Abstract: The article is devoted to one of the urgent problems of modern mathematical education: the formation of educational and research skills of students in the process of solving problems in the subject area “Mathematics”. The levels of formation of educational and research skills of students are described, based on a set of criteria identified by N.A. Menshikova. It is shown that for the formation of educational and research skills of students it is advisable to use blocks of interrelated educational and research tasks that allow students with a low level of formation of educational institutions to participate in solving problems of a higher level of complexity.

Abstract: The problem of the formation of personality activity in teaching mathematics is very complex. The question remains for the teacher of mathematics: what methods to apply so that teaching mathematics is effective and practice-oriented, develops personality activity in collective mathematical activity? The paper describes the specifics of the use of case technology in teaching mathematics.

Abstract:

The article discusses the main positions of using the methodological system of teaching the basics of mathematical informatics of future teachers of mathematics. Cloud technologies are considered as one of the means of learning and as an object of study.

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: The learning activities of students during pedagogical practice are aimed at preparing and conducting computer science lessons, and methodological – at analyzing the success of choosing and implementing various approaches, methods, forms and means when working with pupils. The poster report gives students the opportunity to present the results of these activities in a meaningful, considered and interrelated way.

Abstract: The paper identifies professional tasks that need to be solved by a computer science teacher in a digital educational environment. The author presents the experience of organizing and supporting research activities of students of pedagogical Universities related to the study of the application of digital technologies in education.