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

2025-10-07

AI Summary

This study investigates students’ differential preferences for AI’s multifaceted roles—tutor, tool, collaborator, and peer—in mathematical modeling, and examines the underlying cognitive foundations. Method: A randomized controlled experiment was conducted, integrating psychometric scales with behavioral data to quantify significant associations among design thinking, computational thinking, and mathematical modeling self-efficacy, while identifying role-preference patterns across diverse learner backgrounds. Contribution/Results: The study provides the first empirical evidence that students’ cognitive dispositions significantly predict their AI role selections, revealing pronounced inter-group heterogeneity—not a universal preference. Based on these findings, we propose a learner-characteristic–informed framework for personalized AI support, offering both theoretical grounding and actionable design principles for adaptive, learner-centered AI-augmented mathematical modeling instruction.

Technology Category

• Humans and AI: Learning Human Values and Preferences
• Machine Learning: Learning Preferences or Rankings
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Mathematical modelling (MM) is a key competency for solving complex real-world problems, yet many students struggle with abstraction, representation, and iterative reasoning. Artificial intelligence (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.

Problem

• Investigating student preferences for AI roles in mathematical modeling
• Examining relationships between design thinking and computational thinking
• Identifying how learner dispositions shape expectations for AI support

Innovation

• AI roles include tutor, tool, collaborator, and peer
• Randomized controlled trial reveals student preferences
• Design thinking and computational thinking influence AI role choice