TANGRAM - Revista de Educação Matemática
Tangram is a quarterly scientific journal which publishes papers about different aspects related to the field of Mathematics Education. The journal resulted from the interaction between two Federal University of Grande Dourados (UFGD) research groups linked to the Faculty of Exact Sciences and Technology (FACET), the Faculty of Education (FAED), and the Faculty of Indigenous Intercultural Education (FAIND): one called “Network of Mathematics Education Researches – TeiaMat/CNPq” and, the other, “Technologies of Mathematics Education Research Group – GPTEM/CNPq”. Tangram aims to diffuse results generated from scientific researches, theoretical studies, scientific initiation assignments and notes on pedagogical experiences from primary to higher education. The journal focuses on papers about Mathematics Education and similar areas of study, which can be presented in Portuguese, Spanish and English. Besides the periodic issues, Tangram publishes a thematic edition once a year under the coordination of internal and external members of its team.
Federal University of Grande Dourados (UFGD)
Authors must accept the publication rules when submitting the journal, as well as agree to the following terms: (a) The Editorial Board reserves the right to make changes to the Portuguese language in the originals to maintain the cultured standard of the language, while respecting the style of the authors. (b) Authors retain the copyright and grant the journal the right to first publication, with the work simultaneously licensed under the Attribution-NonCommercial-ShareAlike 3.0 Brazil (CC BY-NC-SA 3.0 BR) that allows: Share - copy and redistribute the material in any medium or format and Adapt - remix, transform, and create from the material. CC BY-NC-SA 3.0 BR considers the following terms: Attribution - You must give the appropriate credit, provide a link to the license and indicate whether changes have been made. You must do so under any reasonable circumstances, but in no way that would suggest that the licensor supports you or your use. NonCommercial - You may not use the material for commercial purposes. Sharing - If you remix, transform, or create from material, you must distribute your contributions under the same license as the original. No additional restrictions - You may not apply legal terms or technological measures that legally restrict others from doing anything that the license permits. (c) After publication, authors are allowed and encouraged to publish and distribute their work online - in institutional repositories, personal page, social network or other scientific dissemination sites, as long as the publication is not for commercial purposes.
Família, escola e matemática: o que dizem as crianças, seus pais e mães?
This article results from research carried out with an early childhood education class at a public school, in the municipality of Nossa Senhora do Socorro-SE. It aims to present the ideas about mathematics that permeate the speeches of children, as well as their fathers and mothers. Researchers from mathematics education and childhood studies serve as theoretical support for the research. It is characterized as a case study with a qualitative approach, using interviews as one of the procedures for data production. The results stand out as follows: children still express positive ideas about mathematics, although restricted to school and numbers; Fathers and mothers reiterate the importance of mathematics for adult life and say it is a difficult area. In this way, such ideas are more related to a fixed mindset perspective than to growth. It concludes with an emphasis on a partnership and effective construction between family and school, in order to instigate a growth mentality in relation to mathematics, demystifying myths and beliefs regarding this field of knowledge since childhood.
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Reimagining Calculus: A Reflective Analysis of Potentials in High School
Mathematics teachers often face learning difficulties among students, which can persist into higher education, especially in calculus, where there are high failure rates. This study proposes introducing calculus concepts in high school to mitigate these difficulties. Through qualitative and bibliographic research, it analyzes teaching sequences that connect applications and pedagogical possibilities. Examples such as Riemann sums and the method of exhaustion, using GeoGebra, demonstrate that an early approach to calculus concepts allows students to expand their mathematical knowledge. Benefits include a better understanding of approximation in calculus, development of logical-algebraic reasoning, and a clearer view of the limitations and possibilities in area calculations.
A brincadeira cantada “Corre Cotia”: uma tarefa formativa no desenvolvimento do conhecimento especializado a respeito da regularidade de crescimento na Educação Infantil
This article presents the elaboration of a task " sung joke Corre cotia" for the development of specialized knowledge about growth regularities. For this we used the methodology of the exploratory type founded by Gil and carried out the technique of literary research, in which we sought researches that dealt with tasks for the specialized knowledge of the teacher. From the studies carried out we elaborate the Formative Task using the five dimensions for writing the activity to the student and the reflections on the domains and subdomains of the theoretical model of Carrillo. We consider that the task will provide reflections on materials intended for teacher training.
A comunidade de que vejo I: percepções acerca da vivência ribeirinha como potencialidades para um ensino de matemática interdisciplinar
In the contemporary educational context, transdisciplinarity in mathematics education emerges as an approach capable of connecting abstract concepts to students' realities, making learning more meaningful. This study focuses on the Amazonian riverside community of São Sebastião da Brasília, Parintins-AM, investigating how its daily life can enrich educational practices. Through qualitative, exploratory, and descriptive research, which includes bibliographic review, photographic records, and direct observation, the study identifies mathematical manifestations in the everyday lives of riverside communities, contextualizing mathematics in a practical and relevant manner. This approach not only improves mathematics education but also fosters a deeper appreciation of cultural and environmental diversity. It empowers students to face academic challenges and actively participate in their communities, resulting in meaningful and lasting learning.
Ensino Exploratório e Estudo de Aula no contexto da Matemática: algumas aproximações em pesquisas
The article analyzes researches that focus on exploratory teaching and lesson study in the Math context. The following is questioned: What are the approaches between exploratory teaching and lesson study in articles in the field of Mathematical Education? Qualitative research, of review of literature, with approaches of systematic review in data collection and some steps of the state of knowledge. Data was collected through content analysis, with the proposition of the categories: a) Tasks in the perspective of exploratory teaching, and b) lesson study and its relationship with practice (professional and teaching). The results and discussions show the relationship between exploratory teaching and lesson study by math tasks; by the active role of the student to solve tasks and the group discussion and the teacher in the planning and class management; by the collective work of teachers and by the professional development with emphasis in the proposition of teaching practices based on exploratory teaching and the reflection regarding such practices. It is pointed out the necessity of other review studies to show the proximity and distance between the lesson study and teaching in the exploratory approach.
Registros de Representação Semiótica de funções quadráticas: uma análise das soluções utilizadas por licenciandos em Matemática
In the midst of the difficulties that students have in studying and understanding the concept of functions and the importance of content that interacts with different areas of knowledge, such as Natural Sciences and their Technologies, and due to the fact that their teaching is developed by the Mathematics teacher, this research sought to identify the types of semiotic representation registers used by Mathematics graduates in tasks on quadratic functions, after moments of socialization on the Theory of Semiotic Representation Registers. The research was developed with students from the 2nd and 8th periods of the Mathematics degree course on a campus of the Federal Institute of Espírito Santo. This is qualitative, participatory research, with interaction between researcher and subjects. It was possible to observe that the students initially registered in quadratic functions primarily through the algebraic register and rarely through graphs, however, after the moment of socialization, the students showed themselves to be more developed in the representation of the mathematical object addressed, using algebraic registers, graphs, tabular, in mother tongue and others. In this way, when using the Theory of Semiotic Representation Registers. No Mathematics teaching process can contribute to improving Mathematics learning rates in Brazil, for students at any educational level.
A Argumentação como Recurso Didático para o Ensino da Matemática na Educação Básica
Este texto, elaborado para uma conferência sobre a argumentação para acadêmicos da Universidade Federal de Sergipe, tem por objetivo esclarecer a diferença entre argumentação explicativa, justificativa, probatória e demonstrativa. Também discute o espaço da Retórica, da Dialética e da Lógica no contexto didático e mostra como pode ser conduzido um processo de ensino da Matemática na perspectiva da argumentação. Identifica e discute possíveis posturas comunicativas do professor, indicando a melhor vertente. Além disso, propõe exemplos aplicáveis em sala de aula, analisa os níveis de argumentação que são apresentados por alunos da Educação Básica e conclui apontando benefícios educativos de um trabalho didático conduzido nessa perspectiva.
Debora Cristina da Silva Araújo Torezani
The geometry in the basketry of the Karipuna people: an ethnomathematical perspective
This article analyzes the geometric representations present in the basketry of the Karipuna indigenous people from Manga village, located in the Uaçá Indigenous Land, in the municipality of Oiapoque/AP, Brazil. The research highlights how the art of weaving goes beyond utilitarian aspects, constituting a process of cultural meaning with strong didactic potential for teaching mathematics through ethnomathematics. Through bibliographic studies of undergraduate theses from the region, it was possible to identify geometric shapes and symbols that express traditional knowledge. The results indicate that such practices can support intercultural pedagogical approaches, strengthen indigenous schooling, and contribute to teacher education, valuing ethnoknowledge and fostering cultural revitalization.
Avaliação da Aprendizagem no Ensino Superior: relatos de professores de ciências e matemática durante aulas remotas
This text presents the results of a qualitative research study that aimed to identify and discuss the evaluation processes during the pandemic period and their impact on post-pandemic evaluation practices. To this end, interviews were conducted with 13 professors from the undergraduate programs in Mathematics, Physics, Chemistry, and Biology at a public institution in Mato Grosso do Sul. After transcription, the corpus was analyzed based on its content and discussed in light of the concepts of Gatti (2020), Moran (2020), Luckesi (2018), among others, to examine how students were evaluated in remote classes during the COVID-19 pandemic. The reports indicate that while some participants faced difficulties in assessing distance learning, others saw the moment as an opportunity to explore new resources and reflect on their assessment practices.
Matemática Recreativa nas Aulas de Matemática: uma experiência no 7º ano do Ensino Fundamental
This article presents some results of a master’s research that aimed to investigate how Recreational Mathematics (RM) regularly inserted into a class of the final years of elementary school can contribute to students’ attitudes. The idea for developing this investigation arose from the desire to intervene in the apathy and demotivation of students. Considering that motivation can influence the learning of any subject, we sought in RM an alternative to engage students more actively. Thus, a set of playful activities and challenges were selected and proposed weekly to 7th-grade students of a public school in the state of Paraíba (Brazil). The observation of the class’s behavior, before, during, and after the application of the activities, was recorded through notes in a field notebook, audio recordings, questionnaires, and notes from the students themselves. We then carefully read the transcripts and field notes, looking to identify positive and negative attitudes of the students in regular math classes as well as in activities involving RM. As results, we observed that the regular insertion of this type of activity led to changes in students’ attitudes in class, an increase in attendance, and the completion of proposed tasks - even after the end of the playful activities. We concluded that the systematic insertion of RM in classes has the potential to awaken students’ interest/motivation in mathematics and can contribute to assisting teaching practice.
The practice developed with students of the Doctorate in Mathematics and Science Teaching (Renoen) course at the Federal Institute of Northeast Brazil involved quadrilaterals, their recognition, definition, and classification. The objective was to examine the contributions of pedagogical practice following the premises of the Federathi Sequence (SF) combined with Augmented Reality (AR) as mediators for a pedagogical practice that favors the development of geometric thinking, in which these teachers can identify, define, and classify quadrilaterals relevant to the first three levels of the Van Hiele model. Methodologically, the research is qualitative and basic in nature. Regarding the objectives, it is exploratory and field-based. The Didactic Session (SD) developed for this workshop followed the premises of the SF and the analysis of the levels of geometric thought of the Van Hiele Model. It was concluded that most participants were familiar with the Sólidos RA application, with an activity based on problematizations. In this process, we noticed a transition from level (1) Visualization to level 2 (Analysis), as well as from level 2 (Analysis) to level 3 (Informal Deduction), indicating that the tool favors improvements in the teaching and learning process of Geometry in Basic Education, in order to enable an effective development of geometric thinking.
Da farinha à sala de aula: a utilização da balança de dois pratos como estratégia pedagógica para o ensino de frações
Este artigo apresenta um relato de experiência que tem por objetivo descrever os resultados alcançados, por meio do desenvolvimento de uma oficina elaborada por estudantes do Curso de Licenciatura em Matemática da Universidade Federal do Recôncavo da Bahia (UFRB), no âmbito do Programa Institucional de Bolsas de Iniciação à Docência (PIBID), subprojeto Matemática. A oficina consistiu na manipulação de uma balança de dois pratos e de uma atividade relacionada à temática “Farinha de Mandioca”, para desenvolver o conteúdo de frações, buscando estabelecer uma conexão entre o conteúdo matemático e a realidade dos estudantes. A implementação da oficina ocorreu em uma turma do 6º ano do Ensino Fundamental de uma escola pública localizada na cidade de Amargosa-BA. Após o desenvolvimento da oficina, analisamos os resultados de maneira reflexiva e qualitativa. Identificamos, a partir das observações e atividades desenvolvidas, um retorno promissor quanto à participação dos estudantes, no que diz respeito as suas interações e resoluções da atividade proposta. Concluímos, nesse sentido, sobre a importância de adotar, na prática docente, metodologias diversificadas e que estejam presentes no cotidiano do estudante, a fim de tornar o aprendizado mais atrativo e facilitar a revisão e fixação dos conceitos abordados. Assim, enfatizamos ainda sobre a relevância do PIBID na formação acadêmica dos cursos de Licenciaturas, ao proporcionar um contato mais próximo entre universidade e escola.
WEB 2.0 tools and the teaching of educational media in Mathematics teacher education
In this text, we aim to present the contributions of Web 2.0 tools and active learning methodologies in the study of Educational Media for Mathematics Teaching, highlighting their significance for teacher education. We begin with the question: What are the contributions of using Web 2.0 tools in the training of mathematics teachers? We conducted an action research in Mathematics teacher training classes at the Federal Institute of Education, Science, and Technology of Rio Grande do Norte. This methodology involved cycles of planning, action, observation moments, and analysis of the practices developed, making adjustments to the improvements needed throughout the process. Considering the continuous evolution of technologies, especially those connected to the internet, it becomes impractical to consider teacher training disconnected from this reality. Therefore, we need to reflect on the impact of information and communication technologies in the context of educational change and innovation. Through the use of Web 2.0 tools, we can personalize and contextualize the learning process, selecting activities that can be recombined and remixed according to the individual needs of each student, thus generating significant impacts on the training of mathematics teachers.
Tecnologias Digitais em Livros Didáticos de Matemática do Novo Ensino Médio
Ao longo dos anos, a sociedade acompanhou diversos avanços tecnológicos, dentre eles, as diversas mídias desenvolvidas para incentivar e aprimorar os processos de ensino e aprendizagem. Uma forma dessas tecnologias serem compartilhadas e integradas ao cotidiano escolar se efetiva mediante os Livros Didáticos de Matemática. No campo da Educação Matemática, diversas pesquisas e discussões têm sido realizadas acerca desse tema. Nesse contexto, este trabalho apresenta os resultados de uma pesquisa de Iniciação Científica concluída, cujo objetivo principal é compreender de que modo as tecnologias digitais estão presentes em coleções de Livros Didáticos de Matemática, aprovados pelo Programa Nacional do Livro e do Material Didático (PNLD), de 2021, voltadas ao Novo Ensino Médio. Com uma abordagem qualitativa, discutimos, neste texto, como as tecnologias se fazem presentes em duas coleções de Livros Didáticos de Matemática, categorizando os tipos de tecnologias identificadas e suas funções nas situações em que aparecem. Os resultados apontam uma notável quantidade de menções ao uso das tecnologias, que foram divididas em cinco grandes grupos: calculadora; GeoGebra; planilha eletrônica; acesso à site; vídeos, filmes e podcast. Apesar da grande variedade de mídias, observa-se que as tecnologias se fazem presentes tendendo à domesticação, dispondo de poucas oportunidades que incentivem a exploração e a investigação.
EDITORIAL: EDUCAÇÃO MATEMÁTICA CRÍTICA POR MEIO DE PRÁTICAS MATEMÁTICAS EMANCIPATÓRIAS E TRANSFORMADORA E COM JUSTIÇA SOCIAL
This article explores possibilities for establishing dialogue between differences. Furthermore, it seeks, through pedagogical imagination, to create new opportunities for dialogical interactions in mathematical education. Pedagogical imagination is a methodological approach to investigating situations that do not yet exist but may come to exist. It opens new educational possibilities for research. Through this process, we present opportunities to establish dialogue between regional, economic, cultural, racial, ethnic, and national differences. In conclusion, dialogue between differences can offer additional support for critical learning, which has not been widely explored before. Thus, dialogue amongst differences is suggested as part of the practice of critical mathematical education.
Challenging black people’s invisibility in the media of Brazil
The article’s aims is to analyze the contribution of Mathematics Education to reading and writing situations that involve racism in the Brazilian media. To this end, we will discuss landscapes of investigation in which students were invited to analyze the (in)visibility of black people in the media of Brazil. In the first landscape of investigation, entitled “Media and Racism,” the students of the final years of a public elementary school in Juiz de Fora, in Minas Gerais, Brazil, analyze the presence of black children in Brazilian magazines. In the second landscape of investigation, entitled “Billboards: analyzing race and representativeness issues,” undergraduates in Education Research Degree analyze the presence of black and indigenous people in the billboards of a city in the state of Mato Grosso do Sul. This study shows that in the two investigated landscapes of investigations, the students identified the disproportionality between the percentage of black people in Brazil and the percentage of their presence in magazines and billboards. The data also provide evidence that the landscapes of investigation have enabled students to use mathematics to identify situations of oppression and the fact that mathematics classrooms might constitute a place to challenge racism. At any educational level, the mathematics classroom could become a learning environment for the critical reading of different social practices, thus unveiling asymmetric processes and power relations established upon racial relations of the same nature.
25 Anos de ‘Cenários para Investigação’: Teorizações, Temáticas e Ideias Skovsmoseanas na Educação Matemática Crítica
The aim of this article is to present the perceptions of two mathematics educators with different lengths of teaching experience and how these mathematics educators reflect on and have been influenced by the ideas of Critical Mathematics Education (CME) and the article Scenarios for Inquiry by Ole Skovsmose. In this way, we recall the main themes and theorizations made by Skovsmose (2000), as well as presenting experiences of how these themes and theorizations have impacted our work as critical mathematics educators, presenting contributions based on Skovsmose's theorizations..
This paper is part of a doctoral thesis conducted by the author. The mathematics identities of Black students can be neglected at times. Moreover, the experiences that they have had and are having can influence the ways they come to understand and perceive the importance of mathematics in their present and future. Utilizing the concept of foregrounds I attempt to learn about the ways Black students, and one of their teachers in Newark view their environments and their perceptions of mathematics and how this may connect to their thoughts and ambitions of the future. To do so I interviewed several middle school students, their teacher, and researched the backgrounds and foregrounds of the participants and of the city of Newark.
Dialogue between three heteronyms by Fernando Pessoa about teachers who teach mathematics to students with Autism Spectrum Disorder
The general objective of this text is to discuss interpretations of a dialogue between three heteronyms of Fernando Pessoa, based on an interview with a teacher who teaches mathematics to students with autism spectrum disorder. The research question is: “What are the challenges faced when it comes to including students with autism spectrum disorder in mathematics teaching?” The interview was recorded and then narrated in three different versions. The dialogue proposed in this work emerged from the narratives. This research is ongoing, with partial results found to date.
Possibilities and obstacles of critical mathematics education in teacher training
This article deals with the propositions of Critical Mathematics Education (CME) in the contexts of initial training of mathematics teachers. This qualitative research aimed to investigate the inclusion of CME in initial training courses for mathematics teachers. The research was theoretically based on Critical Mathematics Education and guidelines for the training of mathematics teachers in Brazil. The qualitative research used a semi-structured interview as its data production methodology and the analysis was based on the precepts of Discursive Textual Analysis (DTA). The research subjects were 17 teacher trainers from different higher education institutions in Brazil that are close to EMC. With the help of analytical categories, possibilities, limits and obstacles, requirements and some proposals for the inclusion of CME in the training of mathematics teachers were identified. It is concluded that the epistemology of the mathematics teacher is one of the main elements to be considered, which can be both a possibility and an obstacle for the insertion of CME. This highlights the need for epistemological and ideological-critical training. Therefore, the main requirements are training for the trainers themselves, as well as collective actions aimed at disseminating CME
Cooperação Investigativa na Prática da Modelagem Matemática com Ênfase na Justiça Social: uma Análise no Contexto do Sistema Prisional
Abstract: This qualitative study, part of a master's research project, aimed to identify elements of investigative cooperation—such as establishing contact, perceiving, recognizing, positioning oneself, thinking aloud, reformulating, challenging, and evaluating—present in the practice of mathematical modeling with an emphasis on social justice, carried out with students from the Association for the Protection and Assistance of Convicts (APAC). The practice of mathematical modeling, guided by the perspective of Critical Mathematics Education, followed the five stages proposed by Burak and Klüber: 1)selection of the theme; 2) exploratory research; 3) identification of the problem(s); 4) problem-solving and development of the mathematical concept in the context of the theme; 5) critical analysis of the solution(s). The research participants were third-year high school EJA (Youth and Adult Education) students, with four in a semi-open regime and six in a closed regime. We chose to construct an experience report as a means to identify teaching and learning processes, as well as moments of dialogue expression and, consequently, elements of investigative cooperation. As data collection instruments, we used audio recordings of the lessons and a field diary to document the observations of the teacher-researcher throughout the development of the proposal. To identify and analyze actions inherent to investigative cooperation, we were inspired by discursive textual analysis, following its four procedural stages, of which the first three (unitization, categorization, and communication) complete a preparatory cycle for the self-organization phase. In this article, we begin by presenting the socio-critical perspective of mathematical modeling within the framework of Mathematics Education that underpinned our research. Next, we detail the methodological approach adopted. Finally, we present our analysis in the concluding remarks.
Educação Matemática Crítica e resistência: possibilidades diante do avanço neoliberal nas escolas públicas
Este artigo tem por objetivo analisar como a Educação Matemática Crítica pode se constituir como uma forma de resistência, ou, ainda, de insubordinar-se criativamente diante das limitações impostas por um modelo curricular neoliberal, que se propaga e se estabelece como a única possibilidade no Ensino Médio do estado de São Paulo. A pesquisa foi realizada na disciplina de Estágio Supervisionado em Ensino de Matemática II com enfoque no Ensino Médio, com licenciandos do último semestre de um curso de Licenciatura em Matemática de uma Universidade Pública do Estado de São Paulo. Os participantes analisaram o material curricular estadual e avaliaram sua capacidade de estimular o pensamento crítico e a criatividade dos estudantes, bem como avaliaram a autonomia docente para realização de atividades críticas, sobretudo por meio dos cenários para investigação. Os resultados indicam que, apesar das restrições, é possível que os professores se subvertam criativamente e ressignifiquem o material. No entanto, os professores entrevistados pelos licenciandos apontaram que essa prática, embora viável, é exaustiva devido à sobrecarga de trabalho e às exigências das avaliações externas, que reforçam um currículo rigidamente estruturado. Ainda assim, destacamos a importância de persistir na construção de práticas pedagógicas que promovam uma educação libertadora, ampliando as possibilidades de formação crítica dos estudantes e desafiando as estruturas que perpetuam desigualdades na sociedade.
Cenas do filme Narradores de Javé nas aulas de Matemática: ambientes de aprendizagem na perspectiva da Educação Matemática Crítica
A pesquisa objetivou analisar uma atividade matemática relacionada a cenas do filme Narradores de Javé à luz dos ambientes de aprendizagem na perspectiva da Educação Matemática Crítica. Para isso, o estudo sustentou-se nos construtos teóricos da Educação Matemática Crítica, particularmente, em ambientes do tipo cenários para investigação. Os dados foram construídos a partir da análise documental da atividade matemática proposta, que explora conceitos vinculados à unidade temática Probabilidade e Estatística, a partir de questões sociais e ambientais em aulas de matemática envolvendo cenas do filme citado. Como categorias analíticas, utilizaram-se os ambientes de aprendizagem definidos na articulação entre a lista de exercícios, os cenários para investigação e as referências à matemática pura, à semirrealidade e à realidade. Os resultados indicam que a diversidade de ambientes de aprendizagem para o ensino da matemática é essencial para a produção de conhecimentos matemáticos. A diversidade de ambientes envolvendo cenários para investigação se faz necessária para lidar tanto com fins puramente matemáticos quanto com as práticas sociais e ambientais diante de uma perspectiva crítica.
Uma atividade fundamentada na Educação Estatística: olhares da Educação Matemática Crítica
The objective of this article is to understand how an interdisciplinary activity based on Statistical Education can help problematize students' living conditions. The research subjects are students from a 3rd year high school class at a state school in the city of Belo Horizonte. The methodological procedure was participant observation and group interviews with students. The data is qualitative in nature. This article presents data from two groups. The study is based on the theoretical approach of Critical Mathematics Education and Statistics Education. Data analysis indicates that students attribute different meanings to the activity and that these may be related to the students' life-world. The nature of the activity favored discussing the situation involving many young school students who become young mothers, a frequent case at the school where the study took place.
Educação Matemática Crítica na formação do professor que ensina Matemática: um mapeamento sistemático de Teses e Dissertações (2014-2024)
Este artigo aponta resultados de um mapeamento sistemático, proveniente de uma investigação com abordagem qualitativa, realizada com o objetivo de mapear Teses e Dissertações brasileiras publicadas entre 2014 e 2024 sobre a Educação Matemática Crítica (EMC) na formação docente. O levantamento bibliográfico buscou responder à seguinte indagação: o que apontam as pesquisas empíricas brasileiras acerca da Educação Matemática Crítica na formação do professor que ensina Matemática? No intuito de responder a esta pergunta, o levantamento das produções acadêmicas foi realizado em duas bases de dados: na Biblioteca Digital Brasileira de Teses e Dissertações (BDTD) e no Catálogo de Teses e Dissertações da CAPES (CTDC). A partir do mapeamento realizado, foi possível identificar uma variedade de temas e conteúdos inter-relacionados com a EMC nas pesquisas, com uma frequência maior sobre a Modelagem Matemática e sobre a Educação Estatística. Também foi possível perceber um quantitativo maior de pesquisas voltadas para a formação continuada de professores, bem como uma ausência de pesquisas com a participação de graduandos em Pedagogia no período compreendido entre os anos 2015 e 2022.
Possibilidades de desenvolvimento de letramento financeiro por meio da Teoria das Situações Didáticas e os Cenários para Investigação
This article presents an excerpt from a doctoral research project focused on presenting possibilities for the development of financial literacy through the Theory of Didactic Situations (TSD) and the Scenarios for Investigation with the theme of Financial Education (FE). The general objective of the research was to analyze how activities in didactic sequences can contribute to the development of financial literacy in mathematics undergraduates, using the Theory of Didactic Situations (TSD) and Scenarios for Investigation. The research problem focused on investigating the didactic characteristics of activity sequences that enhance financial literacy in mathematics undergraduates.
Cristiane Azevedo dos Santos Pessoa Pessoa
Mapeamento de Pesquisas sobre a Produção de Farinha de Mandioca e Etnomodelagem: Relações com a Perspectiva da Educação Matemática Crítica
Based on the need to address cultural diversity in the context of mathematics classrooms, this research aims to analyze how the production of cassava farinha and the knowledge of rural producers have been addressed in academic research that is based on Ethnomodelling, based on perspective of Critical Mathematical Education (EMC), I don't teach Mathematics. For this purpose, searches will be carried out on academic data bases, which will result in the selection of 11 investigations. Among the results, the localized investigations evidence the contribution of the cultural knowledge of farmers to contextualized learning. Therefore, we need to develop research in the educational context of a pedagogical proposal based on the knowledge of farinha production, for the Middle School, addressing the contents of the geometric thematic unit. Therefore, it is expected that pedagogical proposals based on Ethnomodelling can provide diverse forms of learning that valorize the sociocultural knowledge of students.
Foregrounds of students in a field school: an analysis in the light of the critical mathematics education
This research was developed within the framework of a master's degree that is anchored in studies on field education and critical mathematics education (CME). It is particularly interested in the concept of foreground, which, in turn, refers to the background and middleground. The article presents part of the research that aimed to identify and analyze the activities carried out by 31 students in the 8th and 9th grades of elementary school at a field school in the Agreste of Pernambuco, their desires and dreams, and the importance they attributed to the mathematics studied at school for their future. The data were produced using the following instruments: a questionnaire with students, an interview with a community representative, and a documentary study with a source in the IBGE Automatic Recovery System (Sidra) to identify the productive activities in the place. The data show that at the time of the survey, they were mainly carrying out domestic, study, and leisure activities. Most students answered that they intended to attend high school in an urban area, leaving the rural areas in search of new opportunities; and that mathematics could contribute to social advancement. These results align with the community representative's answer when he revealed the tendency toward rural exodus and the failure to recognize the rural territory as a place of opportunities. The identification of students' foregrounds and the link with their backgrounds and middlegrounds provide important clues to guide mathematics teaching in field schools.
“A vida tem preço?”: reflexões a partir da Educação Matemática Crítica na formação inicial
This article explores a mathematical situation from a critical and contextualized approach in teaching and learning, based on the Critical Multicontextual Exploration of Problems (CMEP) methodology. The central proposal was to problematize the value of life through a critical analysis of social and economic issues, using as a starting point the text “Does Life Have a Price?” by Skovsmose. The research was conducted with a group of 15 students from a Mathematics Teaching Degree program at a Public University in Paraíba, Brazil, and was based on a qualitative approach, with students reflecting on economic decisions and their social impacts. During the activity, students discussed topics such as cost-benefit analysis in business decisions, the implications of economic crises, corruption, and risk behaviors, such as drunk driving. Additionally, they were encouraged to propose mathematical problems, linking mathematical knowledge with sociopolitical issues. The results showed that, through problematization, students were able to integrate their mathematical knowledge with their experiences and social contexts, generating reflections on economic relationships and their consequences. The research reinforces the importance of a Mathematics education that goes beyond technical skills, fostering the development of critical and aware citizens, capable of understanding and intervening in the social and economic dynamics surrounding them. CMEP proved to be an effective methodology for promoting meaningful and transformative teaching.
Reflexões sobre os conceitos de alfabetização matemática, letramento matemático e matemacia a partir da perspectiva da Educação Matemática Crítica
This theoretical essay, resulting from the results of completed master's research, aims to discuss the concepts of mathematical alphabetization, mathematical literacy and how these are linked to the concept of mathemacy in the process of teaching mathematics through the concepts established by Mathematics Education Criticism. This is qualitative research, which through bibliographical study came to the conclusion that mathemacy, by expanding and absorbing the concepts of mathematical alphabetization and mathematical literacy, creates minimum conditions for critical training in an emancipatory perspective.
Qual celular escolher? Estudantes de 5º ano tomando decisões relacionadas a finanças: uma análise na perspectiva dos atos dialógicos
In this article, an excerpt from a larger PhD study, we aimed to 1) Examine students’ decision-making in situations related to finances, which involved mathematical and non-mathematical aspects and 2) Identify, from the perspective of the Investigative Cooperation Model, dialogical acts established in the proposed discussions. As a theoretical framework, we used Critical Mathematics Education discussed by Ole Skovsmose. As methodological procedures, students participated in the dialogue moment: “Which cell phone to choose”. We identified that 5th grade students have reflections on themes related to the proposed discussions, presenting their points of view and daily experiences, favoring the proposed discussions. Regarding the promotion of dialogical acts, we noticed the presence of most of these acts, with establishments of contact, positions, perceptions, challenges and evaluations. We emphasize the importance of studies that propose moments of dialogue to students, in which they become agents in the teaching and learning processes.
Projetos Integradores no novo ensino médio: caminhos para a cidadania crítica
The National Textbook and Teaching Material Program (PNLD) has distributed Integrative Project (PI) textbooks in the New High School curriculum. This study analyzes the contributions of these PIs to students' critical education through the lens of Critical Mathematics Education, considering three dimensions of analysis: (i) the depth of discussions and the treatment of sociopolitical aspects, (ii) the support provided to teachers for these discussions, and (iii) the critical use of mathematics for reading the world. This is done through an analysis of the PI textbook with the highest circulation in the PNLD 2021, the first edition after the High School Reform. Anchored in a qualitative approach, we follow the theorEMa system methodology, and the results indicate that sociopolitical aspects are addressed superficially, with a predominant focus on individual rather than collective actions or changes; that there is little to no support for teachers to approach the topics critically; and that mathematics is rarely used as a tool for better understanding of contexts, being treated in a technical, instrumental, and disconnected manner from real-world situations.
Critical Mathematics Education in Youth and Adult Education
This article aims to verify how the field of Critical Mathematics Education (EMC) has approached Youth and Adult Education (EJA) in its recent academic works. Taking as a reference two concerns dear to EMC, mathematics and reading and writing about the world through mathematics, we seek to understand how such concerns have been presented in research that takes EJA - a form of Basic Education whose students are crossed by different issues social - as a research context. As a research methodology, we carried out a systematic literature review - which relied on both qualitative and quantitative techniques to produce and analyze the data and results. Using journal articles, dissertations and theses that had the aforementioned themes as their central themes, we observed a preference for studies based on classroom experiences, in addition to a recurrence in the use of works that interconnect EJA and EMC. Furthermore, Financial Education was a frequent topic, helping to contextualize mathematical content from a critical perspective. As final notes, we noticed a theoretical consonance in the research analyzed, but the absence of theses reveals a possible gap to be filled in the future.
The present study aims to investigate how the context in TPACK — Technological Pedagogical Content Knowledge) and Critical Mathematics Education - EMC can influence teachers' epistemological decisions during the process of integrating digital technologies (DT) to teaching mathematics. We used the Generic Interview Survey and the semi-structured interview to answer the following question: how does knowledge of the context (XK) affect the way teachers make decisions about what and how to teach mathematics? The research results allowed us to infer that just the inclusion of technologies in mathematics teaching is not enough to alleviate the problems of equity, quality and contemporaneity in teaching. As a possibility for future investigations, we propose the integration of Critical Mathematics Education, the TPACK model and artificial intelligence in teacher training by offering a holistic approach to mathematics education.
A landscape of investigation in the field education
In this article, we present an excerpt from a master's degree research that is based on the theoretical assumptions of Critical Mathematics Education and Field Education. One of the specific objectives of this research is to understand how projects based on landscapes of investigation can contribute to critical learning in Field Education. To achieve this objective, we carried out participant research in which we developed two landscapes of investigation in a 3rd year elementary school class at a municipal school located in the rural area of ​​a town in the interior of Bahia. In this article we bring data produced with the development of one of the landscapes of investigation. We clarify that by carrying out our participant research, we understand, in the light of Paulo Freire, that, in Field Education, the landscapes of investigation in mathematics classes provide the exercise of citizenship by democratizing the possibility of the naturalness of mathematics as a condition of be in the world.
Expansão dos ambientes de aprendizagem: possibilidades de novas referências por meio de tarefas em livros didáticos de Matemática
This article aims to present an expansion of the references used by Ole Skovsmose when addressing learning milieus, within the scope of Critical Mathematics Education. It provides a context for the beginning of this discussion, as well as other authors in the scope of Mathematics Education who also made contributions to modify learning milieus. Based on this, and with data from a research that analyzed Mathematics textbooks, examples of tasks are presented that allow us to understand an expansion of references within learning milieus. These new references encompass ‘camouflaged pure mathematics’ and a ‘possibly real’ context. While the first demarcates the terrain between pure mathematics and semi-reality, the second involves a transversal look at all other references. It is hoped that this text will serve as a reflection for researchers and teachers interested in critical views on the teaching and learning of Mathematics.
Critical Mathematics Education and Tangram Journal:
This research aims to present an analysis of the theoretical and practical contributions of Critical Mathematics Education (CME) through a Systematic Literature Review (SLR) of articles published in the academic journal Tangram, highlighting the themes addressed, the identified potentialities, and the challenges reported throughout the 21st century. To achieve these objectives, the methodology employed was an SLR based on the PRISMA protocol (Preferred Reporting Items for Systematic Reviews and Meta-Analyses). A search was conducted using the descriptor “critic” in Portuguese, English, and Spanish, resulting in 59 studies, of which nine were selected for the sample after applying eligibility criteria, based on their alignment with the CME theme. The review was guided by the following research question: What are the contributions, challenges, and advances presented by articles on Critical Mathematics Education published in the Tangram journal? The explored articles, which address themes such as sustainability, financial education, social justice, and the use of digital technologies in Mathematics teaching, identified contributions including strengthening the connection between Mathematics and social issues, promoting ethical and cultural reflections; the use of investigative scenarios to engage students in real-world problems; and the promotion of critical citizenship through the analysis of statistical data and the modeling of everyday situations.
Educação Financeira nos Anos Finais do Ensino Fundamental: uma Análise Comparativa de Livros Didáticos e Apostilas do SEE de Mato Grosso na perspectiva dos Ambientes de Aprendizagem
In this article we present the results of a research that aimed to analyze the presence of Financial Education in a collection of textbooks and in the handouts of the Structured Education System (SEE) of Mato Grosso in the final years of Elementary School from the perspective of the learning environments proposed by Skovsmose (2000). We carried out qualitative research in the documentary modality in which the corpus was constituted by a collection of textbooks approved by the National Textbook Program (PNLD) in the year 2024, and the handouts from the Structured System of the State of Mato Grosso from the final years (6th to the 9th year) of Elementary School. The data were analyzed using Content Analysis procedures from the perspective of Bardin (1977) and Rodrigues (2019), through which we sought to map, classify and analyze the way in which the 420 questions, 197 questions coming from a collection of textbooks and 223 questions in the SEE booklets addressed Financial Education in light of the theoretical contributions of Learning Environments. The research results indicated that there is a predominance of the Exercise Paradigm to the detriment of Research Scenarios in the way in which the topic of Financial Education is inserted in the SEE textbook and handouts. We concluded that to address Financial Education in the final years of Elementary School, the textbook collection analyzed has better movement between the different Learning Environments than the booklets made available by the SEE of Mato Grosso.
Educação Matemática Crítica, Inclusão e Narrativa Pedagógica: Uma Proposta Formativa para Professores em Formação Inicial
he article addresses the challenges and possibilities of teacher training that integrates the perspectives of Critical Mathematics Education, Inclusive Education, and teacher subjectivity. Grounded in reflective and (auto)biographical narrative practices, the research is conducted with undergraduate Mathematics and Pedagogy students at the Federal University of Bahia (UFBA). This approach seeks to promote initial training that connects technical, human, and cultural dimensions, fostering more inclusive pedagogical practices aligned with the demands of diversity. Critical Mathematics Education is highlighted as a tool for social emancipation, encouraging reflection on social and structural contexts through mathematics. Simultaneously, Inclusive Education emphasizes the need to develop pedagogical strategies that embrace individuals' singularities, ensuring accessibility and equity in teaching. Valuing teacher subjectivity emerges as a central element, enabling educators to align their experiences and trajectories with educational practices. The research employs the narrative documentation of pedagogical experiences as its core methodology, connecting individual knowledge with collective demands. Expected outcomes include strengthening the theoretical, political, and practical competencies of future teachers, alongside valuing subjectivities and diversity in educational practices. It concludes that the integration of Critical Mathematics Education, Inclusivity, and teacher subjectivity is essential for transforming initial teacher training and fostering a more accessible education aligned with contemporary realities.
Proposição de Problemas como propulsora de uma Educação Matemática CríticaA Proposição de Problemas como propulsora de uma Educação Matemática Crítica
This article discusses the potential of Problem Posing as a way to promote Critical Mathematical Education. To this end, the results of the first author's doctoral thesis will be presented, showing how activities using Problem Posing has enabled reflections on socio-political-cultural issues. The research, conducted with 24 undergraduate students in Mathematics at a public university in Paraíba, highlights how activities based on the Problem Exploration-Posing-Solving teaching approach can encourage students to reflect critically on socio-political-cultural issues, using mathematics beyond a technical discipline. Critical Mathematical Education involves the education of citizens capable of questioning and transforming reality through mathematical reflection, a practice that goes beyond conventional teaching. In this context, Problem Posing offers students the opportunity to become co-constructors of knowledge, developing mathematical skills while discussing relevant social issues. The results this research indicate that activities using Problem Posing have effectively contributed to a more comprehensive Mathematics teaching-learning, which promote the development of critical-reflective thinking and enable the strengthening of students' relationship with mathematics, allowing them to perceive their role in articulating social issues. It is concluded that Problem Posing, from the perspective of Critical Mathematics Education, enhances mathematics teaching aimed at the formation of critical citizens, capable of understanding and intervening in relevant social issues through mathematics and beyond.
Cenários para investigação em aulas de matemática: superando situações-limite na formação e na prática docente
This article presents how it is possible to overcome extreme situations in teacher training and in mathematics classes by adopting scenarios for investigation as a teaching practice. With the aim of developing actions aimed at overcoming extreme situations, we proposed a continuing education program that was developed with five teachers from the initial years of elementary school at a state school in São Paulo. This investigation, the result of a doctoral research, has a qualitative approach and characteristics of action research. The data produced were interpreted in the light of Dialogical Discourse Analysis. The results showed that the teachers were subjected to a bureaucratization of the school system that resulted, in their perception, in extreme situations that, in principle, could not be overcome. However, the awareness-raising process developed and the work with scenarios for investigation made it possible to develop actions to overcome these situations in teacher training and in mathematics classes.
“Projeto Dengue”: a modelagem matemática e a leitura e escrita do mundo com a matemática em projetos de trabalho
Education should address sociopolitical issues that affect the educational context, allowing students to use mathematics and other knowledge to understand and act on their reality, critically and collaboratively. Therefore, it is necessary to have educational proposals that allow students to develop these competencies. The objective of this work is to understand the perception of high school students, participants in a work project, regarding the relevance of the problem, pedagogical strategy, mathematical learning, and the skills of writing and reading the world with mathematics. The qualitative, exploratory research, approved by the ethics committee, included 25 third-year high school students - 15 composed the analysis corpus. The data collection instrument was an online questionnaire, subjected to thematic content analysis, with predefined categories. The results indicate that the teaching strategy is interesting and capable of assigning practical meanings to theoretical content, although it is complex. Despite indicating the importance of addressing real problems, some students do not feel capable of dealing with new problems using mathematics. However, they identified interdisciplinarities, attributing importance to mathematics, to modeling, and gaining confidence to manipulate these tools. The analysis outlined possibilities and limitations regarding the use of this non-traditional teaching strategy. The practical application of the content and the approach to real problems contributed to the critical formation of the students. However, such proposals should be more frequent throughout Basic Education so that students change their view of mathematics and the social role of the school.
Contributions of dialogic Modelling practices to student formation in the early years of Elementary School
This article presents the analysis of a Mathematical Modeling practice, with dialogical characteristics, developed with students in the fifth year of elementary school. We seek to answer: What contributions to the training of students can be evidenced in a Mathematical Modeling practice developed with Elementary School students with the theme “Air Pollution”? As data we considered: notes from the researcher's field notebook, audio/video recordings, student productions and questionnaire. The analysis, of a qualitative nature, was supported by theoretical references on Modeling, Critical Mathematics Education and dialogues. We highlight the contributions: initiative in learning, initiative and autonomy in the search for solutions, ability to use mathematics to understand reality, ability to use mathematics to reflect and position oneself critically, ability to dialogue, confidence and autonomy to make decisions, development citizenship and ability to act collaboratively
Critical Mathematical Education: Reflections on the teaching of Mathematics in Brazil based on excerpts from the History of Science
This paper portrays the immediate function and pragmatic nature of mathematics in Brazil since colonization and its impact on teaching, with the excessive emphasis on methods and techniques to the detriment of the study of concepts. The text presents facts from the history of science in Brazil that illustrate the need for mathematics with these characteristics to meet the economic and political needs of the nation. The objectives of the article are to highlight historical passages that relate the trajectory of science in our country and the role of mathematics in this process at different times, to point out some consequences of extreme pragmatism for the education of individuals in this area of ​​knowledge, and to carry out a critical analysis regarding the teaching of mathematics from this context. This study is bibliographical and its theoretical framework is constructed, especially, from works focused on the history of science in Brazil and on the teaching of mathematics.
Aproximações entre Educação Matemática Crítica e Alfabetização/Letramento na produção científica da área da Educação Matemática
Este trabalho visa apresentar um estudo bibliográfico cujo objetivo é investigar a relação entre Educação Matemática Crítica (EMC), alfabetização e letramento a partir da produção científica em artigos de periódicos da área da Educação Matemática. Na análise dos trinta e oito artigos selecionados foi possível notar mais que o quíntuplo de trabalhos referentes ao letramento, em relação aos trabalhos acerca de alfabetização, e destes, o letramento estatístico correspondeu ao maior número de estudos. As categorias que emergiram foram: alfabetização; alfabetização ou letramento matemático; alfabetização ou letramento estatístico e probabilístico; letramento digital e letramento docente, sendo observada de forma transversal a EMC. Identificou-se uma aderência das concepções trazidas pelo letramento digital, bem como pela alfabetização ou letramento estatístico e probabilístico à EMC. A alfabetização ou letramento matemático teve concepções distintas que ora se aproximavam da EMC, ora mostravam certa incompletude. Por fim, os estudos que trataram de alfabetização (no sentido mais estrito do termo) e letramento docente não mostraram relação com a EMC.
This theoretical essay explores how Critical Statistical Literacy (CST) and Critical Statistical Consciousness (CSC) enhance Critical Statistical Education (CSE) in the context of Critical Mathematics Education (CME), in order to promote citizenship and democratic education. Based on a broad theoretical foundation, the text discusses how CST promotes analytical and reflective skills in the treatment of statistical data in sociopolitical contexts, while CSC emphasizes awareness of the impact of statistics on the construction of social realities. The articulation between CSE, CST, and CSC highlights an educational approach that transcends technical education, integrating social and political reflections into pedagogical practices. This perspective encourages the formation of engaged citizens, capable of questioning social inequalities and proposing well-founded solutions. In addition, the text discusses challenges, such as teacher training and institutional barriers, highlighting the need for critical pedagogical practices that align statistics with the demands of social justice and the democratization of knowledge. The study concludes that CST and CSC extend the reach of CSE by connecting statistical skills with criticality, aligning with CME as a transformative practice for the 21st century. This integration not only forms reflective individuals, but also contributes to an education committed to social justice and the democratization of knowledge.
Uso(s) da Modelagem Matemática na formação inicial de professores para uma Educação Matemática Crítica
Teacher education has been a widely discussed topic in research within the field of Mathematics Education (Valente, 2021). Which elements should be prioritized? What should be done in classroom practices with future teachers? What is the role of undergraduate students (future teachers) in the production of mathematical knowledge in basic education? It was from such concerns that this work emerged. Focused on the discussion of mathematical modeling (Meyer, Caldeiras, and Malheiros, 2021), articulated with the proposals of Critical Mathematics Education (Skovsmose, 2000), we consider the possibility of thinking about teacher education within a critical-reflective scenario in the production of mathematical knowledge. Thus, we present two narratives that seek to problematize some ways in which, by taking Mathematical Modeling as a Curricular Unit in undergraduate and graduate courses, it can be approached to contribute to a critical, problematizing, and reflective teacher education for students. The results point to mathematical modeling as an important tool in problematizing the notion that it is not enough to "know Mathematics" to "be a Mathematics teacher" and that school mathematics is not merely a simplification of academic mathematics or a didacticization of everyday mathematics.
“Linguagem matemática” e Educação matemática crítica: vetores opostos na Base Nacional Comum Curricular
In the National Common Curricular Base (BNCC), different meanings are attributed to the term “mathematical language” and the objective of this work was to investigate how such inflation occurred and what its implications are for the teaching of Mathematics. The research, of a bibliographic nature, consisted of investigations into the concept presented, considering the indicative method for analysis. No explicit definitions of the terms studied were found in the BNCC; there is too much use of related terms around “mathematical language”; and, in addition to this present terminological inflation, there is the conceptual inflation with multiple meanings for the same term mentioned. The vast majority of uses of the term investigated are notational, related to formal logic. This use converges with neoliberal ideas of education, reducing the curricular component to teaching the mastery of form and the fetishism of technology, distancing the discipline from Critical Mathematics Education, since abstraction gives way to “knowing how”.