In modern conditions of modernization of the higher education the problems of vocational training of teachers are actual. Society will be need, first of all, those experts who can generate a large number new, occasionally non-standard decisions, who possess the high degree adaptability, as well as ability and proficiency, "intuition" to select the most effective idea from a set of non-standard ones. Essential change of views of values of modern education demands to create a new educational product, a basis for which is a competence-based approach, constructive teaching where individual motivated data retrieval, its interpretation, processing and analysis for the purpose to obtain new knowledge is a priority instead of information awareness of a trainee, digestion and reproduction of educational material. The most important purpose of modern education is to give to a future expert a certain complex of knowledge and abilities and to create that a trainee has a setting for self-training and self-organization, continuous expansion and increasing knowledge and abilities that is a key for continuation of study during all life. An expert, who possesses research competence, is able actively and productively to analyze the actual information, to create and choose more effective algorithms, resources, technologies, and not just to use ready, sometimes outdated, algorithms and the facts. In my opinion, application of the principles of development of divergent thinking in the field of professional development of a teacher is especially interesting, as is in the broadest sense, area of professional interests of teachers.