IMPLEMENTATION OF THE CONCEPT OF KNOWLEDGE FOUNDATION IN THE PRE-SERVICE MATHEMATICS TEACHERS’ PROFESSIONAL TRAINING

Abstract

According to university standards, in addition to elementary mathematics and methods of teaching mathematics, students study foundational courses in higher mathematics, which consider the material that goes far beyond the school curriculum. At the same time, students have the wrong idea that they are being taught not material that will be useful to them in their future professional activities. One of the main tasks in the study of higher mathematics in institutions of higher education is the formation of students' awareness that without knowledge of the scientific foundation of elementary mathematics, they will not become highly qualified mathematics teachers. It is necessary to generalize and systematize the concepts of the school mathematics course, investigate their properties, and form a scientific view of them from the standpoint of higher mathematics (in particular, the possibility of introducing relevant concepts and theories based on the axiomatic method). The authors suggest introducing the concept of foundation of knowledge of pre-service mathematics teachers during their professional training. This idea is demonstrated in the example of the formation, systematization, and deepening of students' knowledge about the function, the possibility of introducing basic functions in a single way, which would make it possible to clarify their main content and identify common features. Such a universal approach is possible within the framework of the axiomatic definition of basic functions through functional equations. This example confirms the fact that pre-service mathematics teachers' awareness of the "consequences" of one or another discipline for professional activity, and understanding of cross-curricular connections is possible through the implementation of the concept of foundation of students' knowledge in the course of their professional training.