Bridging MOOCs, Smart Teaching, and AI-Assisted Learning: A Unified Quantitative Model

MOOCs, Smart Teaching (ST), and AI-assisted learning support different stages of higher education, yet a unified quantitative basis for analyzing their contributions, course design, and resource allocation remains limited. This study develops a mathematical model integrating MOOC-based pre-class learning, ST-based in-class adaptation, and AI-assisted post-class personalization. Learner mastery is represented as a bounded multidimensional state, with a common exponential learning-response function describing how instructional resources reduce remaining knowledge gaps. The stages differ in their allocation rules: predefined course-content emphasis for MOOCs, feedback-driven class-level adaptation for ST, and individualized gap-based allocation for AI-assisted learning. Simulations across 100 independently generated classes demonstrate stable cumulative progression and quantify stage-wise gains, while budget analysis reveals diminishing returns from additional AI support. For a fixed learner and learning mechanism, varying course-content emphasis shows a strong association between course-learner alignment and post-MOOC mastery. An optimal AI allocation is also derived under a fixed budget: supported components reach a common residual mastery gap, while components below this threshold receive no resources. A controlled comparison yields over 14% greater learning gain than proportional allocation. These analyses make the instructional process quantitatively analyzable and provide a basis for examining course-learner fit and coordinating limited learning resources. The model offers an analytical foundation for instructional decisions, with practical application requiring empirical estimation of learner states and calibration of learning-response parameters.