This article discusses the implementation of technologies of online learning in the mode of massive open online courses, namely, online classes, which are considered as a platform for distance learning and interactive communication between students and teacher. These technologies allow to provide the choice of content, rate, forms of work for students, to increase level of individualization and personification of education, to facilitate learning irrespective of place and time of being, to decrease subjectiveness of evaluation of learning results, to make the learning process more accessible. Theoretical foundations of connectivism are considered as a learning theory implementing the learning process on the basis of online information technologies. This approach changes the role of the teacher, who, acting as a tutor, regulates the pace and volume of students' work, organizes the exchange of information, thereby creating a community. This article determines the reasons and features of creation of communities of teachers and students during studying in massive open online course. In the frames of this study, network community is considered as a group of students and teachers participating in interactive communication by means of network tools, social networks and messengers. This communication format allows to solve the problems of formation not only of subject but also of meta-subject results of learning, namely, communicative properties of students. The features of construction of communicative activity in these communities are exemplified by the course titled Preparing students for USE in mathematics (profile level), implemented in Volgograd State Socio- Pedagogical University on Miroznai platform. Examples of classes are discussed, each being devoted to solution to one of the task types presented in ESU in mathematics of profile level. Analysis of execution of tests proposed in the course demonstrates that the results of the considered students are somewhat higher than those of students studying in isolation.