Exploring university mathematics professors’ perceptions and use of GenAI: a conceptual fields approach
Publicado 2025-10-20
Palavras-chave
- Artificial intelligence,
- Educational technology,
- Teacher education,
- Higher education,
- Cognition
- Conceptual Fields ...Mais
Como Citar
Copyright (c) 2025 Denilsón Andrés Silgado-Tuñón, Patricia Sureda, José Iván López-Flores, Emmanuel Magallanes

Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
Resumo
Generative Artificial Intelligence (GenAI) is rapidly transforming higher education, challenging traditional pedagogical norms, and prompting a re-evaluation of teaching and learning practices. This study analyzes the operational invariants guiding university mathematics professors' action schemes when interacting with GenAI, using the Theory of Conceptual Fields (TCF) as a theoretical framework. Semi-structured interviews were conducted with ten active university mathematics professors, focusing on the eight dimensions of Technological Pedagogical Content Knowledge (TPACK). Transcriptions were analyzed to infer enacted theorems (ETs), classified into eight thematic categories: general functionality, prompt construction, knowledge validation, academic applications, ethics and regulation, relationship with teaching and learning, teacher knowledge and use, and limitations and risks. Results revealed a predominantly pragmatic usage scheme, with GenAI perceived as a search engine, process optimizer, and code generator. However, contradictory ETs indicate that the conceptual field is still under construction. Teachers primarily use GenAI for text editing, content generation, and idea organization, but its direct classroom use remains limited. Epistemological ambivalence exists regarding Gen's authority, with concerns about errors. Ethical and regulatory issues are not yet central. Findings highlight the need for critical, reflective, and context-sensitive appropriation of GenAI in university mathematics education, supported by professional development and institutional policy.
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Referências
- Alshamy, A., Al-Harthi, A. S. A., & Abdullah, S. (2025). Perceptions of Generative AI Tools in Higher Education: Insights from Students and Academics at Sultan Qaboos University. Education Sciences, 15(4), 501. https://doi.org/10.3390/educsci15040501
- Cabellos, B., de Aldama, C., & Pozo, J-I. (2024). University teachers’ beliefs about the use of generative artificial intelligence for teaching and learning. Frontiers in Psychology, 15, 1468900. https://doi.org/10.3389/fpsyg.2024.1468900
- Corica, A., Parra, V., Sureda, P., Schiaffino, S., & Godoy, D. (2024). Fractal de Koch: análisis de respuestas de IA generativa y un profesor de matemática. Revista Iberoamericana de Tecnología en Educación y Educación en Tecnología (TE&ET), 89-99. https://doi.org/10.24215/18509959.37.e8
- Kang, Y. J. (2024). A study on the didactical application of ChatGPT for mathematical word problem solving. Mathematical Education Communications, 38(1), 49-67. https://doi.org/10.7468/jksmee.2024.38.1.49
- Kwon, O. N., Oh, S. J., Yoon, J. E., Lee, K. Y., Shin, B. C., & Jeong, W. (2023). Analyzing mathematical performances of ChatGPT: Focusing on the solution of national assessment of educational achievement and the college scholastic ability test. Mathematical Education, 37(2), 233-256. https://doi.org/10.7468/jksmee.2023.37.2.233
- Larico-Hanco, R. (2024). Impacto de la Inteligencia Artificial Generativa Chatgpt en la Enseñanza Universitaria. Em SciELO Preprints. https://doi.org/10.1590/SciELOPreprints.9332
- Lee, G. M., Lee, Y. J., & Kim, H. J. (2023). Analysis of adaptive learning in Korea's AI mathematics learning platforms. Journal of the Korean School Mathematics Society, 26(3), 245-268. https://doi.org/10.30807/ksms.2023.26.3.004
- Mishra, P., & Koehler, M. J. (2006). Technological Pedagogical Content Knowledge: A Framework for Teacher Knowledge. Teachers College Record, 108(6), 1017-1054. https://doi.org/10.1111/j.1467-9620.2006.00684.x
- Mishra, P., Warr, M., & Islam, I. (2023). TPACK in the age of ChatGPT and Generative AI. Journal of Digital Learning in Teacher Education, 39(4), 235-251. https://doi.org/10.1080/21532974.2023.2247480
- Parra, V., Sureda, P., Corica, A., Schiaffino, S., & Godoy, D. (2024a). Can generative AI solve Geometry problems? Strengths and weaknesses of LLMs for geometric reasoning in Spanish. International Journal of Interactive Multimedia and Artificial Intelligence, 8(5), 65-74. https://doi.org/10.9781/ijimai.2024.02.009
- Parra, V., Sureda, P., & Corica, A. (2024b). Teoría de Situaciones Didácticas e Inteligencia Artificial: diseño de propuestas para enseñar las nociones de muestra y población en educación secundaria. Uno: Revista de Didáctica de Las Matemáticas, (104), 43-50. http://hdl.handle.net/11336/241263
- Ruediger, D., Blankstein, M., & Love, S. J. (2024). Generative AI and Postsecondary Instructional Practices: Findings from a National Survey of Instructors. (Vol. 320892). Ithaka S+R. https://doi.org/10.18665/sr.320892
- Silgado-Tuñón, D. A., & López-Flores, J. I. (2025a). Inteligencia Artificial Generativa en la Educación Superior: una Revisión Sistemática. Unión - Revista Iberoamericana de Educación Matemática, 21(73). Recuperado a partir de https://union.fespm.es/index.php/UNION/article/view/1709
- Silgado-Tuñón, D. A., & López-Flores, J. I. (2025b). Inteligencia Artificial Generativa en el aula: ¿aliada o amenaza para la enseñanza de las matemáticas? Revista Electrónica Tecnologías Emergentes en la Educación, 2(1), 53-66. https://doi.org/10.71713/retee.v2i1.3512
- Sureda, P., & Otero, M. (2025). Lo exponencial en la Escuela Secundaria de Adultos: análisis de invariantes operatorios. Educación matemática, 37(1), 101-126. https://doi.org/10.24844/EM3701.04
- Sureda, P., Corica, A., Parra, V., Godoy, D., & Schiaffino, S. (2024). La evaluación en educación matemática: aportes de chatbots y futuros profesores de matemática. Edutec, Revista Electrónica De Tecnología Educativa, (89), 64-83. https://doi.org/10.21556/edutec.2024.89.3243
- Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, 10(23), 133-170. https://acortar.link/MW7yqs
- Vergnaud, G. (2007a). Forma operatoria y forma predicativa del conocimiento, en M. R. Otero, I. Elichirebehety, M. Fanaro, A. Corica y P. Sureda (eds.), Primer Encuentro Nacional sobre Enseñanza de la Matemática, Tandil, Buenos Aires, Argentina.
- Vergnaud, G. (2007b). ¿En qué sentido la teoría de los campos conceptuales puede ayudarnos para facilitar aprendizaje significativo? Investigações em Ensino de Ciências, 12(2), 285-302. https://ienci.if.ufrgs.br/index.php/ienci/article/view/475
- Vergnaud, G. (2013). Pourquoi la théorie des champs conceptuels? Journal for the Study of Education and Development, 36(2), 131-161. https://doi.org/10.1174/021037013806196283



