Using Hierarchical Bayesian Analysis to Identify At‐Risk Students in Engineering Mathematics Prerequisites

ABSTRACT Engineering educators need practical methods to identify which students are struggling and which course topics require additional instructional support. This study applies hierarchical Bayesian analysis to student performance data from the ASSISTments 2009 dataset containing 446,844 responses from 4151 students across 110 mathematical skills that form critical prerequisites for engineering courses to extract actionable insights for instructors. Our analysis reveals three distinct student performance groups requiring different interventions: a low‐ability group (17.4% of students) needing foundational support, a middle group (49.1%) benefiting from targeted practice, and a high‐ability group (33.5%) requiring enrichment rather than repetition. The analysis also ranks course topics by difficulty, identifying specific skills like “Percent Discount” and “Quadratic Formula” as unexpectedly challenging. For instructors, these findings translate directly to classroom decisions: allocate extra time to the five hardest topics, provide remedial support to the bottom quartile of students, and offer advanced projects to top performers. The hierarchical Bayesian approach achieves strong predictive accuracy (0.831 AUC) while maintaining full interpretability–unlike black‐box machine learning methods, instructors can see why a student or topic is flagged as problematic. This work demonstrates how statistical modeling of routine assessment data can support data‐driven instructional decisions in engineering education.