Logic is the mirror of thought, and not vice versa;in classes, relations et nombres; essai sur les groupements de logistique et la réversibilitié de … - Jean Piaget

From the point of view of the practice or application of rules four successive stages can be distinguished. A first stage of a purely motor and individual character, during which the child handles the marbles at the dictation of his desires and motor habits. This leads to the formation of more or less ritualized schemas, but since play is still purely individual, one can only talk of motor rules and not of truly collective rules. The second may be called egocentric for the following reasons. This stage begins at the moment when the child receives from outside the example of codified rules, that is to say, some time between the ages of two and five. But though the child imitates this example, he continues to play either by himself without bothering to find play-fellows, or with others, but without trying to win, and therefore without attempting to unify the different ways of playing. In other words, children of this stage, even when they are playing together, play each one "on his own " (everyone can win at once) and without regard for any codification of rules. This dual character, combining imitation of others with a purely individual use of the examples received, we have designated by the term Egocentrism. A third stage appears between 7 and 8, which we shall call the stage of incipient cooperation. Each player now tries to win, and all, therefore, begin to concern themselves with the question of mutual control and of unification of the rules. But while a certain agreement may be reached in the course of one game, ideas about the rules in general are still rather vague. In other words, children of 7-8, who belong to the same class at school and are therefore constantly playing with each other, give, when they are questioned separately, disparate and often entirely contradictory accounts of the rules observed in playing marbles. Finally, between the years of 11 and 12, appears a fourth stage, which is that of the codification of rules. Not only is every detail of procedure in the game fixed, but the actual code of rules to be observed is known to the whole society. There is remarkable concordance in the information given by children of 10-12 belonging to the same class at school, when they are questioned on the rules of the game and their possible variations.

"Every observer has noted that the younger the child, the less sense he has of his own ego. From the intellectual point of view, he does not distinguish between external and internal, subjective and objective. From the point of view of action, he yields to every suggestion, and if he does oppose to other people's wills — a certain negativism which has been called "the spirit of contradiction" — this only points to his real defenselessness against his surroundings. A strong personality can maintain itself without the help of this particular weapon. The adult and the older child have complete power over him. They impose their opinions and their wishes, and the child accepts them without knowing that he does so."

To perceive is to construct intellectually, and if the child draws things as he conceives them, it is certainly because he cannot perceive them without conceiving them. But to give up gradually the spurious absolutes situated away and apart from the context of relations that has been built up during experience itself is the work of a superior kind of rationality. When the child comes to draw things as he sees them, it will be precisely because he has given up taking isolated objects in and for themselves and has begun to construct real systems of relations which take account of the true perspective in which things are connected.