Dobryakov

The paper presents the review of the basic mathematical models used in modern learning systems. We discuss the models of knowledge, the learner, the learning process, the control of educational achievements, and also some other models. As models of knowledge we present the frame-model, formal-logic models and models based on semantic networks. Such classes of the pupil models, as overlay models, imitating models, difference models, perturbation and stereotypical models are considered. From all variety of the training process models the review includes the models based on the Petry networks, probability models and the models based on the finite-state automations. As models of the control of educational achievements of the learner the paper presents the models based on the classical test theory (CTT) and models based on the item response theory (IRT).