What is desired is that the teacher ceased being a lecturer, satisfied with transmitting ready-made solutions. His role should rather be that of a mentor stimulating initiative and research.

Chance... in the accommodation peculiar to sensorimotor intelligence, plays the same role as in scientific discovery. It is only useful to the genius and its revelations remain meaningless to the unskilled.

The most developed science remains a continual becoming

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.

Our problem, from the point of view of psychology and from the point of view of genetic epistemology, is to explain how the transition is made from a lower level of knowledge to a level that is judged to be higher.

What we see changes what we know. What we know changes what we see.

If logic itself is created rather than being inborn, it follows that the first task of education is to form reasoning.