The method of "small groups" in teaching mathematics to students of technical universities

The article considers an approach to resolving the contradiction between the need to activate the educational and cognitive activities of students aimed at developing the mathematical thinking of future engineers, taking into account individual abilities and the established system of organizing classroom classes in higher mathematics, focused on front-line activities. The purpose of the study is to adapt the "small group" methodology for the study of mathematics by undergraduates, to develop and test educational and methodological support for this activity. The research hypothesis is that improving the effectiveness of mathematical and creative thinking formation can be achieved by organizing "small group" learning at different stages of learning new knowledge and developing intellectual skills, which provides: consideration of the psychological and pedagogical features and didactic properties of this method, as well as the specific conditions of its implementation in teaching mathematics; compliance with the specifics of the sections of the subject, the stage of cognitive activity and the didactic tasks of this stage; creation of a task bank and their typology by type of activity; development of methods for monitoring and organizing students' classroom work. Students' work in small groups is considered as one of the methods of interactive learning. The didactic properties and functions of the mathematics teaching methodology in collaboration are described. A model of interaction is defined, and its correspondence to the elements of cognitive activity and educational tasks is theoretically substantiated. The typological features of tasks for the "small group" methodology are indicated. The controlled results, semantic correspondences and computational criteria of learning in the development of computational skills, critical thinking, and analysis of results are determined. The positive aspects, possible difficulties are noted and the results of the application of the considered methodology are presented. The practical recommendations are aimed at organizing classroom classes in higher mathematics at technical universities, as well as at using advanced training courses for higher school teachers.