Globalization challenges education, continuing education of teachers and managerial educational staff. To make „train of education” follow the tracks of globalization, it is required to take into consideration cosmological heights of education, to redefine the philosophical foundations of education (post-modernism), scientific progress of pedagogy (Competence pedagogy) and related disciplines (psychology – quantum psychology, cybernetics / Informatics – big data ; management – innovation management and management of knowledge; physiology – neural complex of consciousness and subconsciousness). This article presents one of the possible palette of the system of continuing education of teaching staff, which answers the challenges of globalization.