A delightful story appears on page 106 (10.8 Education and Development) of Marvin Minsky's book "The Society of Mind" (Picador Edn 1988). The story relates to the psychologist Piaget's experiments on children of their understanding of conservation of quantity under transformation.
All this reminds me of a visit to my home from my friend Gilbert Voyat, who was then a student of Papert and Piaget and later became a distinguished child psychologist. On meeting our five-year-old twins, his eyes sparkled, and he quickly improvised some experiments in the kitchen. Gilbert engaged Julie first, planning to ask her about whether a potato would balance best on one, two, three or four toothpicks. First, in order to assess her general development, he began by performing the water jar experiment. The conversation went like this:
Gilbert: "Is there more water in this jar or in that jar?"
Julie: "It looks like there's more in that one. But you should ask my brother, Henry. He has conservation already."
Gilbert paled and fled.