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Re: [xmca] Numbers - Natural or Real?



On 30 June 2011 09:52, Andy Blunden <ablunden@mira.net> wrote:

> I don't really have an opinion on this matter, but I would be interested in
> listening in on those who may have an informed opinion.
> I see two different approaches to the teaching of mathematics.
>
>   One takes the /Natural/ Numbers as the basic concept of the subject
>   The Other takes the /Rational/ Numbers as the basic concept of the
>   subject
>

The Davydov example, described in "Cultural-Historical Approaches to
Designing for Development" describes quantity as the basic concept.  Which
seems sensible to me.

Both magnitude and multitude are variants of quantity -- a concept that
entails a number along with a unit of measure.


>
>   One takes /counting/ as the basic Action
>   The Other takes /comparison/ of two lengths as the basic Action.
>

In both cases I would ascribe measuring as the "basic action", which
includes the pattern matching found in counting apples.

Huw
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