Re: [xmca] Numbers - Natural or Real?

[David Kellogg <vaughndogblack@yahoo.com>]

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> wrote:


From: Andy Blunden <ablunden@mira.net>
Subject: Re: [xmca] Numbers - Natural or Real?
To: "Culture ActivityeXtended Mind" <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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