Adaptive Learning in Higher Education: A Stochastic Modeling Approach Revealing Absorbing States and Dominant Adaptive Parameters

Abstract

This study evaluates the effectiveness of adaptive learning methods using an integrated stochastic modeling framework. Empirical analysis based on real data from 30 students, and stochastic simulation-based analysis (DTMC, Monte Carlo, Sobol, and HBM) used for modeling, probabilistic validation, and parameter sensitivity exploration. A Discrete-Time Markov Chain was applied to model transitions in learner ability, and Monte Carlo simulation was used to validate the probabilistic behavior. The Sobol sensitivity method identified the dominant parameters, while Hierarchical Bayesian Modeling accounted for inter-student variability. The findings show consistent upward transitions, with no students regressing to lower ability states and those in the High category remaining in an absorbing state. Sensitivity analysis indicates that adaptivity level (α) has the strongest influence on performance improvement, followed by difficulty ratio (λ) and feedback frequency (β). The Bayesian model explains more than 70% of the variance in learning gains. Overall, the study concludes that stochastic modeling provides a robust framework for evaluating adaptive learning systems and demonstrates that well-designed adaptive mechanisms significantly enhance student performance, with engagement measured through system interaction logs.