Re: Too narrowly defined: DIVISION SIGN & COLON

From: Martin J. Dürst <>
Date: Wed, 11 Jul 2012 09:49:24 +0900

On 2012/07/11 4:37, Asmus Freytag wrote:

> I recall, with certainty, having seen the ":" in the context of
> elementary instruction in arithmetic,
> as in "4 : 2 = ?", but am no longer positive about seeing ÷ in the same
> context.

I remember this very well. In grade school, we had to learn two ways to
divide, which were distinguished by using two symbols, ':' and '÷', and
different verbs, the German equivalents of "divide" and "measure".

I'll explain the difference with two examples:

a) There are 12 apples, and four kids. How many apples does each kid
get? [answer: 3 apples]

b) There are 12 apples, and each kid gets 4 of them. For how many kids
will that be enough? [answer: for 3 kids]

I think a) was called 'divide' and b) was called 'measure', but I can't
remember which symbol was used for which.

When we were learning this, I thought it was a bit silly, because the
numbers were the same anyway. It seems to have been based on the
observation that at a certain stage in the development of arithmetic
skills, children may be able to do division (in the general, numeric
sense) one way but not the other, or that they get confused about the
units in the answer. But while such an observation may be true, I don't
think such a stage lasts very long, definitely not as long as we had to
keep the distinction (at least through second and third grade).

Also, I think this may have been a local phenomenon, both in place and
time. But if one searches for "geteilt gemessen", one gets links such as
So maybe some of this is still in use.

Regards, Martin.
Received on Tue Jul 10 2012 - 19:51:12 CDT

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