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

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.