AI-supported hybrid learning in exploratory geometry: For higher education

Sara Cruz 1 2 3 * , Floriano Viseu 3
More Detail
1 Applied Artificial Intelligence Laboratory, Polytechnic Institute of Cávado and Ave, Barcelos, PORTUGAL
2 Center for Research and Innovation in Education, Polytechnic Institute of Porto, Porto, PORTUGAL
3 Research Center on Education, University of Minho, Braga, PORTUGAL
* Corresponding Author
EUR J SCI MATH ED, Volume 14, Issue 3, pp. 471-488. https://doi.org/10.30935/scimath/18798
Published: 23 June 2026
OPEN ACCESS   24 Views   10 Downloads
Download Full Text (PDF)

ABSTRACT

The abstract nature of mathematical concepts often impedes learners’ comprehension, particularly within geometry, a difficulty accentuated at the transition from secondary to higher education, where students shift from procedural fluency to formal, axiomatic reasoning. The goal of this study was to understand how a hybrid flipped learning design, mediated by Moodle and supported by artificial intelligence (AI), articulating tangram, GeoGebra, and Polypad, improves performance in geometry and qualifies students’ geometric reasoning, by mapping the appropriation of AI-generated explanations in asynchronous interactions. Methodologically, we adopted a mixed-methods, single-group pre-/post-design (n = 22) within a hybrid flipped learning cycle streamlined to asynchronous preparation via Moodle and AI tools and studio-style, in-class sessions; qualitative data comprised forum posts analyzed through directed content analysis. Pre-/post-comparisons showed statistically significant gains on all four domains, robust to parametric and non-parametric tests; effect sizes ranged from large to very large, with distributional shifts across outcomes. Individually, improvement was most widespread for spatial reasoning and mathematical problem-solving; geometric properties improved for 15 students; geometric deduction was heterogeneous. Qualitatively, students increasingly named and justified properties, described transformations with greater precision, and used AI-generated explanations as scaffolds to verify reasoning, explore alternative representations, and correct misconceptions while maintaining authorship of arguments. These findings indicate the promise of multimodal, AI-supported hybrid designs for early undergraduate geometry learning, while acknowledging limits of causal inference, small sample size, and absent follow-up.

CITATION

Cruz, S., & Viseu, F. (2026). AI-supported hybrid learning in exploratory geometry: For higher education. European Journal of Science and Mathematics Education, 14(3), 471-488. https://doi.org/10.30935/scimath/18798

REFERENCES

  • A’ini, Q., & Khoiriyah, R. (2024). Merevolusi pendidikan dengan kecerdasan buatan chatbots: Meningkatkan pembelajaran dan penilaian [Revolutionizing education with artificial intelligence chatbots: Improving learning and assessment]. Jurnal Multidisiplin Ibrahimy, 2(1), 54-71. https://doi.org/10.35316/jummy.v2i1.5510
  • Abar, C. A. A. P., & de Almeida, M. V. (2024). Contributos do GeoGebra para exploração do pensamento computacional no contexto da geometria [Contributions of GeoGebra to the exploration of computational thinking in the context of geometry]. REMATEC, 19(48), Article e2024003. https://doi.org/10.37084/REMATEC.1980-3141.2024.n48.e2024003.id590
  • Abrahamson, D., Tancredi, S., Chen, R. S. Y., Flood, V. J., & Dutton, E. (2023). Embodied design of digital resources for mathematics education: Theory, methodology, and framework of a pedagogical research program. In B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook of digital resources in mathematics education (pp. 1-34). Springer. https://doi.org/10.1007/978-3-030-95060-6_8-1
  • Al Hakim, V. G., Meng-Heng, L. I. N., Chang, C. Y., Jen-Hang, W. A. N. G., Chang, C. K., Zhuang, Y., & Su-Hang, Y. A. N. G. (2024). Marrying physical and virtual realms: An embodied, multi-modal approach to situational learning in digital reality. The 32nd International Conference on Computers in Education, 2024, 1-11. https://doi.org/10.58459/icce.2024.4882
  • Barbosa, A., & Vale, I. (2025). Rebuilding manipulatives through digital making in teacher education. STEM Education, 5(4), 515-545. https://doi.org/10.3934/steme.2025025
  • Boltayevich, E. B., Ergashevna, Y. N., Ganiyevna, A. N., Masharipovich, M. M., Zaynobidinovna, K. M., & Batyrovna, U. M. (2024). LMS information system development concept and principles. International Conference of Computer and Informatics Engineering, 2024, 1-7. https://doi.org/10.1109/IC2IE63342.2024.10748038
  • Brum, E. D. C. M., Viera, M. A., & Ferreira, R. K. A. (2023). Aprendizagem significativa em matemática por meio da utilização de materiais concretos no ensino médio: Um ensaio em construção [Meaningful learning in mathematics through the use of concrete materials in high school: An essay in progress]. Revista Ibero-Americana de Humanidades, Ciências e Educação, 9(3), 365-380. https://doi.org/10.51891/rease.v9i3.8794
  • Clark-Wilson, A., Robutti, O., & Thomas, M. (2020). Teaching with digital technology. ZDM Mathematics Education, 52, 1223-1242. https://doi.org/10.1007/s11858-020-01196-0
  • Cohn, C., Snyder, C., Fonteles, J. H., TS, A., Montenegro, J., & Biswas, G. (2025). A multimodal approach to support teacher, researcher and AI collaboration in STEM+C learning environments. British Journal of Educational Technology, 56(2), 595-620. https://doi.org/10.1111/bjet.13518
  • Costa, J. F. S. (2023). Aprendendo números inteiros: Uma experiência baseada na teoria dos campos conceituais [Learning integers: An experience based on the theory of conceptual fields]. Revista de Educação Matemática, 20(1), Article e023104. https://doi.org/10.37001/remat25269062v20id483
  • Da Costa, N. M. L., & Prado, M. E. B. B. (2015). A integração das tecnologias digitais ao ensino de matemática: Desafio constante no cotidiano escolar do professor [The integration of digital technologies into mathematics teaching: A constant challenge in the teacher’s daily school life]. Perspectivas da Educação Matemática, 8(16). https://periodicos.ufms.br/index.php/pedmat/article/view/1392
  • Dabingaya, M. (2022). Analyzing the effectiveness of AI-powered adaptive learning platforms in mathematics education. Interdisciplinary Journal Papier Human Review, 3(1), 1-7. https://doi.org/10.47667/ijphr.v3i1.226
  • Dalmon, D. L., Isotani, S., & de Oliveira Brandão, L. (2010). Melhorando a geometria interativa com o uso de tutores rastreadores de padrões: iGeom e CTAT [Improving interactive geometry with the use of pattern-tracing tutors: iGeom and CTAT]. Anais do XVI Workshop de Informática na Escola, 2020, 1413-1416. https://doi.org/10.5753/wie.2010.25420
  • Gökçearslan, S., Tosun, C., & Erdemir, Z. G. (2024). Benefits, challenges, and methods of artificial intelligence (AI) chatbots in education: A systematic literature review. International Journal of Technology in Education, 7(1), 19-39. https://doi.org/10.46328/ijte.600
  • Herrera, L. M., Juárez Ordóñez, S., & Ruiz-Loza, S. (2024). Enhancing mathematical education with spatial visualization tools. Frontiers in Education, 9, Article 1229126. https://doi.org/10.3389/feduc.2024.1229126
  • Hill, C. J., Bloom, H. S., Black, A. R., & Lipsey, M. W. (2008). Empirical benchmarks for interpreting effect sizes in research. Child Development Perspectives, 2(3), 172-177. https://doi.org/10.1111/j.1750-8606.2008.00061.x
  • Hoffmann, D. S., Martins, E. F., & Basso, M. V. D. A. (2009). Experiências física e lógico-matemática em espaço e forma: Uma arquitetura pedagógica de uso integrado de recursos manipulativos digitais e não-digitais [Physical and logical-mathematical experiences in space and form: A pedagogical architecture for the integrated use of digital and non-digital manipulative resources]. Anais Do Simposio Brasileiro De Informatica Na Educacao. https://bitly.cx/bkfv0
  • Holmes, W., Bialik, M., & Fadel, C. (2019). Artificial intelligence in education promises and implications for teaching and learning. Center for Curriculum Redesign. https://curriculumredesign.org/wp-content/uploads/AIED-Book-Excerpt-CCR.pdf
  • Jain, V., Singh, I., Syed, M., Mondal, S., & Palai, D. R. (2024). Enhancing educational interactions: A comprehensive review of AI chatbots in learning environments. 11th International Conference on Reliability, Infocom Technologies and Optimization (Trends and Future Directions), 2024, 1-5. IEEE. https://doi.org/10.1109/ICRITO61523.2024.10522392
  • Janisch, A. B. L., & Jelinek, K. R. (2023). Atividades experimentais no ensino da matemática mediadas pela prática docente e nas perspectivas vygotskiana, piagetiana e ausubeliana [Experimental activities in mathematics teaching mediated by teaching practice and from Vygotskian, Piagetian, and Ausubelian perspectives]. Revista de Iniciação à Docência, 8(1), Article e12608. https://doi.org/10.22481/riduesb.v8i1.12608
  • Kahneman, D. (2011). Thinking, fast and slow. Farrar, Straus and Giroux. https://www.bibsonomy.org/bibtex/a1400a299a00de009ec8eda73e6289af
  • Kampff, A. J. C., Machado, J. C., & Cavedini, P. (2004). Novas tecnologias e educação matemática [New technologies and mathematics education]. Revista Novas Tecnologias na Educação, 2(2), 1-11. https://doi.org/10.22456/1679-1916.13703
  • Leikin, R., & Guberman, R. (2023). Creativity and challenge: Task complexity as a function of insight and multiplicity of solutions. R. Leikin (Ed.), Mathematical challenges for all (pp. 325-342). https://doi.org/10.1007/978-3-031-18868-8
  • Lieban, D. (2023). Entre o digital e o físico: Integrando recursos com o GeoGebra para práticas criativas em espaços de aprendizagem [Between the digital and the physical: Integrating resources with GeoGebra for creative practices in learning spaces]. Revista do Instituto GeoGebra Internacional de São Paulo, 12(2), 67-88. https://doi.org/10.23925/2237-9657.2023.v12i2p067-088
  • Margolis, J. (2020). Multiple team membership: An integrative review. Small Group Research, 51(1), 48-86. https://doi.org/10.1177/1046496419883702
  • Marshall, H. W., & Kostka, I. (2020). Fostering teaching presence through the synchronous online flipped learning approach. TESL-EJ, 24(2), 1-14. https://eric.ed.gov/?id=EJ1268565
  • Meylani, R. (2024). A critical glance at adaptive learning systems using artificial intelligence: A systematic review and qualitative synthesis of contemporary research literature. Batı Anadolu Eğitim Bilimleri Dergisi, 15(3), 3519-3547. https://doi.org/10.51460/baebd.1525452
  • Mustafa, A. N. (2024). The future of mathematics education: Adaptive learning technologies and artificial intelligence. International Journal of Science and Research Archive, 12(1), 2594-2599. https://doi.org/10.30574/ijsra.2024.12.1.1134
  • National Council of Teachers of Mathematics. (2024). Artificial intelligence and mathematics teaching: A position of the National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. https://www.nctm.org/standards-and-positions/Position-Statements/Artificial-Intelligence-and-Mathematics-Teaching/
  • Neha, F., & Bhati, D. (2025). DeepSeek models in STEM education: Capabilities, applications, and challenges. TechRxiv. https://doi.org/10.36227/techrxiv.174198447.71647707/v1
  • Rafee, B. M., Ramesh, V., Zaheed, S. M. & Khatoon, S. (2024). Can hybrid learning change education? International Journal of Social Science, 1(2), 1-16. https://nsfjournals.com/article-files/pdf/h3UiHSGPbITDkMqnRa3A-1715971162.pdf
  • Rebolledo-Mendez, G., Huerta-Pacheco, N. S., Baker, R. S., & du Boulay, B. (2022). Meta-affective behaviour within an intelligent tutoring system for mathematics. International Journal of Artificial Intelligence in Education, 32(1), 174-195. https://doi.org/10.1007/s40593-021-00247-1
  • Redecker, C. (2017). European framework for the digital competence of educators: Digcompedu. Publications Office of the European Union. https://doi.org/10.2760/159770
  • Roca, M. D. L., Chan, M. M., Garcia-Cabot, A., Garcia-Lopez, E., & Amado-Salvatierra, H. (2024). The impact of a chatbot working as an assistant in a course for supporting student learning and engagement. Computer Applications in Engineering Education, 32(5), Article e22750. https://doi.org/10.1002/cae.22750
  • Rocha, R. P., & da Silva, M. D. F. (2021). Uma revisão sistemática abordando o tangram, o GeoGebra e as opções de isometria do plano [A systematic review addressing the tangram, in GeoGebra, and the options for isometric plane calculations]. Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 23(1), 741-768. https://doi.org/10.23925/1983-3156.2021v23i1p741-768
  • Sain, Z. H., Vasudevan, A., & Lama, A. V. (2024). The emerging future of AI chatbots in higher education. Jurnal Ilmiah Didaktika, 25(1), 93-107. https://doi.org/10.22373/jid.
  • v25i1.25583
  • Santos-Trigo, M. (2024). Problem solving in mathematics education: Tracing its foundations and current research-practice trends. ZDM Mathematics Education, 56, 211-222. https://doi.org/10.1007/s11858-024-01578-8
  • Skill, T. D., & Young, B. A. (2002). Embracing the hybrid model: Working at the intersections of virtual and physical learning spaces. New Directions for Teaching and Learning, 2002(92), 23-32. https://doi.org/10.1002/tl.76
  • Subiyantoro, S., Degeng, I. N. S., Kuswandi, D., & Ulfa, S. (2023). Exploring the impact of AI-powered chatbots (ChatGPT) on education: A qualitative study on benefits and drawbacks. Jurnal Pekommas, 8(2), 157-168. https://www.semanticscholar.org/paper/Exploring-the-Impact-of-AI-Powered-Chatbots-(Chat-A-Subiyantoro-Degeng/b05f684a379727a47e279e12f23b1ae4308f3ae7
  • Tang, C. M., & Chaw, L. Y. (2024). Student learning performance evaluation: Mitigating the challenges of generative AI chatbot misuse in student assessments. Proceedings of the European Conference on E-Learning, 23(1), 357-364. https://doi.org/10.34190/ecel.23.1.2567
  • Tohari, B., & Rahman, A. (2024). Konstruktivisme Lev Semonovich Vygotsky dan Jerome Bruner: Model pembelajaran aktif dalam pengembangan kemampuan kognitif anak [Constructivism of Lev Semonovich Vygotsky and Jerome Bruner: An active learning model in the development of children’s cognitive abilities]. Nusantara: Jurnal Pendidikan Indonesia, 4(1), 209-228. https://doi.org/10.14421/njpi.2024.v4i1-13
  • Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352-402. https://doi.org/10.1037/a0028446
  • Wang, T., Lund, B. D., Marengo, A., Pagano, A., Mannuru, N. R., Teel, Z. A., & Pange, J. (2023). Exploring the potential impact of artificial intelligence (AI) on international students in higher education: Generative AI, chatbots, analytics, and international student success. Applied Sciences, 13(11), Article 6716. https://doi.org/10.3390/app13116716
  • Zawacki-Richter, O., Marín, V. I., Bond, M., & Gouverneur, F. (2019). Systematic review of research on artificial intelligence applications in higher education–Where are the educators? International Journal of Educational Technology in Higher Education, 16, Article 39. https://doi.org/10.1186/s41239-019-0171-0