The principal goal of education in the schools should be creating men and women who are capable of doing new things, not simply repeating what other … - Jean Piaget

Thus, even in those fields in which logic does not normally play a part, there exist outline structures which are the precursors of logical structures, and which can be formulated in terms of the algebra of logic. From a comparative point of view, these outline structures are of great interest. It is not inconceivable that a general theory of structures will at some future date be worked out, which will permit the comparative analysis of structures characterizing the different levels of development. This will relate the lower level outline structures to the logical structures characteristic of the higher stages of development. The use of the logical calculus in the description of neural networks on the one hand, and in cybernetic models on the other, shows that such a programme is not out of the question.

Considering that the square game is only one of the five or ten varieties of the game of marbles, it is almost alarming in face of the complexity of rules and procedure in the square game, to think of what a child of twelve has to store away in his memory. These rules, with their overlapping and their exceptions, are at least as complex as the current rules of spelling. It is somewhat humiliating, in this connection, to see how heavily traditional education sets about the task of making spelling enter into brains that assimilate with such ease the mnemonic contents of the game of marbles. But then, memory is dependent upon activity, and a real activity presupposes interest.

"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."