The authors analyze results of "cognitive teaching" preschool children the concept of quantity invariance (with the help of a procedure used by B. Inhelder, H. Sinclair, M. Bovet). Having repeated Inhelder's teaching experiments and having obtained the same results the authors come to a conclusion that there may exist a completely different interpretation of them. The basic disagreement point consists in the obvious underestimation on the part of Geneva researchers of the importance of the external organization of children's cognitive activity. However necessity for such organization is obviously assumed in the "cognitive teaching" although only inderectly and incompletely. B. Inhelder's and P. Ya. Galperin's models of "developing teaching" are compared from the standpoint of how the conditions enabling the children to act consciously in problem situations are provided in them.