John Holt in "How Children Learn"

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One of the puzzles we had in my fifth-grade class was a geometrical puzzle called Hako. You
began with a number of thin, flat, rectangular plastic pieces arranged a certain way in a
shallow box. The aim was to slide them around, without turning them or lifting them out of
the box, so as to finish with the largest piece, a square, at the opposite end of the box from
which it started. Though I spent many hours on it, I was never able to do it. This exasperated
me. What exasperated me even more was that I seemed to be able to prove that the puzzle was
impossible--though I knew it was not. Like most people, I began by moving the pieces around
in a kind of blind, haphazard way. Before long, and unwisely, I grew impatient with this.
There were too many possible moves, this could go on forever. The thing to do was use the
brain and figure it out. So, moving the pieces very carefully, and analyzing each move, I
deduced that in order to get the large piece from the top to the bottom, certain other things had
to happen along the way. There had to be a point at which certain of the pieces were going up
past the big piece while it was going down. Then, still carefully analyzing, I showed that this
could only happen if certain other pieces moved in certain ways. Finally, I proved that they
could not be moved in those ways. Therefore the problem was impossible.

The trouble was, I knew it wasn't impossible. Companies don't sell impossible puzzles; they
would be sued, or worse. Besides, the puzzle had been mentioned in Scientific American.
Besides that, and worst of all, some students had done it. With all my heart I wanted to
believe that they had lied or cheated, but I couldn't convince myself; they weren't the type. I
remember thinking furiously, "I suppose anyone could do this puzzle if he were willing to sit
in front of it like a nitwit, moving the pieces around blindly, until just by dumb luck he
happened to get it. I haven't got time for that sort of thing." More to the point, I felt above that
sort of thing.

I went back to the puzzle many times, hoping that I would find some fresh approach to it; but
my mind kept moving back into the little groove it had made for itself. I tried to make myself
forget my supposed proof that the problem was impossible. No use. Before long I would be
back at the business of trying to find the flaw in my reasoning. I never found it. Like many
other people, in many other situations, I had reasoned myself into a box. Looking back at the
problem, and with the words of Professor Hawkins in my ears, I saw my great mistake. I had
begun to reason too soon, before I had allowed myself enough "Messing About," before I had
built a good enough mental model of the ways in which those pieces moved, before I had
given myself enough time to explore all the possible ways in which they could move. The
reason some of the children were able to do the puzzle was not that they did it blindly, but that
they did not try to solve it by reason until they had found by experience what the pieces could
do. Because their mental model of the puzzle was complete, it served them; because mine was
incomplete, it failed me.