Evaluating AI, Traditional, and Hybrid Learning Effectiveness: A Compartmental Model with APOS-Defined Mastery

Abstract

This paper extends the Dynamic Peer Learning Evaluation (DPLE) model, it is a refinement of the Traditional versus Peer Learning (TPL) model, along three structural dimensions. First, the peer-learning pathway is redefined as an AI-assisted learning pathway. This reflects the growing role of conversational and adaptive AI tutoring systems in providing on-demand, dialogic support once offered only by human peers. Second, a hybrid compartment is introduced to represent students who use both traditional instruction and AI-assisted learning at the same time. Under a strict two-pathway structure, these students are indistinguishable from single-pathway learners. Third, the Mastery compartment is redefined using APOS theory (Action, Process, Object, Schema). Under this definition, mastery is achieved only when a student reaches the Schema level of conceptual understanding, not by an unspecified notion of curriculum completion. APOS is used strictly as a measurement definition for the Mastery state. It is not modelled as an internal transition sequence within the ODE system. The resulting model has five compartments: Unengaged (U), Traditional learners (T), AI-assisted learners (A), Hybrid learners (H), and Mastery (M). It is governed by a system of nonlinear ordinary differential equations with interaction-driven recruitment and hybridisation terms. The model also introduces the Relative Mastery Efficiency (RME), a normalised index that expresses each pathway's mastery transition rate as a proportion of the fastest-performing pathway. This allows traditional, AI-assisted, and hybrid learning to be ranked together. A seven-step application procedure is also provided for practitioners. It extends the DPLE procedure with an APOS-based mastery-assessment step. As with the TPL and DPLE models, the DHLE model is presented here as a fully developed theoretical framework, ahead of empirical validation, which is now ready to proceed using longitudinal classroom data.