The purpose of this study is to identify a set of strategic and effective technologies of pedagogical
education in a university on the basis of the analysis of the problems of teacher training. The research
methodology is based on Hamel's concept of 'core competence'. This concept involves the analysis
of management strategies based on a matrix of significant problems. The study used methods
of questioning, interviewing, analysis and comparison, methods of summarizing the results of
statistics, and learning outcomes. According to Prigozhin's typology, the problems can be divided
into embedded, socio-cultural and situational, and the wording of the problems are classified as
denominative, causal and antithesis. On the basis of the matrix obtained from this analysis, we
define the set of technologies of pedagogical education; psychological and pedagogical conditions
of realization of technologies at the level of baccalaureate, pedagogical master's degree program,
and professional retraining of workers of education. The organizational and pedagogical model of
realization of technologies in the conditions of a classical university is developed. The results are
implemented in practice through the curriculum, programs of professional retraining of the Kazan
(Volga) Federal University.