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Re: Cool Math Lessons
Posted:
Feb 28, 2012 2:00 PM
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What do you mean by "figure out a fraction"?
To understand fractions we all start with examples,
I'll just say "pies" to make it definite, be it a real pie or a picture of a pie. We come to understand the notation "1/3" by relating it to the thing we already understand (a portion of a pie). We come to understand expressions like 1/3 + 1/3 again by relation to our real pies or pie pictures. After a while and some practice and many more examples, we internalize the algorithms for forming sums of 1/5 + 1/8. We don't lean on the pictures anymore - we trust (maybe!) the algorithm to work instead, because for one thing, its faster.
So, what's it mean to understand fractions? There are various things above that in missing can leave holes in our understanding. If we haven't internalized a symbolic algorithm, does that mean we don't understand fractions? If we can use the algorithm to find answers but we cannot come up with a picture to realate to our "pre-mathematical" intuitions, can we say we fully understand fractions?
Joe N
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