The national educational initiative "Our New School" will have a direct influence on the content and technologies of pedagogical education in Russia, and is aimed at providing the system of general education with the qualified teachers who are currently needed. In this article, the author emphasizes that in connection with attributing vital significance to the fundamental character of the training of educators who work with gifted youngsters, the pedagogical community should ensure provision of psychological and pedagogical support and the development and use of educational technologies that will permit talented youngsters to be detected and show what they can do. Higher education's tasks in regard to the accomplishment of these problems must not be forgotten. In consideration of the tasks involved in the training of the new schoolteacher, and taking account of the pedagogical community's powerful accumulated potential, the author argues that it is logical to decide on the leading pedagogical universities and classical universities that are to serve as centers of pedagogical education. The area of collaboration with pedagogical colleges is extremely important. The author proposes to draw up a target program with the title "Pedagogical Cadres," for the purpose of accomplishing the tasks of training the new kind of teacher for the new school system in Russia.