Abstract: The article the role and place of the course «Elementary mathematics» in the subject-methodical preparation of the future teacher of mathematics at the present stage of higher pedagogical education.

Abstract: The article presents using the van Hiele theory of geometric thinking for the organization of mixed training of students of the pedagogical Department of the N.I. Lobachevsky Institute of mathematics and mechanics KFU on the basis of SPOC course «Elementary mathematics: Plane geometry». Training includes the use of various IT-techniques and tools that can improve the quality of learning and form the necessary professional competence of the future teacher of mathematics. The course implements the technology of project-modular and inverted learning.

Abstract: In the article describes the principles of creating an educational space at the master's level that meets new meanings in education, and offers effective forms of interaction of participants in the educational process, corresponding to the selected principles.

Abstract: The problems of teaching elementary mathematics for foreign citizens at Perm National Research Polytechnic University are considered.