53. Cherry: Three.
54. Observer: What if he clicks on his red button now to see what happens?
[The robot “clicks” on the red button and the blue blocks turn into a slide].
55. Cherry: Oh! So it only needed two.
56. Observer: Do you know why?
Cherry shakes her head in a ’no’ motion.
57. Observer: So you don’t understand why, do you remember (what had to be
done)?
58. Cherry: So there’s two... [thinking for a few seconds]. Ten, so... oh yeah,
you have to times it by two to get twenty.
59. Observer: Twenty?
60. Cherry: No I mean divide. Divide ten by two and you get... uhm... five...
yeah what he did. No, no divide ten by five and you get... ten by five... two.
Yeah, that’s what he did.
Cherry finally is able to explain how the number two was derived as the
correct answer. As Kuuti [] notes, initially each operation is a conscious
action, consisting of orientation, i.e. planning in the consciousness by using a
model, and execution phases. When, however, the corresponding model is
good enough or the action has been practiced long enough, the orientation
phase will fade and the action will be collapsed into an operation. Indeed, in
Cherry’s case, a phase of conscious planning took place when she was
originally asked to identify how many blocks she would add to the slide area
if she were Spike. An execution phase followed where she showed where she
would place the five blocks she had identified as being the correct answer for
fixing the slide area. However, when Spike completed the slide area correctly
by placing only two blocks, a contradiction occurred between Spike’s action
and Cherry’s model. Cherry had to question her model and drastically change
it as it proved to be incorrect. Using a kind of “backward thinking” process to
explain why the correct answer was such and resolve the contradiction, she
came up with a new model (in which the original number of blocks is divided
by the denominator) that could later be generalized. In fact, in the next task,
which was to compare the two fractions for increasing the area of the swings,
she used her newly constructed model to come up with a correct response
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