Abstract. The article describes the experience of building the interaction between a teacher and fulltime students at the Academy of the FPS of Russia in the context of restrictions on contact work associated with countering the spread of the new corona-virus infection. The aim of the work was to substantiate the importance of operational feedback and competent organization of pedagogical communication within the framework of e-learning. The methodological framework of the study was made up of analysis, synthesis, induction, systematization and generalization. The study was carried out throughout the year in the classroom work on the disciplines of the mathematical cycle with cadets and junior students of economic specialties. As a result, it was found that in order to maintain the quality of education at a proper level, when conducting classes in video-conference mode, it was necessary to combine work in the electronic information and educational environment (hereinafter also referred to as EIEE) of the educational organization with the use of discipline workbooks specially developed by the authors. The structure of the educational process based on the EIEE Moodle, the Zoom program and author's workbooks on the subject is shown. Conclusions are made about the importance of the symbol-by-symbol recording of calculations and analytical formulas and the gradual drawing of graphs for the qualitative mastery of the conceptual apparatus with a high degree of abstractness. The described experience of designing the classes will be useful to the teaching staff of educational organizations of the Federal Penitentiary Service of Russia. Key words: educational technology, e-learning, electronic information and educational environment, teaching methods of mathematical disciplines, video-conference.

In the current sanitary and epidemiological situation and the total transition to a distance format of communication between the teacher and the student, the problem of maintaining the quality of the educational services provided at the proper level becomes especially urgent. One of the options for solving this problem is seen by the authors in a well-established feedback loop with students and a competent organization of pedagogical communication within the framework of e-learning. This article describes the experience of organizing distance communication in the classroom in the disciplines of the mathematical cycle with junior-year students of economic specialties, conducted using video conferencing, electronic information and educational environment and author's workbooks on the subject. The effectiveness of this method is confirmed by the results of checking the residual knowledge of students in mathematics, carried out when licensing their specialty.

The article is about the need of introducing a propaedeutic course of visual or combinatorial geometry, which precedes the systematic study of geometry to resolve children´s problems related to the axiomatic method. The author approves the importance of this course in the formation of geometric preliminary concepts, the development of visual-figurative thinking, positive motivation to study mathematics and the "awakening of thought" among the most gifted schoolchildren. The thematic planning of elective course "Task on Graph Paper", the basic features of solving these tasks and the two possible levels of achievement of the result on a specific example are presented.

Рассматривается использование элементов технологии полного усвоения знаний при проведении занятий по дисциплинам математического цикла в вузе. Приводится структура учебного процесса, организованного на базе данной технологии, с акцентом на выполнение индивидуальных заданий и перечисляются основные требования, предъявляемые к самим заданиям, и положения, на которые следует опираться при построении практических занятий на их основе. Показано, что применение описанной технологии повышает эффективность обучения: активизирует работу студентов во время занятий, вселяет в них уверенность в собственных силах и мотивирует к достижению результатов-получению и усвоению знаний. Ключевые слова: технология полного усвоения знаний, педагогические технологии, организация занятий по математическим дисциплинам, индивидуальные задания по математике.

The article is about the role of communication process both in everyday life and in professional pedagogical activity. The article deals with the disclosure of communication functions in various pedagogical situations related to the teacher’s activities as a source of knowledge, as a researcher of students and as an organizer of collective activity. The importance of taking into account the individual psychological characteristics of the pupils, especially adolescents is noted. The article compares the different classifications of accentuations and considers the results of the experiment to identify them in the tenth graders, the authors provides recommendations on the organization of classes in the study groups and the preferred type of tasks for all types of accentuations described by A.E. Lichko.