Developing Students' Mathematical Competencies Based on the Competency-Based Approach in the Modern Educational System

The need to adapt the educational process to the requirements of the modern information society, in which analytical thinking, problem-solving skills, and the ability to work with quantitative information are of particular importance. Traditional approaches to teaching mathematics, which are mainly focused on memorizing algorithms and completing routine tasks, do not fully ensure the preparation of competitive graduates. In this regard, the transition to a competency-based model of education becomes especially significant. To analyze the theoretical foundations and practical aspects of forming students’ mathematical competencies based on the competency-based approach in the modern educational system. Special attention is given to the structure of mathematical competencies, which includes logical thinking, mathematical modeling, interpretation of results, use of digital technologies, as well as the ability to apply mathematical knowledge in real-life situations. The study also examines the pedagogical conditions for the effective implementation of the competency-based approach. These include the integration of practice-oriented tasks into the educational process, the use of active and interactive teaching methods, the development of students’ independent learning activities, and the application of modern information and communication technologies. In this context, the role of the teacher is transformed: the teacher acts as an organizer and coordinator of the educational process, promoting students’ cognitive activity and supporting their individual learning trajectories. The implementation of the competency-based approach in mathematics teaching contributes to a significant improvement in the quality of knowledge acquisition and the development of stable mathematical competencies among students. A positive dynamic is observed in the formation of skills to apply mathematical knowledge in practical and interdisciplinary situations. The competency-based approach contributes to the formation of sustainable mathematical competencies, the development of students’ cognitive independence, and the enhancement of the practical orientation of mathematics education in the context of modern educational reforms.