Problem-based learning as a component of higher mathematics education in technical universities

Abstract

The article discusses the effectiveness of problem-based learning as a component of higher mathematics education at technical universities, in particular, on the example of using this method in the training of future engineers. Problem-based learning is defined as one of the most promising approaches to modernizing the educational process in the context of globalization and technological change. The authors explore the main theoretical aspects of problem-based learning, its place in the education system, and the possibilities of its integration into mathematics teaching in technical universities. One of the main problems is the insufficient use of active learning methods in traditional pedagogical practice, which significantly limits the level of student engagement in the learning process. Problem-based learning allows to change the approach to teaching, making learning more interactive, practically oriented and adapted to the needs of future professionals. The article includes a review of existing research on the use of problem-based learning in other educational contexts and analyzes its impact on the effectiveness of the educational process in technical universities. A comparative analysis of the learning outcomes of students working with traditional methods and students using the problem-based approach reveals a significant increase in the efficiency of learning and the development of practical skills among the participants of the experimental group. The pedagogical experiment revealed a significant improvement not only in academic results, but also in students' ability to apply mathematical methods to real-world engineering problems. The authors also offer recommendations for the further development of problem-based learning in technical universities, including the study of its integration with other active learning methods and the use of digital technologies to create problem situations. In addition, the article emphasizes the need to improve teaching approaches that take into account the individual characteristics of students and the specifics of academic disciplines.