Introduction to the school curriculum on the history of discussion issues highlighted a number of problems faced by teachers in their teaching. On the pages of pedagogical publications there are materials that offer different versions of the lessons, but the problem of organizing systematic training of teachers to teach controversial issues of historical science in the process of improving their skills in organizations of additional vocational education remains, as a rule, out of sight. In this article on the example of testing of a modular course "Formation of teachers readiness to teach controversial issues of historical science" in the organization of additional professional education pre-accepted attempt to understand approaches to the management of the development process of innovative training course and its implementation in the traditional educational process of advanced training of teachers of history and political sciences from secondary schools. Starting from the proposed J. K. Babanskii cycle management activities, the authors propose a different layout stages of the cycle, analyze them consistently and argue their necessity for successful testing of the modular course. Two clusters — theoretical "Discussion questions of historical science in the educational process of the organization of general education" and practical "Technologies of studying of discussion questions of historical science in the educational process of the organization of general education" are described in detail. Variants of their implementation are offered for each cluster. Specific recommendations for the practical implementation and management of the modular course are summarized in five tables. The use of these materials can greatly facilitate the task of introducing a modular course "Formation of teacher's readiness to teach controversial issues of historical science" into the educational process of training courses for teachers of history and social science.

Keywords: professional development, continuing professional education, management activity, monitoring of quality, debatable questions of science.