Influence of interactive teaching methods on mathematical knowledge acquisition

The purpose of the study was to assess the expediency and effectiveness of using interactive methods in teaching mathematics in institutions of higher education. Special attention was paid to the analysis of such methods as group discussions, role-playing games, multimedia technologies and project activities. The results showed that these methods not only increase the level of assimilation of mathematical knowledge, but also contribute to the development of practical skills, critical thinking and the ability to analyze the material in depth. Within the framework of the research, the implementation of the method of competence ratios was justified, which allows to evaluate the effectiveness of interactive learning according to five key components: meaningful, practical, logical-structural, technological and informational. The application of this method contributes to the comprehensive analysis of the effectiveness of interactive approaches due to the use of extensive parameters. The evaluation is based on the measurement of such competencies as the ability to work in a team, the adaptability of knowledge to practical situations, analytical thinking and the ability to justify one's decisions. It was found that interactive methods increase students' motivation, reduce the level of stress during learning, and improve understanding of multi-format educational mathematical material. The results of the study substantiate the need for a wider implementation of interactive methods in teaching mathematics, thus forming recommendations for the professional use of digital platforms and multimedia technologies, which contribute to the individualization of the educational process and help students to learn the proposed educational material more deeply and qualitatively. The study confirms that the systematic use of interactive methods in higher education is an effective means of improving the quality of mathematics education and ensuring its compliance with modern professional requirements. The results of the study can be used to develop new curricula and courses in mathematics, create interactive manuals and digital platforms, which will optimize the process of learning and increase student success. The study is also valuable for educational reforms aimed at modernizing teaching and increasing its efficiency.