Modeling the dynamics of mastering fundamental concepts of discrete mathematics in the context of digitalization of higher education

Abstract

The digital transformation of the higher education system highlights the need to improve the efficiency of mastering fundamental mathematical disciplines, which are characterized by high abstraction and the difficulty of forming stable cognitive structures among students. The purpose of the study is to model the process of mastering the basic concepts of discrete mathematics using digital assessment tools and predicting learning outcomes. Research methods include mathematical modeling, time-series analysis of educational indicators, graph-theoretic methods to describe cognitive connections, statistical evaluation of the level of knowledge formation, and computer modeling using learning analytics collection systems. An approach based on the construction of transition functions between the states of understanding the educational material was applied. Results. The regularities of knowledge formation in discrete mathematics among students of higher education institutions in the context of the digitalization of the educational process are characterized. The peculiarities of mastering key concepts, such as relations, graphs, Boolean functions and combinatorial structures, are analyzed, taking into account the influence of interactive educational platforms, educational analytics systems and adaptive electronic resources. The expediency of mathematical modeling of the learning process as a tool for displaying individual educational trajectories and cognitive load parameters is substantiated. The results demonstrate a non-linear relationship between the intensity of use of digital resources and the level of concept assimilation. It has been established that the combination of adaptive test modules with visualization of data structures increases the accuracy of tasks and reduces the time required to form sustainable knowledge. The proposed model enables identifying critical points in the educational process where cognitive barriers arise and making corrections to educational strategies based on predictive assessments. Conclusions. The effectiveness of formalized approaches to analyzing educational activity in the digital environment has been established. A model is presented that provides a toolkit for optimizing educational content, improving the quality of specialist training, and justifying management decisions in higher education. The obtained results are of practical importance for the development of electronic courses and learning support systems focused on personalized interaction with education seekers.