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Re: Non-Euclidean Arithmetic
Posted:
Sep 3, 2012 9:19 PM
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On Mon, Sep 3, 2012 at 12:32 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
>>When a teacher says "added x number of times" they write the multiplicand x number of times, not the addition symbol. When I ask you what is the sum of 12, 34, 16 and 7 (4 addends) I am asking what is SUM(12,34,16,7) and the algorithm to do that is to start with 12, then add 34, then add 16, then add 7.
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> Sometimes I've seen the wording like so: multiplication is the *taking* of one quantity as many times as there are units in the other.
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This is an example of Jonathan's point that speakers of English need to consider that actually saying what they actually mean is a good thing, not a bad thing. Precision in the use of language is a good thing, not a bad thing, and teaching it is a good thing, not a bad thing.
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> The "addition", *if* any, (if that's what to be done) is left implicit, according to the problem at hand. I can multiply the contents of my cookie jar without necessarily ever adding it all up.
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Therefore what? The only point being made here is is that if you're going to teach that multiplication is repeated addition, then maybe you might consider that it's better to be more precise in your use of language.
> Bottom line, though, is almost every school child and the occasional adult knows what is meant in today's understanding.
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How does this excuse the exalting of not actually saying what one actually means?
This I would think would be most true in mathematics, where I would think that we would want to teach students that precise use of language is to be exalted, not denigrated.
That you and Hansen want to denigrate the idea that in mathematics classes of all places we should want to be precise in our use of language, to strive to actually say what we actually mean, makes one wonder.
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