Optimal educational intervention strategies for cognitive learning dynamics
Year: 2026
Type: article
Abstract: In this study, a compartmental mathematical model describing learning dynamics within a large educational population is proposed based on concepts inspired by educational neuroscience. The model incorporates key cognitive processes, including working memory, long-term memory consolidation, forgetting dynamics, retrieval practice, and adaptive memory retention. Three optimal control strategies representing spaced repetition, pedagogical support, and dropout reduction interventions are introduced to improve long-term learning outcomes and reduce forgetting. Theoretical analysis is carried out to establish the positivity, boundedness, and existence of solutions. The learning persistence threshold is derived, the equilibrium points are characterized, and the local stability of the learning-free equilibrium is established. In addition, a sensitivity analysis is performed to identify the parameters that most strongly influence the learning persistence threshold. Pontryagin’s Maximum Principle is then applied to characterize the optimal control strategies. Numerical simulations demonstrate that spaced repetition increases the final long-term learner population by approximately 36.04%, while dropout reduction achieves an improvement of about 110.81%. The combined application of the three control strategies provides the best performance, increasing the final long-term learner population by approximately 160.40% compared with the uncontrolled scenario, while substantially reducing forgetting. These results demonstrate that mathematical modeling and optimal control theory provide a useful quantitative framework for analyzing learning dynamics and designing effective neuroscience-inspired educational intervention strategies.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
SDG: Quality education
Open Access status: gold
Estimated APC paid: $1,470
OpenAlex ID: W7213618207