for example, to see whether in the developing subject, i.e. the child, integers are directly constructed starting from class logic by biunivocal corr… - Jean Piaget

Each time one prematurely teaches a child something he could have discovered himself, that child is kept from inventing it and consequently from understanding it completely.

It is when the child is accustomed to act from the point of view of those around him, when he tries to please rather than to obey, that he will judge in terms of intentions. So that taking intentions into account presupposes cooperation and mutual respect. Only those who have children of their own know how difficult it is to put this into practice. Such is the prestige of parents in the eyes of the very young child, that even if they lay down nothing in the form of general duties, their wishes act as law and thus give rise automatically to moral realism (independently, of course, of the manner in which the child eventually carries out these desires). In order to remove all traces of moral realism, one must place oneself on the child's own level, and give him a feeling of equality by laying stress on one's own obligations and one's own deficiencies. In this way the child will find himself in the presence, not of a system of commands requiring ritualistic and external obedience, but of a system of social relations such that everyone does his best to obey the same obligations, and does so out of mutual respect. The passage from obedience to cooperation thus marks a progress analogous to that of which we saw the effects in the evolution of the game of marbles: only in the final stage does the morality of intention triumph over the morality of objective responsibility. When parents do not trouble about such considerations as these, when they issue contradictory commands and are inconsistent in the punishments they inflict, then, obviously, it is not because of moral constraint but in spite of and as a reaction against it that the concern with intentions develops in the child. Here is a child, who, in his desire to please, happens to break something and is snubbed for his pains, or who in general sees his actions judged otherwise than he judges them himself. It is obvious that after more or less brief periods of submission, during which he accepts every verdict, even those that are wrong, he will begin to feel the injustice of it all. Such situations can lead to revolt. But if, on the contrary, the child finds in his brothers and sisters or in his playmates a form of society which develops his desire for cooperation and mutual sympathy, then a new type of morality will be created in him, a morality of reciprocity and not of obedience. This is the true morality of intention and of subjective responsibility.

Thus arises the second tendency, which consists in regarding logical and mathematical relations as irreducible, and in making an analysis of the higher intellectual functions depend on an analysis of them. But it is questionable whether logic, regarded as something eluding the attempts of experimental psychology to explain it, can in its turn legitimately explain anything in psychological experience.