Introduction
In this interview, Caitlin shows her whole number thinking.
She correctly makes the biggest number, as is predicted from whole
number thinking. However, when making the smallest number, she shows
that she cannot distinguish between 3.01 and 3.1. To Caitlin, both
of these are 3 wholes and 1 extra bit.
Comments: Text in italics
Interviewer: Text in red
Caitlin: Text other colour |
Interviewer:
I have a number that starts 3 point something
something and you get to choose the rest of the number. |
Interviewer:
Here are the cards to choose from...
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Interviewer:
...marked
0,1,2,3,4,5,6,7,8 and 9. I'm going to ask you to make the
biggest number that you can by choosing any two of these cards.
Caitlin:
Any cards?
Interviewer:
Yes
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Caitlin selects the 9 and 8 cards and puts them in place, correctly
making the biggest number.
Interviewer:
OK, now we'll put those cards back
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Interviewer:
...and could you make another number, this
time as small as you can?
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Caitlin selects the 1 card and places it alone. Interviewer
reminds her to use two cards.
Interviewer:
OK, what if you have to choose two of the
cards to make your number?
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Caitlin selects the 0 card and makes 3.01.
Interviewer:
Could we just look at those two numbers that
you made? Did you make it bigger or smaller when you changed it?
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Caitlin:
Ummm, I think they're the same...because
the zero doesn't matter...
Caitlin thinks 3.01 is the same as 3.1, that each is 3 wholes
and 1 extra bit.
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