A qualitatively new social task set before the educators at the stage of the developed socialism is discussed. Main thrusts are to be directed at promotion of self-initiative in a growing man, at forming in him of higher social responsibility. The society-imposed system of education must overtake children's mental development and guide it. It is important therefore to use in the organization of such "overtaking education" the data from psychology concerning development of the personality in ontogenesis. Review of a number of regularities discovered by psychologists and of possible ways of using them for particular educational aims is provided.