Cognitive and attitudinal effects of a General Mathematics leveling workshop mediated by generative AI with socratic tutor prompt
DOI:
https://doi.org/10.70577/bpksp840Keywords:
mathematics education; artificial intelligence; higher education; active learning; student attitudes.Abstract
The mathematical gaps with which students enter university, particularly in abstract reasoning about the function concept, constituted the initial cognitive problem of this study, whose mitigation requires brief high-impact formative devices. The objective was to evaluate the cognitive and attitudinal effects of a General Mathematics leveling workshop mediated by generative artificial intelligence (GenAI) with a Socratic tutor prompt, implemented at the Instituto Tecnológico de Costa Rica. A quantitative single-group pre-experimental design with pre- and post-measurements was applied, corresponding to the quantitative component of a convergent parallel mixed-methods study whose qualitative component is reported in a complementary publication. Twenty-two first-year students completed a 15-item isomorphic test on the function concept and an 18-item Likert attitudinal scale. Data were analyzed using descriptive statistics, Student's t-test for related samples, Wilcoxon test, exact McNemar test, Mann-Whitney U test, and Cohen's d effect size. The intervention produced a mean improvement of 24.85 points (t(21) = 6.14; p < .001; Cohen's d = 1.31), with 86.4% of students improving. The gain was greater in the algebraic dimension (+34.1 pp; d = 1.63) than in the conceptual one (+18.7 pp; d = 0.69). The attitudinal assessment was markedly positive (Disposition M = 4.49; global α = .921; ω = .953), with a significant gap by prior AI experience in utility (p = .035) and disposition (p = .022). Internal triangulation between instruments identified an asymmetric pattern: GenAI mediation under Socratic tutoring generated substantial procedural gains and robust technological acceptance, but encountered a limit in the graphic-symbolic register of the function concept. It is concluded that GenAI with a Socratic tutor prompt constitutes an effective device for mitigating cognitive lag in procedural content within brief university leveling workshops, but does not replace the explicit didactic treatment of epistemological obstacles associated with articulation between representation registers.
Downloads
References
Almassaad, A., Alajlan, H., y Alebaikan, R. (2024). Student perceptions of generative artificial intelligence: Investigating utilization, benefits, and challenges in higher education. https://doi.org/10.3390/systems12100385
Artigue, M., y Winsløw, C. (2010). International comparative studies on mathematics education: A viewpoint from the anthropological theory of the didactic. Recherches en Didactique des Mathématiques, 30(1), 47–82.
Bernabei, M., Colabianchi, S., Falegnami, A., y Costantino, F. (2023). Students' use of large language models in engineering education: A case study on technology acceptance, perceptions, efficacy, and detection chances. Computers and Education: Artificial Intelligence, 5, 100172. https://doi.org/10.1016/j.caeai.2023.100172
Braun, V., y Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
Brousseau, G. (1998). Théorie des situations didactiques. La Pensée Sauvage.
Chan, C. K. Y., y Hu, W. (2023). Students' voices on generative AI: Perceptions, benefits, and challenges in higher education. International Journal of Educational Technology in Higher Education, 20(1), 43. https://doi.org/10.1186/s41239-023-00411-8
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2.ª ed.). Lawrence Erlbaum Associates.
Creswell, J. W., y Plano Clark, V. L. (2018). Designing and conducting mixed methods research (3.ª ed.). SAGE Publications.
Davis, F. D. (1989). Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS Quarterly, 13(3), 319–340. https://doi.org/10.2307/249008
Dunn, T. J., Baguley, T., y Brunsden, V. (2014). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. British Journal of Psychology, 105(3), 399–412. https://doi.org/10.1111/bjop.12046
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https://doi.org/10.1007/s10649-006-0400-z
Eccles, J. S., y Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153
Escobar-Pérez, J., y Cuervo-Martínez, Á. (2008). Validez de contenido y juicio de expertos: Una aproximación a su utilización. Avances en Medición, 6(1), 27–36.
Hernández-Sampieri, R., y Mendoza, C. P. (2018). Metodología de la investigación: Las rutas cuantitativa, cualitativa y mixta. McGraw-Hill.
Kasneci, E., Sessler, K., Küchemann, S., Bannert, M., Dementieva, D., Fischer, F., Gasser, U., Groh, G., Günnemann, S., Hüllermeier, E., Krusche, S., Kutyniok, G., Michaeli, T., Nerdel, C., Pfeffer, J., Poquet, O., Sailer, M., Schmidt, A., Seidel, T., … Kasneci, G. (2023). ChatGPT for good? On opportunities and challenges of large language models for education. Learning and Individual Differences, 103, 102274. https://doi.org/10.1016/j.lindif.2023.102274
Pintrich, P. R., Smith, D. A. F., García, T., y McKeachie, W. J. (1991). A manual for the use of the Motivated Strategies for Learning Questionnaire (MSLQ). National Center for Research to Improve Postsecondary Teaching and Learning. https://eric.ed.gov/?id=ED338122
Rittle-Johnson, B., y Schneider, M. (2015). Developing conceptual and procedural knowledge of mathematics. En R. Cohen Kadosh y A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 1118–1134). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014
Shapiro, S. S., y Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3–4), 591–611. https://doi.org/10.1093/biomet/52.3-4.591
Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach's alpha. Psychometrika, 74(1), 107–120. https://doi.org/10.1007/s11336-008-9101-0
Strzelecki, A. (2024). To use or not to use ChatGPT in higher education? A study of students' acceptance and use of technology. Interactive Learning Environments, 32(9), 5142–5155. https://doi.org/10.1080/10494820.2023.2209881
Sweller, J., van Merriënboer, J. J. G., y Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 31(2), 261–292. https://doi.org/10.1007/s10648-019-09465-5
Yan, L., Sha, L., Zhao, L., Li, Y., Martinez-Maldonado, R., Chen, G., Li, X., Jin, Y., y Gašević, D. (2024). Practical and ethical challenges of large language models in education: A systematic scoping review. British Journal of Educational Technology, 55(1), 90–112. https://doi.org/10.1111/bjet.13370
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Melvin Ramírez Bogantes , Esteban Quesada Ávila , Francine Araya López (Autor/a)
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Eres libre de:
- Compartir : copiar y redistribuir el material en cualquier medio o formato
- Adaptar : remezclar, transformar y desarrollar el material
- El licenciante no puede revocar estas libertades siempre y cuando usted cumpla con los términos de la licencia.
En los siguientes términos:
-
- Atribución : Debe otorgar el crédito correspondiente , proporcionar un enlace a la licencia e indicar si se realizaron cambios . Puede hacerlo de cualquier manera razonable, pero no de ninguna manera que sugiera que el licenciante lo respalda a usted o a su uso.
- No comercial : no puede utilizar el material con fines comerciales .
- CompartirIgual — Si remezcla, transforma o construye sobre el material, debe distribuir sus contribuciones bajo la misma licencia que el original.
- Sin restricciones adicionales : no puede aplicar términos legales ni medidas tecnológicas que restrinjan legalmente a otros hacer algo que la licencia permite.
