino Médio: Possibilidades de Ensino envolvendo Projeto de Aprendizagem Estatístico (PAE)

Hermison Bruno Baia Palheta — 2025-04-09

O presente artigo faz parte de um recorte de uma tese de doutorado em andamento que analisa as orientações da Base Nacional Comum Curricular- BNCC e Documento Curricular do Estado do Pará DCEPA para o trabalho com projeto de aprendizagem na Educação Estatística no ensino médio. Este artigo teve como objetivo analisar em que ponto o currículo para a educação estatística no ensino médio está conectado com a metodologia de Projeto de Aprendizagem Estatística (PAE). A metodologia utilizada será de cunho qualitativo baseado numa revisão bibliográfica e documental. As considerações finais revelam que embora a metodologia do PAE apresente desafios aos estudantes e professores da educação básica surgem como uma possibilidade de transformação de práticas pedagógicas inovadoras. Quanto as habilidades analisadas na BNCC e DCEPA, ambas não deixam claro para o trabalho com Projeto de Aprendizagem Estatístico no ensino médio, porém, observamos que elas nos dão pistas e contribuem para o desenvolvimento da estatística em contextos reais a vida do estudante, reafirmando a sua função social na formação do sujeito enquanto cidadão, que necessita estar preparado para atuar na sociedade e compreendê-la em todos os seus aspectos.

Laboratórios, Olimpíadas, Pensamento Computacional: reflexões sobre a juventude entre produções curriculares em Matemática

Filipe Santos Fernandes — 2025-01-30

This text aims to discuss the relationships between the curriculum production in mathematics and the expected and demanded ways of life for and by youth. To achieve this, we consider three practices that we understand as producers of the mathematics curriculum - the Mathematics Teaching Laboratory, the Brazilian Public Schools Mathematics Olympiad, and Computational Thinking - which assume strategic and beneficial roles in the school environment for the academic and past lives of young people, providing them with competencies and skills for social and work-related interaction. We seek, therefore, to discuss how the ideologies and discourses that produce such practices may be associated with the elaboration of a hegemonic and generalist thinking about youth, recognizing certain behaviors, knowledge, attitudes, and aspirations as more valuable, while making others dissident, inadequate, and often dangerous. Finally, we place these practices within a neoliberal educational perspective, in the naming, classification, and hierarchization of young people based on marks that, by characterizing successful or unsuccessful relationships with school mathematical knowledge, become determinants in shaping certain ways of life and in the production of exclusion processes through the curriculum.

Inclusão Escolar e Ensino da Matemática: o que revelam as professoras dos anos iniciais do Ensino Fundamental?

Mariana Araujo Ferreira — 2025-03-05

Neste artigo, expomos uma pesquisa que teve como objetivo investigar as formas de adequação curricular e metodológica na disciplina de Matemática direcionadas a estudantes com Transtorno do Espectro Autista (TEA), propostas por professoras dos primeiros anos do Ensino Fundamental. Mediante uma pesquisa de campo de modelo exploratório, realizamos a coleta de dados por meio de questionários enviados às professoras que atuam com estudantes com Transtorno do Espectro Autista (TEA) nos anos iniciais do Ensino Fundamental. Com os dados da investigação, buscamos analisá-los a partir dos princípios da Teoria Histórico-Cultural (THC). Como resultados identificamos que a formação continuada específica para atuar com os estudantes com TEA é falha, o que para as profissionais dificulta o processo de adequar-se ao currículo e elaborar proposições de ensino para esses alunos. As docentes participantes indicaram como uma possível solução o uso de materiais concretos, jogos, como uma forma de adequação metodológica para o ensino de matemática.

THE ACTION OF IDENTIFYING FAKE NEWS FROM THE PERSPECTIVE OF FUTURE SCIENCE AND MATHEMATICS TEACHERS

Maria Rosângela dos Santos Alves — 2025-04-18

Estudos acerca de habilidade são relevantes para o contexto de ensino e aprendizagem. Dentro dos estudos sobre essa temática, diagnosticar a compreensão inicial acerca de um determinado conhecimento é relevante, pois o uso de estratégias de avaliação formativa e somativa pode ajudar os educadores a monitorar o progresso dos alunos em relação ao seu aprendizado. Diante disso, o presente estudo tem como objetivo caracterizar a compreensão de futuros professores acerca da ação de identificar fake news. O contexto estudado foi o Instituto de Formação de Educadores (IFE), campus da Universidade Federal do Cariri (UFCA), localizado na cidade de Brejo Santo-CE e teve como participantes estudantes de formação inicial do curso de Licenciatura Interdisciplinar em Ciências Naturais e Matemática. Como instrumento de coleta de dados foi utilizado a Prova Pedagógica, os dados foram analisados de acordo com a orientação adotada como referência. Os resultados abordam as compreensões dos participantes, que teve como referência o Esquema da Base Orientadora Completa da Ação (EBOCA) para identificação de fake news. Partindo de uma orientação adequada, visando comparar as aproximações e distanciamentos dos participantes, foi possível identificar, a partir do diagnóstico realizado com os estudantes de graduação que suas respostas se aproximam parcialmente do modelo de orientação adotado como referência. Esse fato revela a importância de abordar o tema no contexto de formação de educadores, visando desempenhar um papel fundamental na educação dos estudantes, capacitando-os para ensinar sobre a importância do pensamento crítico, possibilitando que ele não seja manipulado por terceiros.

THE POTENTIAL OF ROLEPLAYING GAMES IN MATHEMATICS TEACHING

Thiago de Vasconcelos Barros — 2025-04-09

This work presents a study that aims to analyze the use of Roleplaying Games (RPG) as a methodological possibility for teaching and learning Mathematics. To this end, we aimed to provide a systematic mapping of the literature on Brazilian studies—Theses and Dissertations—that propose possibilities for using Roleplaying Games (RPG) in Mathematics education. The methodological approach adopted included the search, selection, and extraction of data from theses and dissertations in Portuguese and English, available on the CAPES and BDTD platforms, covering the period from 2019 to 2023, based on the guidelines proposed by Kitchenham and Charters (2007). From the researched set, 12 studies were selected, showcasing the use of RPG for various purposes, target audiences, methods, content, and research approaches. The results provided a synthesis of the identified studies, highlighting elements such as the chronological distribution of research over the period, the geographical concentration of investigations, the variety of mathematical content incorporated into RPG practices, and the pedagogical benefits of this approach. We conclude by emphasizing the potential of RPG as a pedagogical tool in Mathematics education, for the understanding and appreciation of this approach.

Learning related to the multiplicative field in solving proportional fourth problems in the 6th year of Elementary School: the case of Mariana

Sara Rodrigues Ferraz — 2025-01-30

Understanding elementary arithmetic operations has historically been one of the pillars of school life. In the transition from the initial years to the final years of elementary school, this is generally one of the mathematical skills that students are expected to have built up. However, national assessments show that this expectation has not been realized in most Brazilian public schools. In view of this, based on the Conceptual Fields Theory, a set of tasks on the multiplicative field was designed and developed in a 6th grade class at a public school in Ouro Preto (MG). This article analyzes the process experienced by a student when solving problems involving the proportional fourth. The research, which was qualitative in nature, was carried out over a period of four months, during regular math class times, and focused on the learning of notions associated with the multiplicative field. The data was produced through audio and video recordings of some of the activities carried out, the researcher's field diary, records produced by the student throughout the work and an interview with her. The results show that the student used different procedures throughout the process and that, although her answers do not allow us to specify exactly which strategy she adopted at each moment, mathematical knowledge about the fourth proportional was mobilized. Other learning was also identified (relating to classmates and the teacher, knowing how to listen to classmates and the teacher, constructing and expressing arguments, etc.) which played an important role in the process. The work carried out proved to be a possibility for learning mathematical concepts involved in the multiplicative field, favoring the transition and adaptation of schemes from additive to multiplicative thinking.

Financial Education in Pedagogical Projects of Mathematics Degree courses offered at the Federal Institutes of Education, Science and Technology

Caroline de Melo Ferreira — 2025-01-30

In this article, we objectively map, describe and analyze how the topic of Financial Education appears in the Pedagogical Projects of the Mathematics Degree (LM) Courses (PPC) offered by the Federal Institutes of Education, Science and Technology (IF) in the Southeast and South regions. Initially, we started from a repository published in 2021 by a group of researchers from the Brazilian Society of Mathematics Education who mapped out the courses that were adapted to the National Curricular Guidelines published in 2015 and, at the time, still in force (CNE Resolution /CP 02/2015). Given the recent changes to the until recently considered new guidelines, published between 2019 and 2020, we carried out a search to update the available PPC (in 2024). Therefore, of a qualitative and inventory nature, this research brings together a corpus of 39 FI PPCs, of which we identified 62 curricular components, courses for the discussion of Financial Education (PE) in the initial training of mathematics teachers. From this quantity, we constructed four groupings in order to organize the discussion perspectives of those present, namely: Financial Education, Financial Mathematics, Financial Education & Mathematics and Other Titles; and we also carried out a critical reading of bibliographic materials that support the curricular components. From the final results, we highlight that: (i) although its presence is still timid, the reformulation process provided the expansion of PE dissemination and (ii) there is a sign, still incipient, of reflections regarding this theme in training contexts that involve the field of Pedagogical Practices disciplines and the development of extension curricularization.

Matemática e Arte na Educação Básica: Um olhar interdisciplinar a partir de uma Revisão Sistemática de Literatura

Veronice Meira da Silva — 2025-04-10

Este artigo, que compõe uma tese de doutorado estruturada no formato multipaper, apresenta os resultados de uma Revisão Sistemática da Literatura (RSL), que teve por objetivo mapear e analisar pesquisas de mestrado e doutorado que discutem a utilização da Arte no ensino de Matemática, no âmbito da Educação Básica. Para tanto, utilizou-se como plataforma de buscas, a Biblioteca Digital Brasileira de Teses e Dissertação (BDTD), com o propósito de responder à seguinte questão norteadora: Quais são as características das pesquisas brasileiras que discutem a utilização da Arte no ensino de Matemática, desenvolvidas no âmbito da Educação Básica? Para isso, seguimos os passos descritos por Sampaio e Mancini (2007) para a produção de uma RSL, e nos apoiamos em Bardin (1977) para apresentação e tratamento dos dados, sob a luz da Análise de Conteúdo. Ao todo, analisamos 13 pesquisas, sendo 10 dissertações e 3 teses, as quais foram selecionadas mediante protocolo de pesquisa construído previamente, utilizando como descritores os termos “ENSINO DE MATEMÁTICA” AND “ARTE” e aplicando critérios de inclusão e exclusão. Suas conclusões nos revelam que, de modo geral, se originaram de uma insatisfação pela forma como a Matemática normalmente é ensinada, de forma mecanizada, e como a disciplina é recebida pelos estudantes, quase sempre com desmotivação. A partir desse ponto, os pesquisadores se dispuseram a trabalhar com a Matemática de forma mais contextualizada, descolando o ensino da disciplina de uma prática memorística e atrelando-o às conexões com a Arte. Verificamos uma estreita relação entre as Artes Visuais e a Geometria, considerando a predominância destas duas unidades temáticas no universo pesquisado. A partir do panorama esboçado com esta RSL, seguiremos para o delineamento da nossa pesquisa, que se empenha em interpretar as representações de signos presentes em produções artísticas de estudantes e professores da Educação Básica, com foco no entrelaçamento do ideal artístico com conceitos matemáticos.

Abordando a geometria presente na brincadeira “Pular elástico”

Thayane Camile dos Santos — 2025-09-21

Este artigo tem como objetivos apresentar o material didático “Pular elástico: brincando com a geometria”, desenvolvido pelo projeto de extensão “Sem mais nem menos nas escolas” da Universidade Federal de Alagoas (Ufal), e descrever os resultados de suas aplicações. O material foi criado para revisar conceitos geométricos e minimizar dificuldades no aprendizado de figuras geométricas, usando a brincadeira “Pular elástico”. As aplicações do material ocorreram em turmas do 7º ano do Ensino Fundamental e da 2ª série do Ensino Médio, de duas escolas da rede pública de Maceió, Alagoas. Ao todo, participaram 174 estudantes, organizados em 58 grupos. Eles receberam o elástico e a atividade impressa, conheceram um pouco sobre as possíveis origens da brincadeira, compreenderam as regras e os níveis da brincadeira e, após brincar, responderam a um questionário. Apesar dos desafios encontrados nos resultados em relação à identificação de figuras geométricas, a atividade proporcionou momentos de interação e engajamento, ressaltando a importância de aprofundar o estudo dessas formas para uma melhor compreensão de suas propriedades e aplicações.

Ethnomathematics encounters with a Postgraduate class

Saulo Macedo de Oliveira — 2025-06-11

The aim of this paper is to present a report on a class taught by master's students in the subject Teaching Work and Internship: Theory and Practice, of the Postgraduate Program in Education at the State University of Montes Claros, highlighting the encounter between Ethnomathematics and researchers in training. To this end, the methodology is based on observations, discussions and reflections generated through the class and the practice carried out in the classroom. We held a mock lesson with 32 students, introducing Ethnomathematics and then practicing using Mancala. This led to fruitful discussions, questions were raised and the feedback from the participants was positive. The main results show that the game provides opportunities to develop different cognitive skills, especially counting, numerical sequences, symmetry, logical reasoning and basic operations. We conclude that the experience of providing a dynamic and contextualized lesson allowed us to experience a moment of knowledge exchange, contributing to our training process, highlighting the importance of different methodological strategies in the teaching of mathematics, not just prioritizing formalized teaching.

Modelagem Matemática e Novo Ensino Médio: entrelace de diferentes papéis em uma mesma pesquisa

Régis Forner — 2025-02-27

My objective with this experience report is to present my perceptions regarding the possibilities of implementing Mathematical Modeling in classes of the formative itineraries of the exact sciences area in the context of the New High School in the state of São Paulo, taking as a bias the simultaneous execution of three roles, namely, of the Mathematics teacher/researcher in Mathematics Education and of the Teaching Supervisor. To this end, I make some considerations regarding the themes involved based on my experience and how the convergences occurred during my professional and academic career. At the end, I present documents sent to the funding agency in which they state what was expected of my participation in the project and what ended up being accomplished. In this movement, I present some complaints and announcements that occurred while performing both roles. I understand that this reflection is necessary to collaborate in research in Mathematical Modeling, to question the way in which public policies enter schools and how research and supervisory action can collaborate so that these policies can be rethought and proposed according to the reality of public schools.

Editorial

Reginaldo Fernando Carneiro — 2025-09-12

Editorial

As compreensões de licenciandos em Pedagogia sobre o uso do EAMvRP para o ensino da geometria

Érika Janine Maia-Afonso — 2025-09-12

Este artigo tem como objetivo analisar as compreensões de licenciandos em Pedagogia sobre o Ensino-Aprendizagem da Matemática via Resolução de Problemas (EAMvRP) para ensinar geometria nos Anos Iniciais do Ensino Fundamental. A pesquisa, de abordagem qualitativa, foi realizada com 27 licenciandos de uma universidade pública do interior do Paraná, participantes de uma formação docente dentro da disciplina de Metodologia do Ensino da Matemática II. Durante a formação, aconteceram discussões na direção teórico-prática referente à literatura sobre a Resolução de Problemas no ensino-aprendizagem da matemática nos Anos Iniciais e, de modo específico, no ensino-aprendizagem da geometria. A coleta de dados ocorreu por meio de questionários e a análise foi realizada com base na Análise de Conteúdo. Os resultados revelaram que os futuros pedagogos compreendem que o EAMvRP contribui para, dentre outros aspectos, dar significado para a matemática, contextualizar o ensino e tornar o aluno agente principal no processo de construção do seu conhecimento. Além disso, percebem a importância do uso dos conhecimentos prévios dos alunos e do trabalho em equipe. Em contrapartida, no que tange a elaboração e implementação de propostas de ensino nos Anos Iniciais, os licenciandos demonstraram incertezas direcionadas à demanda do tempo necessário tanto para o planejamento da proposta quanto para a sua implementação em sala de aula, dificuldades para realizar a previsão de estratégias para resolver o problema, e preocupação em relação as dificuldades dos alunos da Educação Básica para resolverem problemas. Concluímos que os encontros formativos possibilitaram momentos de reflexões atrelados a articulação entre teoria e uma possível prática de sala de aula, o que contribuiu para que fosse gerado um espaço de formação que favoreceu a compreensão dos conhecimentos do conteúdo (da geometria) e dos conhecimentos pedagógicos (uso da Resolução de Problemas para ensinar matemática) dos futuros pedagogos.

Difficulties of 6th Grade Students in the Stages of the Problem-Solving Process Involving GCD

Flavia Hisayo Ribeiro Matsuo — 2025-09-12

Este trabalho trata-se de um recorte da dissertação da primeira autora, que aborda o processo de resolução de problemas e o conteúdo de Máximo Divisor Comum (MDC) no 6° ano do Ensino Fundamental, cujo objetivo é analisar as dificuldades desses alunos na resolução de um problema que envolve o MDC. De natureza qualitativa, nosso estudo envolveu a implementação de uma situação de Matemática com 30 alunos de uma escola pública no Paraná. Os resultados mostraram que as dificuldades ocorreram na compreensão da linguagem, dos termos matemáticos, em elaborar um plano de solução adequado e cometeram erros na execução das operações aritméticas de multiplicação e divisão. Apesar disso, conseguiram identificar corretamente a natureza do problema e demonstraram a tendência de apresentar respostas completas, utilizando frases para expressar suas conclusões.

Dinheiro em Discussão: Implementação da Educação Financeira através de Resolução de Problemas

Juliana Bueno Gonçalves — 2025-09-12

This paper presents the implementation of an Educational Product that proposes a teaching-learning-assessment methodology for Financial Education through Problem Solving, originally developed by researchers in the field. The application took place in a 7th-grade class at a public school in the state of Paraná, using as a starting point the generating problem titled “Community Exchanges.” The proposal encourages reflection on the limits of bartering and the need to create a monetary system, providing a learning environment in which students collaboratively construct knowledge. The teacher plays a central role in this approach, acting as a mediator throughout all stages of the methodology, fostering student autonomy and content formalization. The results reflect student engagement and an expanded understanding of the social role of money.

Teaching-Learning-Assessment Through Problem Solving: An Interdisciplinary Report on the Law of Cosines and Thermodynamics in High School

Tatielen Demarchi — 2025-09-12

This research presents a didactic-pedagogical experience report based on the Teaching-Learning-Assessment Methodology of Mathematics through Problem Solving (MEAAMaRP), as proposed by Onuchic and Allevato (2021). The activity was carried out in an interdisciplinary manner within the subjects of Mathematics and Physics, involving students from the 1st and 2nd years of Brazilian high school. Using formative assessment as the methodological axis, the guiding problem “Sailing in the open sea!” was proposed, addressing concepts such as the Law of Cosines and isothermal transformations. Students, organized in teams, were encouraged to explore and discuss strategies to solve the situation, promoting student protagonism and meaningful learning. The results of the experience show that MEAAMaRP, when combined with interdisciplinary practices, promotes not only conceptual understanding but also increases students' interest and enhances assessment practices. The analysis highlights that moments of mediation, active listening, and systematization supported the collective construction of knowledge, contributing to the integration of teaching, learning, and assessment in a collaborative and reflective environment.

Estimativa de Quantidade de Doces: uma experiência didática baseada na metodologia de Resolução de Problemas de Pólya

Cíntia Cristiane de Andrade — 2025-09-12

This work reports a didactic experience developed in the Problem Solving discipline, in the Mathematics course at a public university in the state of Paraná, using the methodology proposed by George Pólya. The activity was carried out with the problem question “How much candy is in the vase?”, in which three groups of students were challenged to estimate the quantity of candy in transparent glass vases without removing them for direct counting. The dynamics encouraged the use of mathematical techniques and the application of Pólya's problem-solving steps. The report includes the steps of the activity, the strategies followed by the students and reflections on the results obtained. It is concluded that the experience contributed to the students' teaching and learning process, in addition to stimulating the development of mathematical and collaborative work skills.

O ensino através da resolução de problemas como contexto formativo para futuros professores de Matemática: narrativas de vulnerabilidade

Paulo Henrique Rodrigues — 2025-09-12

The objective of this article is to discuss narratives of vulnerability of prospective Mathematics teachers produced in a formative context characterized by a practice based on Teaching Through Problem Solving. To this end, narratives of vulnerability produced by prospective Mathematics teachers, from the 3rd year of a Mathematics Licentiate degree course at a public university in Paraná, were analyzed after their participation in a classroom practice characterized by Teaching Through Problem Solving. As a result, we identified potentialities for prospective teachers, related to the formative context with these characteristics, associated with self-esteem, happiness, tranquility, and reflection.

O Ensino de Paridade na via Resolução de Problemas Hands-on: Passeio do Cavalo no Tabuleiro de Xadrez

Luiz Otavio Rodrigues Mendes — 2025-09-12

This research aimed to discuss, through an experience report, Problem Solving combined with Practice, based on the problem entitled Knight's walk on the chessboard, with a focus on teaching parity. Thirty-six students from the 8th and 9th grades of Elementary School participated, working in groups using a chessboard (5x5) and a knight piece from the game itself. The data collected from the field diary were analyzed qualitatively. The activity was conducted with teacher mediation, without ready-made answers, encouraging investigation, the formulation of hypotheses and collaborative work. The main results indicate that the proposal promoted engagement, appreciation of prior knowledge and significant construction of new concepts. The reduced version of the chessboard allowed greater autonomy in exploring the knight's path, while the secondary problems favored the contextualized understanding of parity. In this sense, Problem Solving combined with Practice reveals itself as an interesting path for new research.

Counting Principles through Problem Solving with Prospective Mathematics Teachers

Tallys Yuri de Almeida Kanno — 2025-09-12

The objective of this paper is to present the report of an experience involving the Addition and Multiplication Principles of Counting, through Problem Solving, with Mathematics undergraduate students. Problem Solving, from the perspective in which problems are considered as starting points for teaching and learning Mathematics, was adopted in a training action, developed by the first author, under the guidance of the second author and supervision of the third author, to develop the aforementioned contents in a Mathematics Teaching Practice subject from a Mathematics Teaching degree program of a public university in the state of Paraná. The prospective teachers were able to experience an approach to mathematical content that converges both the recommendations of official curricular documents regarding the work with this content that they are expected to develop with their students, as well as national curricular guidelines for the preservice teacher education in the methodological aspect of their future practice in the classroom.

Introducing Counting Concepts through Problem Solving:

Benildo Virginio de Souza — 2025-09-12

The Fundamental Principle of Counting (FPC) is an essential concept in Discrete Mathematics, with broad applications in everyday life — from organizing menu combinations and arranging clothing to calculating statistical probabilities. However, many students encounter difficulties in understanding this principle, which can impact their performance in more advanced subjects. Thus, this experience report aims to discuss the initial potential for constructing the FPC concept through the Problem-Solving Methodology, going beyond the mere mechanical and uncritical application of algorithms. To achieve this goal, a qualitative, participatory research approach was adopted, developed with a class of 32 8th-grade students at a public elementary school in Brejo da Madre de Deus, Pernambuco, Brazil. Data analysis focused on the solutions provided to a generating problem involving the creation of name tags with specific restrictions regarding numbers and letters. The results revealed a variety of strategies, ranging from systematic enumeration to intuitive generalization of the FPC, as well as difficulties in communicating reasoning and maintaining logical organization. The findings suggest that this approach fostered meaningful conceptual understanding, going beyond the mechanical use of formulas. Thus, problem solving proved to be an effective pathway for developing intellectual autonomy and combinatorial reasoning, although it requires teacher mediation that is attentive to errors as learning opportunities.

What number makes sense? From gap-filling to mathematical learning

Gilberto Vieira — 2025-09-12

This article aims to present and discuss the potential of “What number makes sense?” problems within the context of Mathematics Education. It is a bibliographic study, with a qualitative and theoretical approach, grounded in the contributions of Problem Solving as a methodological strategy for teaching mathematics. A “What number makes sense?” problem consists of presenting students with a word problem containing numerical gaps and a set of numbers that must be inserted in such a way that the situation described makes mathematical, linguistic, and contextual sense. A systematic literature review revealed a scarcity of national academic publications on the topic, which led to the search for foundations in international literature. The study highlights the didactic potential of this type of problem, as it enhances mathematical reading and argumentation through the construction and sharing of solutions. Furthermore, it demonstrates versatility for addressing content and skills from different thematic units, such as Numbers, Quantities and Measurement, among others. The analysis suggests that when well-planned and integrated into teaching methodologies based on Problem Solving—such as MEAAMaRP and EAMvRP—“What number makes sense?” problems can serve as a starting point for learning, fostering active student engagement and contributing to the development of mathematical literacy.

Pre-service teachers’ reflections on understanding different problem-solving strategies and their implications for mathematics teaching

Caleb da Silva Araujo Campelo — 2025-09-12

Este estudo tem como objetivo analisar as reflexões de futuros professores de matemática sobre a importância de conhecer diferentes estratégias de resolução de problemas e suas implicações para a prática docente. A investigação, de natureza qualitativa, foi realizada no contexto da disciplina de Currículo e Didática da Matemática: teoria e prática. Os dados foram produzidos por meio de respostas escritas de licenciandos a duas perguntas reflexivas e organizados por categorias. Os resultados indicam que os participantes compreendem a diversidade de estratégias como um recurso que favorece o desenvolvimento do pensamento crítico, melhora a compreensão dos alunos, amplia o repertório didático e possibilita uma prática mais inclusiva e responsiva. As análises foram fundamentadas no modelo de Ensino-Aprendizagem de Matemática via Resolução de Problemas (EAMvRP). Conclui-se que refletir sobre estratégias contribui significativamente para a constituição do conhecimento pedagógico e matemático dos futuros professores, evidenciando a importância de experiências formativas que integrem teoria e prática por meio da Resolução de Problemas.

Resolução de problemas matemáticos por meio do uso coordenado do ChatGPT e do GeoGebra

Daniel Medina-Alarcón — 2025-09-12

Atualmente, professores e estudantes mobilizam diversas tecnologias digitais na busca por informações relacionadas à compreensão de conceitos, à resolução de problemas e à discussão de ideias. Este estudo examina como um grupo de seis professores em exercício no Ensino Médio integra, de forma coordenada, o ChatGPT e o GeoGebra em atividades de resolução de problemas nos domínios da álgebra, geometria analítica e cálculo diferencial. Sob uma abordagem qualitativa exploratória, a pesquisa visa analisar os diálogos estabelecidos com o ChatGPT e as construções dinâmicas realizadas no GeoGebra durante um seminário de atualização e formação docente, guiado por um marco metodológico de seis fases, que contempla o diálogo inicial, a análise crítica das respostas da ferramenta, a redirecionamento exploratório, a solicitação de métodos alternativos, a reflexão retrospectiva e a construção de modelos dinâmicos no GeoGebra. Os achados revelam dois tipos de raciocínios complementares: o algébrico-analítico, favorecido pelo ChatGPT, que impulsiona a criação de modelos algébricos; e o dinâmico-geométrico, favorecido pelo GeoGebra, que facilita a validação gráfica e a exploração dinâmica. A coordenação de ambas as ferramentas promove processos metacognitivos que permitem aos docentes avaliar e refinar continuamente suas soluções. Conclui-se que a combinação entre inteligência artificial generativa e ambientes de geometria dinâmica configura um modelo pedagógico promissor para o fortalecimento das competências de resolução de problemas.

Set operations in the 1st year Vocational High School through problem solving

Mário Barbosa da Silva — 2025-09-12

This study presents a classroom practice developed with students from the first year of Vocational High School Education and aims to analyse how the Teaching-Learning-Assessment Methodology of Mathematics through Problem Solving can contribute to the understanding of concepts and content related to Set Theory, as well as to the development of students’ mathematical thinking. The analysed protocols showed that this methodology supported both the construction and understanding of mathematical knowledge related to Set Theory, as well as the development of mathematical thinking throughout the problem-solving process and during the plenary discussions. It is also worth highlighting that the assessment process enabled the teacher to identify and address students’ questions and difficulties, thereby promoting mathematical learning.