Development of Mathematical Reasoning through Artificial Intelligence: A Design-Based Learning Framework

This study investigated cognitive progression in mathematical reasoning following the implementation of an artificial intelligence (AI)-supported learning framework. A longitudinal pretest‒posttest design was used with 500 secondary school students. Mathematical reasoning was assessed across eight domains, and cognitive development was examined via latent profile and transition analyses supported by predictive and Bayesian modeling. The findings revealed consistent improvements across all the reasoning domains and identified four distinct reasoning profiles: novice, developing, strategic, and advanced reasoning. Transition analyses indicated substantial movement toward higher reasoning profiles, particularly along the paths from Novice to Developing, Developing to Strategic, and Strategic to Advanced. Critical evaluation and reflective engagement emerged as the strongest predictors of cognitive progression, whereas the frequency of AI use demonstrated comparatively weaker effects. The use of Bayesian evidence strongly supported the effectiveness of the framework. The findings suggest that AI contributes most effectively to mathematical reasoning when learners engage critically and reflectively with AI-generated content rather than using AI primarily as an answer-producing tool.