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Re: Non-Euclidean Arithmetic
Posted:
Sep 3, 2012 9:24 PM
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On Mon, Sep 3, 2012 at 7:46 PM, Robert Hansen <bob@rsccore.com> wrote:
>
> On Sep 3, 2012, at 12:38 PM, Paul Tanner <upprho@gmail.com> wrote:
>
> He is pointing out that there is a problem with the usual way of
> talking about multiplication as repeated addition.
>
>
> I know, but there isn't a problem.
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>
> For example: The phrase "5 added to itself once" can be taken to mean
> 5 + 5. Likewise the phrases "5 added to itself twice and "5 added to
> itself three times" respectively can be taken to mean 5 + 5 + 5 and 5
> + 5 + 5 + 5. And so on.
>
>
> The teacher shows how it is to be taken on the board, dozens of times.
>
> There is no problem.
>
One would think that actually saying what one actually means 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.
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 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, to actually teach this to students, makes one wonder.
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