Generative AI as Metacognitive Scaffolding in Undergraduate Mathematics: A Quasi-Experimental Study of Problem-Solving Performance and Engagement

Abstract This study examines whether generative artificial intelligence (GenAI) can improve university students’ mathematical problem-solving when it is designed not as an answer generator but as a metacognitive scaffold. Building on sociocultural scaffolding, self-regulated learning, and Pólya’s problem-solving model, the study tested a 15-week structured GenAI-supported intervention in Calculus I. A cluster-assigned quasi-experimental pre-test/post-test design was implemented with 128 undergraduates distributed across four tutorial sections: two sections used a Socratic GenAI protocol (n = 60), and two sections received traditional instruction using the same weekly problem sets (n = 68). Students’ solutions were scored with a validated analytic rubric aligned with the four Pólya stages, and outcomes were analyzed using ANCOVA with pre-test adjustment and a multilevel sensitivity model for section-level clustering. Results showed a statistically significant adjusted between-group difference favoring the GenAI-supported group, F(1, 125) = 28.76, p < .001, partial eta squared = .187, with the largest stage-specific effects for carrying out the plan and understanding the problem. Student perceptions were highly positive, and cognitive engagement showed the strongest association with performance gains. The study contributes to educational psychology by specifying a testable instructional mechanism: structured GenAI-supported instruction may support mathematical problem solving when prompts elicit planning, monitoring, explanation, and reflection while discouraging direct solution-seeking.