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Character
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Dialogue
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Mentor:
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You might
want to ask them, "Using only six blocks, how can you keep
the clown moving for the shortest time? How about the longest time?"
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Teacher:
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Great idea!
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Mentor:
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So what do you think IS
the longest time you can make with only six blocks of area?
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Teacher:
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I guess that that would be six seconds
long, at one meter per second (demonstrates to mentor).
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Mentor:
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That is right, if you want
to always be covering ground. But actually you can make the time
as long as you want without this constraint!
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Teacher:
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Huh?
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Mentor:
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Check this out...
(NOTE: While Mentor David
says this on audio live from San Diego, Patti in Toronto takes his
words as cue and makes a graph with a zero velocity segment, demonstrates
to teacher, runs the simulation)
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Teacher:
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Oh, I see. You can make a zero
velocity segment as long as you want. Hmm... that would certainly
make my class think more carefully about what area means... we can
have a long segment with no area at all!
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Narrator:
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It is important for teachers
to discuss student work and share their successes and challenges.
Note how quickly and smoothly the sharing of ideas back and forth
can proceed when interactive mathematical notations are shared as
part of the common ground for this conversation. Imagine trying
to have the previous dialog with only text!
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