The urgency of the problem of designing a new strategy of teacher training due to the reform of education in universities: decrease of pedagogical disciplines, strengthening fundamental (subject) training, etc. The goal of the article lies in identification of the main components of the new strategy of teacher training. A leading approach to the study of this problem was personological. The result was a new model of teacher training. Undergraduate students are deepening their knowledge of the core subjects (be it Mathematics and Physics or Chemistry and Biology), while graduate students are making a choice: whether to be an engineer, researcher, scientist (which means keep deepening one's knowledge) or be a teacher (which means master psychology, pedagogics, and the methodology of teaching a chosen discipline). The new approach has helped identify the indicators and determinants of pedagogical craftsmanship. The results of the study can be useful in designing new strategies for training teachers.