The article presents to the problem area of developing the professional competence of a teacher in the aspect of digitalization of the educational space. This circumstance predetermines the current tasks of the teacher, as well as the priority directions for the development of the professional development system to be responsible for the mastery by teachers of professional skills and functions, that are in demand in the digital educational space. Consequently, the goal of the study is to identify effective ways to develop the digital competence of a teacher. So, the article analyzes modern approaches to defining the concepts of «digital competence of a teacher» and «information and communication competence» in the scientific literature. The author highlights the structural components of a teacher’s digital competence, which include the teacher’s ability to adapt the teaching methods and the content to the conditions of the digital educational space, the teacher’s knowledge of advanced methods of independently preparing digital teaching materials, the ability to use software and modern services in professional activities. The levels of development of a teacher’s digital professional competence are also determined: the micro level, which implies direct interaction between the teacher and students; meso-level, including the design and implementation of an educational course using the capabilities of the educational infrastructure; macro level, characterizing the specifics of the organization and management of the educational process. The author proposes the most effective ways to develop a teacher’s digital competence in the postgraduate education system: organizing problem-based seminars on topical issues of digital didactics; work of a virtual methodological office; organization of network remote support. Particular attention is paid to network remote support, expanding the capabilities and the potential of the system of additional professional education in the development of digital professional competence of a modern teacher; providing new conditions for organizing the process of advanced training, methods of information exchange, access to enormous volumes of educational and methodological resources; allowing the teacher to adapt the content of training students taking into account the professional difficulties of teachers, and the listener to choose the optimal pace of work with the educational material and build a development trajectory taking into account their own professional deficits. In conclusion, the author states the fact that network remote support ensures the implementation of such functions as organizational, training, communicational, developing, evaluation and performance.

Keywords: digital competence, teacher training, network remote support