The description of the longitudinal experiment (1965—1970) which was conducted in N 1 Moscow school with primary pupils (year 1—year 4) is discussed in the article. In addition, the P.Ya. Galperin’s program of forming of initial mathematical concepts is described. The results have demonstrated high achievements in academic performance. More importantly, psychological conclusions concerning principles of organization of the school subjects and organization of the activity based on theory of forming of mental actions were drawn.