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Re: language of division
Posted:
Jan 2, 2005 9:43 PM
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In article <gjqgt0tetd3vkpkkoe3cb8dvncpemuahnv@4ax.com>, kalanamak wrote:
> The text I'm using on teaching children math forbids the use of "goes
> into" when talking about division. They say it is "meaningless". For the
> problem 427/62, they advise the child think aloud along the lines of
> 1) can 6 tens and 2 ones be subtracted from 4 tens and 2 ones? No. Can 6
> tens and 2 ones be subtracted from 4 hundreds and 2 tens? Yes. How many
> times? etc..
> OR
> 2) How many groups of 62 can I make out of 427 objects?
>
> Is this proper or farfetched? If the above is farfetched, is "goes into"
> still commonly used, or, if not, what is used?
> I am not clear from the text how the child goes about answering the 'how
> many times' or 'how many groups' question. Trial and error? Estimation
> and best guess first?
I don't know what elementary teachers now teach (mine tried hard to
avoid "goes into" 40 years ago, so it isn't a new prejudice).
Actually there is nothing inherently wrong with the "goes into" operator.
You can define it easily and unambiguously:
a "goes into" b =def b / a
It is not meaningless, just non-standard.
So far as I can tell, this operator is still used in speech (usually
pronounced "guzinta" around here), but not in writing---there is no
standard symbol for it.
The long-division algorithm has always suffered from the need to guess
how many times the divisor goes into the current part of the dividend.
If you guess low, you'll end up with a remainder that is too big, and
have to increment your guessed digit. If you guess high, you'll end
up with a negative remander and have to decrement your guessed digit.
Unfortunately, the algorithm is usually presented as if people always
guessed perfectly, losing a great apportunity to teach how to recover
from mistakes---a useful skill later on when dealing with more
complicated algorithms.
------------------------------------------------------------
Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus
Professor of Biomolecular Engineering, University of California, Santa Cruz
Undergraduate and Graduate Director, Bioinformatics
(Senior member, IEEE) (Board of Directors, ISCB starting Jan 2005)
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