Every time we teach a child something, we keep him from inventing it himself. On the other hand, that which we allow him to discover for himself will remain with him visible for the rest of his life.

The more the schemata are differentiated, the smaller the gap between the new and the familiar becomes, so that novelty, instead of constituting an annoyance avoided by the subject, becomes a problem and invites searching.

Teaching means creating situations where structures can be discovered.

To express the same idea in still another way, I think that human knowledge is essentially active.

The principle goal of education in the schools should be creating men and women who are capable of doing new things, not simply repeating what other generations have done.

Knowing reality means constructing systems of transformations that correspond, more or less adequately, to reality.

The self thus becomes aware of itself, at least in its practical action, and discovers itself as a cause among other causes and as an object subject to the same laws as other objects.