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Re: [xmca] Numbers - Natural or Real?

David, you cast doubt on the ancient idea that mathematics is the science of quantity and said that Vygotsky was clear on this. If Vygotsky is so clear, then you wouldn't need to go to an English translation of an Italian translation to find Vygotsky refuting the idea that mathematics is the science of quantity. But your re-translation doesn't say this anyway. The colon was a typo. 

-----------------
But let's take up the interesting point you raise anyway, even though it does not say what you claimed it said, it is nonetheless interesting and pertinent.
Am I right here? A child learns to survey the perceptual field and point to things one after another reciting "one," "two,"three," ... and then remember the number they say as they complete the practice. This is called "counting." And I think it is a way children learn to abstract the units from a collection in their perceptual field - pointing to each ion turn and saying the next number. So I think they don't first abstract the actual objects and then abstract number from this. Learning the practice of counting is how they learn to abstract units from a whole.
Now, and this is the wonderful thing I learnt from Anna. Just because the last number I said on completing counting wa "Five!" does not mean that I know that there are 5 things. In fact, "Five" is a property of my counting action; but I have to be taught to see "5" as a *property of the collection of actual things*. AND then I have to learn that "5" is a *quantity* (a cardinal as well as the last ordinal).
So there are two big conceptual leaps involved *after *I learn to abstract things *by counting* them, before I get to the concept of quantity ... and the beginnings of a type of mathematics (since other types of mathematics will grow from other types of quantity).
So Bill, I think the position may be this (and please, I am way out of my comfort zone here, but the July 4 holiday will be over soon and maybe the cavalry will come to our rescue.) Your kids can't see any 2s in the 5 of 54, because they see the 5 as an ordinal. They can see 2 2s in 4, because they have been told so countless times, But they haven't been able to generalise that knowledge because 5 does not "contain" 4, it is just the number "after" 4. OK? What do you think? Does that make sense? 


Andy


David Kellogg wrote:

I don't understand this, Andy. The short answer is "Sure".
What is YOUR short answer supposed to mean? In particular, what does the colon mean? I'm afraid the emoticons that we use in Korea are a little different. dk 

--- On *Sat, 7/2/11, Andy Blunden /<ablunden@mira.net>/* wrote:


    From: Andy Blunden <ablunden@mira.net>
    Subject: Re: [xmca] Numbers - Natural or Real?
    To: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>
    Date: Saturday, July 2, 2011, 5:33 AM

    So the short answer is ":no."
    a

    David Kellogg wrote:
    > Sure, Andy!
    >  This is from Luciano Meccaci's translation of "Thinking and
    Speech", Chapter Six:
> > "If we may say so, the assimilation of a foreign language raises 
    the level of the maternal language (rech) for the child as much as
    the assimilation of algebra raises to a higher level the child’s
    arithmetic thinking, because it permits the child to understand
    any arithmetical operation as a particular case of algebraic
    operations, furnishing the child a freer, more abstract, more
    generalized and at the same time more profound and rich view of
    operations on concrete quantitites. Just as algebra frees the
    thinking of the child from its dependence on concrete numbers and
    raises it to a higher level of more generalized thinking, in the
    same way the assimilation of a foreign language in completely
    diverse ways frees verbal thinking from the grip of concrete forms
    and concrete phenomena of language."
    >
> > David Kellogg 
    >
    > Seoul National University of Education
    >
> > --- On *Fri, 7/1/11, Andy Blunden /<ablunden@mira.net 
    <http://us.mc1103.mail.yahoo.com/mc/compose?to=ablunden@mira.net>>/*
    wrote:
    >
    >
    >     From: Andy Blunden <ablunden@mira.net
    <http://us.mc1103.mail.yahoo.com/mc/compose?to=ablunden@mira.net>>
    >     Subject: Re: [xmca] Numbers - Natural or Real?
    >     To: "Culture ActivityeXtended Mind" <xmca@weber.ucsd.edu
    <http://us.mc1103.mail.yahoo.com/mc/compose?to=xmca@weber.ucsd.edu>>
    >     Date: Friday, July 1, 2011, 10:53 PM
    >
    >     Can you give us your reference here David, in a pubished
    >     translation of Vygotsky?
    >     andy
    >
    >     David Kellogg wrote:
    >     > ... I don't think that quantity IS the basic concept in
    >     mathematics, though. Vygotsky is pretty clear about this: just a
    >     preschooler has to be able to abstract actual objects away from
    >     groups in order to form the idea of abstract quantity, the
    >     schoolchild has to be able to abstract quantities away from
    >     numbers in order to form the idea of RELATIONS between
    quantities,
    >     or OPERATORS.
    >     >
    >
    >
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    --
    ------------------------------------------------------------------------
    *Andy Blunden*
    Joint Editor MCA:
    http://www.informaworld.com/smpp/title~db=all~content=g932564744
    <http://www.informaworld.com/smpp/title%7Edb=all%7Econtent=g932564744>
    Home Page: http://home.mira.net/~andy/ <http://home.mira.net/%7Eandy/>
    Book: http://www.brill.nl/default.aspx?partid=227&pid=34857
    <http://www.brill.nl/default.aspx?partid=227&pid=34857>
    MIA: http://www.marxists.org <http://www.marxists.org/>


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*Andy Blunden*
Joint Editor MCA: http://www.informaworld.com/smpp/title~db=all~content=g932564744 
Home Page: http://home.mira.net/~andy/
Book: http://www.brill.nl/default.aspx?partid=227&pid=34857
MIA: http://www.marxists.org

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