Adaptive Learning and Control in E-Learning Under the Dominant Forgetting Hypothesis

In the modern paradigm of education, adaptive learning and support of its full cycle by methods, criteria, models and technologies are relevant. Especially important is the application of intelligent learning systems with individualization of the process and learning profile (“digital twins”). The development of adaptive learning requires the analysis of the learning process, its objects and subjects, connections, as well as the transition to new competencies and models of process development based on motivations. In this paper, a system analysis of adaptive learning, a number of classical infological, mathematical models and algorithms of adaptation is carried out. Methods of analysis and synthesis of systems, systems engineering, mathematical modeling and identification algorithms, in particular, the apparatus of differential equations are used. The adaptability of learning is considered taking into account the difficulty of memorization and the ease of forgetting the learning material being mastered. The main results of this study are the system analysis and formulation of the principles of adaptive learning by analogy with the principles of D. Hitchins, as well as the analysis of the possibilities of self-organization of adaptive learning. Mathematical models (deterministic and stochastic) of the process of learning material assimilation with a sub-model of its forgetting are proposed and investigated in the article. Using these models, model situational scenarios (experiments) on identification of parameters and states of the trajectory of the learning process development are constructed and investigated. The relation of adaptive learning to the digital learning paradigm is emphasized. A general algebraic formalization of the adaptive system in the form of a cognitive tuple of object-attributes is proposed. The given results can be applied in practice, for example, in adaptive testing and control of students’ knowledge. #CSOC1120