With a friend, I reviewed some classic Piagetian interviews with a few children.  One involved the ordering of lengths. I had cut 10 cellophane drinking straws into different lengths and asked the children to put them in order, from smallest to biggest.  The first two 7-year-olds did it with no difficulty and little interest.  Then came Kevin.  Before I said a word about the straws, he picked them up and said to me, “I know what I’m going to do,” and proceeded, on his own, to order them by length.  He didn’t mean, “I know what you’re going to ask me to do.”  He meant, “I have a wonderful idea about what to do with these straws.  You’ll be surprised by my wonderful idea.”
 
It wasn’t easy for him.  He needed a good deal of trial and error as he set about developing his system. But he was so pleased with himself when he accomplished his self-set task that when I decided to offer them to him to keep (10 whole drinking straws!), he glowed with joy…
 
The having of wonderful ideas is what I consider the essence of intellectual development.  And I consider it the essence of pedagogy to give Kevin the occasion to have his wonderful ideas and to let him feel good about himself for having them.  To develop this point of view and to indicate where Piaget fits in for me, I need to start with some autobiography, and I apologize for that, but it was a struggle of some years’ duration for me to see how Piaget was relevant to schools at all.
 
…If the main thing that we take from Piaget is that before certain ages children are unable to understand certain things-conservation, transitivity, spatial coordinates—what do we do about it?  Do we try to teach the children these things? Probably not, because on the one hand Piaget leads us to believe that we probably won’t be very successful at it; and on the other hand, if there is one thing we have learned from Piaget it is that children can probably be left to their own devices in coming to understand these notions…
 
…any class of children has a great diversity of levels.  Tailoring to an average level of development is sure to miss a large proportion of the children.  In addition, a Piaget psychologist has no monopoly here. When trying to approximate the abilities of a group of children of a given age, able teachers like my colleagues could make as good approximations as I.  …instead of deciding on what children ought to know, or what they ought to be able to do at a certain age, they found activities, lessons, points of departure, that would engage children in real classrooms, with real teachers.  In their view, it was easy to devise all-embracing schemes of how science could be organized for children, but to make things work pedagogically in classrooms was the difficult part.  But, in making things work in a classroom, it was but a small part compared with finding ways to interest children, to take into account different children’s interests and abilities, to help teachers with no special training in the subject…
 
…The having of wonderful ideas, which I consider the essence of intellectual development, would depend instead to an overwhelming extent on the occasions for having them…to allow children to accept their own ideas and to work them through.   

Citation: Duckworth, E. (2006). The having of wonderful ideas and other essays on teaching and learning. Teachers College Press.