The teacher must provide the instruments which the children can use to decide things by themselves. Children themselves must verify, experimentally in physics, deductively in mathematics. One participant asked what Piaget thought of having children of different ages in a class together. He replied that it might be helpful especially for the older ones. They could be given some responsibility of teaching younger ones.
Nobody knows better than a professor that the best way to learn something is to teach it.
What distinguishes a good scientist is that he is amazed by things which seem natural to others. Words, are probably not a short-cut to a better understanding . . . . The level of understanding seems to modify the language that is used, rather than vice-versa. . . . The second goal of education is to form minds which can be critical, can verify, and not accept everything they are offered. The great danger today is of slogans, collective opinions, ready-made trends of thought.