ASPECTS OF THE METHODOLOGY OF TEACHING DIFFERENTIAL EQUATIONS: MODERN APPROACHES, DIFFICULTIES AND METHODS OF OVERCOMING THEM

Abstract

The article presents a set of modern methodological approaches to teaching differential equations in higher education, aimed at overcoming common difficulties students face in mastering both theoretical foundations and the applied content of the course. It is noted that the traditional focus on mechanical computation often fails to ensure deep understanding; therefore, it is advisable to shift the emphasis of the learning process toward developing conceptual insight. One of the leading approaches is the use of multiple representations (analytical, graphical, tabular), which enables students to comprehend concepts from different perspectives, develop the ability to switch between forms of information presentation, and gain a better understanding of the nature of differential equation solutions.

An important component is the contextualization of mathematical abstractions through real-world application problems from the natural and socio-economic sciences. Students work with models that have specific meaning – radioactive decay, population dynamics, epidemiological processes, heat exchange, etc. – which reduces anxiety when studying complex topics and increases interest in the subject. Active learning methods – discussions, small groups, inquiry-based questions, analysis of typical mistakes – contribute to the development of critical thinking, independent analysis skills, and collaborative problem-solving.

Significant attention is given to the use of digital technologies. The article shares experience in using computer algebra systems (Maple, Mathematica, MATLAB), visualization tools (GeoGebra, GeomED, STELLA), and even spreadsheets for implementing numerical methods. Examples are provided of educational projects in which students model real-world processes – pendulum motion, disease spread, heat exchange – completing the full cycle from problem formulation to interpretation of results. This approach promotes not only material comprehension but also the development of interdisciplinary thinking, research skills, and confidence in using mathematics as a tool for exploring the real world. The article may be of interest to mathematics educators, methodologists, researchers, and anyone involved in improving mathematics education.