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.