Modelling Strategic Patterns in High School Students' Mathematical Problem Solving: An AI-Based Approach Integrating Simulated Data and Clustered Process Analysis

Andy Cao^1,2*

• ¹University of Malaya, Kuala Lumpur, Malaysia
• ²Universiti Malaya Faculty of Education, Federal Territory of Kuala Lumpur, Malaysia

This study investigates high school students' problem-solving strategies in number-pattern tasks using an AI-based approach that integrates simulated data and cluster analysis. We generated a simulated dataset of synthetic data representing five documented strategies, namely recursive, explicit-formula, guess-and-check, visual, and linear misconception and validated whether unsupervised clustering could recover these patterns. K-means successfully identified clusters with substantial internal cohesion (Silhouette≈0.60) and external validity (Adjusted Rand Index≈0.65), demonstrating that planted strategy profiles can be rediscovered. Robustness was confirmed through cross-validation, algorithmic triangulation, and sensitivity tests, indicating the stability of the discovered structures. To assess external validity, we applied the same pipeline to real student log data from an online learning platform. Despite noisier behaviour and coarser features, comparable clusters emerged (e.g., efficient solvers, guess-heavy learners, hint-dependent students), aligning with theoretical strategy categories while revealing new patterns such as productive help-seeking. This research provides a validated taxonomy of problem-solving strategies through clustering, bridging simulated and authentic data and illustrate how these clusters can inform adaptive teaching and intelligent tutoring, offering concrete pathways for tailoring instruction to students' strategic profiles.