Cognitive modeling of adaptive learning processes

An approach to modeling adaptive learning processes using signed and weighted directed graphs (digraphs) is examined. The vertices of the digraphs represent the characteristics of educational activities. The orientation, signs, and weights of the digraph arcs define the mutual influence of these characteristics. The dynamics of adaptive learning are modeled within digraphs using a specific impulse process algorithm. An external disturbance is introduced into a particular vertex of the digraph, and the propagation of this impulse is analyzed, enabling the prediction of values at other vertices of the digraph. The problem of optimizing the weights of digraph arcs is formulated, and an algorithm for solving it is proposed to achieve stability in the impulse process. Computational experiments on a digraph revealed that the objective function for optimizing the arcs of a weighted digraph is multiextremal. The occurrence of a local minimum is determined by the initial values of the vector of design variables (weights of digraph arcs) and constraints on these variables. Consequently, the qualifications of the developer of the adaptive learning model who assigns these values are crucial. Cognitive models of adaptive learning can be classified as prescriptive and descriptive. Prescriptive models outline what the adaptive learning process should be, while descriptive models depict existing adaptive learning processes and can be utilized to study their effectiveness. The developed methodology for cognitive modeling of adaptive learning processes allows for the prediction of learning outcomes and can be employed in the research, design, and implementation of adaptation mechanisms and intelligent control in e-learning systems, as well as in the didactic training of teachers in the field of e-learning. .