Investigating Students' Preferences for AI Roles in Mathematical Modelling: Evidence from a Randomized Controlled Trial

Abstract: Mathematical modelling (MM) is a key competency for solving complex real-world problems, yet many students struggle with abstraction, representation, and iterative reasoning. AI has been proposed as a support for higher-order thinking, but its role in MM education is still underexplored. This study examines the relationships among students' design thinking (DT), computational thinking (CT), and mathematical modelling self-efficacy (MMSE), and investigates their preferences for different AI roles during the modelling process. Using a randomized controlled trial, we identify significant connections among DT, CT, and MMSE, and reveal distinct patterns in students' preferred AI roles, including AI as a tutor (providing explanations and feedback), AI as a tool (assisting with calculations and representations), AI as a collaborator (suggesting strategies and co-creating models), and AI as a peer (offering encouragement and fostering reflection). Differences across learner profiles highlight how students' dispositions shape their expectations for AI. These findings advance understanding of AI-supported MM and provide design implications for adaptive, learner-centered systems.