CRITICAL MATHEMATICAL AGENCY IN THE PRODUCTION OF AI MATHEMATICAL MODELS

Authors

DOI:

https://doi.org/10.59666/Arete.1984-7505.v24.n38.5128

Keywords:

Critical Mathematics Agency, Generative Artificial Intelligence, ChatGPT, Mathematical Modeling. Agency

Abstract

This article adopts the concept of critical mathematics agency to analyze the use of generative artificial intelligence technologies in mathematics education. This agency involves students’ ability to engage with mathematics in a personally and socially meaningful way, articulating three dimensions: mathematical understanding, identification as competent mathematical thinkers, and meaningful use of mathematics. These dimensions enable not only conceptual appropriation but also critical application of knowledge. The qualitative study used interviews and questionnaires to investigate how students expressed this agency while developing mathematical models with the support of ChatGPT. The results revealed varying levels of agency among the groups and highlighted critical reflections on AI, including ethical concerns and perceived limitations. Some students carried out critical analyses, while others advocated for more conscious stances toward the results generated by AI. The study concludes that although IA-Gen can foster critical mathematics agency, its full development occurs when students are encouraged to reflect and act upon the social and ethical impacts of these technologies, with the teacher’s mediating support

References

AGUIRRE, Julia.; MAYFIELD-INGRAM, Karen; MARTIN, Danny Bernard. The impact of identity in K-8 mathematics: Rethinking equity-based practices. Reston: National Council of Teachers of Mathematics, 2013.

ARAÚJO, Jussara Loiola. Ser crítico em projetos de modelagem em uma perspectiva crítica de educação matemática. Bolema: Boletim de Educação Matemática, Rio Claro, v. 26, n. 43, p. 839-859, ago. 2012. https://doi.org/10.1590/S0103-636X2012000300005

BAKKER, Arthur; CAI, Jinfa; ZENGER, Linda. Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, Dordrecht, v. 107, n. 1, p. 1–24, 2021. https://doi.org/10.1007/s10649-021-10049-w

BARDIN, Laurence. Análise de conteúdo. São Paulo: Edições 70, 2011. 229 p.

BORBA, Marcelo de Carvalho.; VILLARREAL, Monica. Humans-with-media and the reorganization of mathematical thinking: information and communication technologies, modeling, experimentation and visualization. New York: Springer, 2005. https://doi.org/10.1007/b105001

BORBA, Marcelo de Carvalho. The future of mathematics education since COVID-19: humans-with-media or humans-with-non-living-things. Educational Studies in Mathematics, Dordrecht, v. 108, n. 1-2, p. 385–400, 2021. https://doi.org/10.1007/s10649-021-10043-2

BORBA, Marcelo de Carvalho; SOUTO, Daise. Lago; CUNHA, José Fernandes.; DOMINGUES, Nilton. Humans-with-media: twenty-five years of a theoretical construct in mathematics education. In: PEPIN, B.; GUEUDET, G.; CHOPPIN, J. (org.). Handbook of digital resources in mathematics education. Cham: Springer, 2023. (Springer International Handbooks of Education). https://doi.org/10.1007/978-3-030-95060-6_7-1.

BRANDTZAEG, Petter Bae; YOU, Yukon; WANG, Xi; YUCONG, Lao. “Good” and “bad” machine agency in the context of human-AI communication: the case of ChatGPT. In: DEGEN, H.; NTOA, S.; MOALLEM, A. (ed.). HCI International 2023 — Late Breaking Papers: 25th International Conference on Human-Computer Interaction. Proceedings. Cham: Springer, 2023. (Lecture Notes in Computer Science, v. 14059), p. 3–23. https://doi.org/10.1007/978-3-031-48057-7_1

CEVIKBAS, Mustafa; KAISER, Gabriele; SCHUKAJLOW, Stanislaw. A systematic literature review of the current discussion on mathematical modelling competencies: state-of-the-art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics, Dordrecht, v. 109, n. 2, p. 205–236, 2022. https://doi.org/10.1007/s10649-021-10104-6

LOPES, Aldo Peres Campos e. Contrapondo a ideologia da certeza por meio do conhecimento reflexivo na modelagem matemática. Bolema: Boletim de Educação Matemática, v. 37, n. 77, p. 936–957, 2023. https://doi.org/10.1590/1980-4415v37n77a01

LOPES, Aldo Peres Campos e. Mathematical modelling: a methodology favourable to the manifestation of critical mathematics consciousness. International Journal of Mathematical Education in Science and Technology, [S. l.], p. 1–30, 2024. https://doi.org/10.1080/0020739X.2024.2378191

LOPES, Aldo Peres Campos e; BORBA, Marcelo Carvalho. Seres-humanos-com-ChatGPT em Modelagem Matemática. Seminário Internacional de Pesquisa em Educação Matemática, Brasília, p. 1–15, 2024. Disponível em: https://www.sbembrasil.org.br/eventos/index.php/sipem/article/view/260. Acesso em: 6 ago. 2025.

LOPES, Aldo; BORBA, Marcelo. Do themes of environmental collapse guarantee a socioecological discussion? In: LE ROUX, K. et al. (Org.). Proceedings of the 27th ICMI Study Conference: Mathematics Education and the Socio-Ecological. Quezon City (Philippines), 22–25 jan. 2025. Quezon City: MATHTED; ICMI, 2025. p. 331–338. Disponível em: https://icmistudy27.sciencesconf.org/resource/page/id/15. Acesso em: 6 ago. 2025.

MORAES, Valdison Luiz Cruz de.; AMORIM NETO, Alcides de Castro. EXPLORANDO PERSPECTIVAS FENOMENOLÓGICAS EDUCACIONAIS NA EDUCAÇÃO. Revista Areté | Revista Amazônica de Ensino de Ciências, [S.l.], v. 22, n. 36, p. e24038, dez. 2024. ISSN 1984-7505. https://doi.org/10.59666/Arete.1984-7505.v22.n36.2124

FREIRE, Paulo. Pedagogia do Oprimido. Rio de Janeiro: Paz e Terra, 1970.

FREIRE, Paulo. Educação como Prática da Liberdade. Rio de Janeiro: Paz e Terra, 1979.

HAGENDORFF, Thilo. Mapping the ethics of generative AI: a comprehensive scoping review. Minds & Machines, [S.l.], v. 34, p. 39, 2024. https://doi.org/10.1007/s11023-024-09694-w

JUNG, Hyunyi; WICKSTROM, Megan. Teachers creating mathematical models to fairly distribute school funding. The Journal of Mathematical Behavior, v. 70, 101041, 2023. https://doi.org/10.1016/j.jmathb.2023.101041

MAGGIOLINI, Piercarlo. Um Aprofundamento para o Conceito de Ética Digital. Revista de Administração de Empresas, v. 54, n. 5, p. 585–591, set. 2014. https://doi.org/10.1590/S0034-759020140511

PASA, B. C.; BERTO, C.; SILVA, D. K. da. Estado do conhecimento sobre as perspectivas de inovações educacionais no âmbito da educação matemática. Revista Eletrônica de Educação Matemática, v. 19, p. 1–22, 2024. Disponível em: https://periodicos.ufsc.br/index.php/revemat/article/view/99866. Acesso em: 6 ago. 2025.

RODRIGUES, Raquel Augusta Borges; SANTANA, Geslane Figueiredo da Silva; BARBOSA, Edson Pereira. SALA DE ARTICULAÇÃO: UM ESTUDO COM ALUNOS EM SITUAÇÃO DEFASAGEM EM MATEMÁTICA. Revista Areté | Revista Amazônica de Ensino de Ciências, [S.l.], v. 22, n. 36, p. e24037, dez. 2024. ISSN 1984-7505. https://doi.org/10.59666/Arete.1984-7505.v22.n36.4153.

SILVA, Cíntia da; KATO, Lilian Akemi. Quais Elementos Caracterizam uma Atividade de Modelagem Matemática na Perspectiva Sociocrítica? Bolema: Boletim de Educação Matemática, v. 26, n. 43, p. 817–838, ago. 2012. https://doi.org/10.1590/S0103-636X2012000300004

SOUTO, Daise Lago; CUNHA, José Fernandes; BORBA, Marcelo de Carvalho. Inteligência artificial em educação matemática. Belo Horizonte: Autêntica, 2025.

TURNER, Erin Elizabeth. Critical mathematical agency: Urban middle school students engage in mathematics to investigate, critique, and act upon their world. 2003. Tese (Doutorado em Educação) – University of Texas at Austin, Austin, TX, 2003.

Published

2025-12-26

How to Cite

LOPES, A. P. C. e .; BORBA, M. de C. . CRITICAL MATHEMATICAL AGENCY IN THE PRODUCTION OF AI MATHEMATICAL MODELS. Revista Areté | Revista Amazônica de Ensino de Ciências, [S. l.], v. 24, n. 38, p. e25030, 2025. DOI: 10.59666/Arete.1984-7505.v24.n38.5128. Disponível em: http://periodicos.uea.edu.br/index.php/arete/article/view/5128. Acesso em: 15 jun. 2026.