Gamification for teaching rationalization: Design and justification of an innovative didactic proposal
DOI:
https://doi.org/10.70577/asce.v5i2.839Keywords:
Gamification, Rationalization, Teaching mathematics, Didactics of algebra, Innovative didactic proposal, School motivation.Abstract
Teaching the rationalization of monomials faces documented cognitive obstacles, such as rote memorization, difficulties with the properties of radicals and powers, and math anxiety, which motivates the search for innovative teaching strategies that promote meaningful learning. The purpose of this research was to theoretically design a didactic proposal based on gamification for teaching this topic. Using a qualitative design-based approach, a literature review on gamification in mathematics education was conducted, the concepts involved in rationalization and the associated cognitive obstacles were analyzed, and the proposal was grounded in constructivist, connectivist, and sociocultural theories. The main results include the identification of six fundamental mathematical concepts, six categories of cognitive obstacles, four applicable gamification principles (attention, relevance, trust, and satisfaction), and three levels of game elements (mechanics, dynamics, and aesthetic components). Based on these findings, “Rational Quest: The League of Radicals” was designed, a proposal structured in five progressive levels that integrates narrative, points, badges, boosters, and a final challenge. It is concluded that the proposal constitutes a versatile and theoretically sound tool for transforming the learning of rationalization into a motivating experience.
Downloads
References
Abancin Ospina, R. A., & Castillo Marrero, Z. N. (2022). Tipificación de errores en evaluaciones matemáticas de un primer curso universitario. Explorador Digital, 6(3), 6-27. https://doi.org/10.33262/exploradordigital.v6i3.2196 DOI: https://doi.org/10.33262/exploradordigital.v6i3.2196
Abancin Ospina, R. A., Castillo Marrero, Z. N., Andrés Eloy Salazar Domínguez, & Valverde Aguirre, P. E. (2022). Reflexiones sobre los aspectos que influyen en la popularidad de las ciencias. Conciencia Digital, 5(1.3), 148-167. https://doi.org/10.33262/concienciadigital.v5i1.3 DOI: https://doi.org/10.33262/concienciadigital.v5i1.3.2104
Adams, E. (2014). Fundamentals of game design (3rd ed.). New Riders.
Anderson, W. & Krathwohl, D. R. (Eds.). (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom's taxonomy of educational objectives (Complete ed.). Longman.
Bai, S., Hew, K. F., & Huang, B. (2020). Does gamification improve student learning outcome? Evidence from a meta-analysis and synthesis of qualitative data in educational contexts. Educational Research Review, 30, 100322. https://doi.org/10.1016/j.edurev.2020.100322 DOI: https://doi.org/10.1016/j.edurev.2020.100322
Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes en mathématiques. Recherches en Didactique des Mathématiques, 4(2), 165-198.
Bycer, J. (2018). Game design deep dive: Boss fights. Gamasutra. https://www.gamasutra.com DOI: https://doi.org/10.1201/9780429265563
Collins, A., Joseph, D., & Bielaczyc, K. (2004). Design research: Theoretical and methodological issues. Journal of the Learning Sciences, 13(1), 15-42. https://doi.org/10.1207/s15327809jls1301_2 DOI: https://doi.org/10.1207/s15327809jls1301_2
Deterding, S., Dixon, D., Khaled, R., & Nacke, L. (2011). From game design elements to gamefulness: Defining “gamification”. Proceedings of the 15th International Academic MindTrek Conference: Envisioning Future Media Environments, 9-15. https://doi.org/10.1145/2181037.2181040 DOI: https://doi.org/10.1145/2181037.2181040
Farías, D., Abancin, R.; Pérez, J. (2021). Potenciación en el aula de clases en estudiantes que inician estudios superiores. Revista Paradigma Vol. XLII, Nro. 2, 110-129. DOI: https://doi.org/10.37618/PARADIGMA.1011-2251.2021.p110-129.id958 DOI: https://doi.org/10.37618/PARADIGMA.1011-2251.2021.p110-129.id958
Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques, 14(3), 325-355.
Hanus, M. D., & Fox, J. (2015). Assessing the effects of gamification in the classroom: A longitudinal study on intrinsic motivation, social comparison, satisfaction, effort, and academic performance. Computers & Education, 80, 152-161. https://doi.org/10.1016/j.compedu.2014.08.019 DOI: https://doi.org/10.1016/j.compedu.2014.08.019
Hunicke, R., LeBlanc, M., & Zubek, R. (2004). MDA: A formal approach to game design and game research. Proceedings of the AAAI Workshop on Challenges in Game AI, 4(1), 1-5.
Jonassen, D. H. (1991). Evaluating constructivistic learning. Educational Technology, 31(9), 28-33.
Jonassen, D. H. (1994). Thinking technology: Toward a constructivist design model. Educational Technology, 34(4), 34-37.
Jonassen, D. H. (1999). Constructivist learning environments: Designing technologies to support learning. Educational Technology Publications.
Kapp, K. M. (2012). The gamification of learning and instruction: Game-based methods and strategies for training and education. Pfeiffer. DOI: https://doi.org/10.1145/2207270.2211316
Kalogiannakis, M., Papadakis, S., & Zourmpakis, A. I. (2021). Gamification in science education. A systematic review of the literature. Education Sciences, 11(1), 22. https://doi.org/10.3390/educsci11010022 DOI: https://doi.org/10.3390/educsci11010022
Keller, J. M. (1987). Development and use of the ARCS model of instructional design. Journal of Instructional Development, 10(3), 2-10. DOI: https://doi.org/10.1007/BF02905780
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707-762). Information Age Publishing.
Kitchenham, B., & Charters, S. (2007). Guidelines for performing systematic literature reviews in software engineering (Technical Report EBSE-2007-01). Keele University.
Koivisto, J., & Hamari, J. (2019). The rise of motivational information systems: A review of gamification research. International Journal of Information Management, 45, 191-210. https://doi.org/10.1016/j.ijinfomgt.2018.10.013 DOI: https://doi.org/10.1016/j.ijinfomgt.2018.10.013
Kuo, M. S., & Chuang, T. Y. (2016). How gamification motivates visits and engagement for online academic dissemination: An empirical study. Computers in Human Behavior, 55, 16-27. https://doi.org/10.1016/j.chb.2015.08.025 DOI: https://doi.org/10.1016/j.chb.2015.08.025
Maslow, A. H. (1943). A theory of human motivation. Psychological Review, 50(4), 370-396. DOI: https://doi.org/10.1037/h0054346
Piaget, J. (1970). Psicología y pedagogía. Ariel.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1-36. https://doi.org/10.1007/BF00302715 DOI: https://doi.org/10.1007/BF00302715
Siemens, G. (2004). Connectivism: A learning theory for the digital age. International Journal of Instructional Technology and Distance Learning, 2(1), 3-10.
Siemens, G. (2006). Connectivism: Learning and knowledge today. EducationAU.
Sun, J. C. Y., & Hsieh, P. H. (2018). Gamification in education: A study of the effects of gamification on students' learning motivation and achievement. Journal of Educational Computing Research, 56(6), 819-843.
Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68-78. https://doi.org/10.1037/0003-066X.55.1.68 DOI: https://doi.org/10.1037//0003-066X.55.1.68
Vigotsky, L. S. (1978). El papel del juego en el desarrollo. En Mind in society: The development of higher psychological processes. Harvard University Press.
Wang, F., & Hannafin, M. J. (2005). Design-based research and technology-enhanced learning environments. Educational Technology Research and Development, 53(4), 5-23. DOI: https://doi.org/10.1007/BF02504682
Werbach, K., & Hunter, D. (2012). For the win: How game thinking can revolutionize your business. Wharton Digital Press.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Ramón Antonio Abancín Ospina, Andrés Eloy Salazar Domínguez, Lourdes Emperatriz Paredes Castelo, Carlos Eduardo Cova Salaya
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.
