[Xmca-l] Re: Objectivity of mathematics

[Andy Blunden]

Particularly after reading Peter Moxhays' paper, it is clear to me that 
teaching mathematics, Davydov-style, is orchestrating concept-formation 
in a particular domain of activity, and that what the children are doing 
in forming a concept is a system of artefact-mediated actions: "For 
Davydov," he says, "a theoretical concept is itself a /general method of 
acting/ - a method for solving an entire class of problems - and is 
related to a whole system of object-oriented actions." Pure Vygotsky, 
and also equally pure Activity Theory except that here the object 
becomes a "theoretical concept," which is characteristically Vygotsky, 
the point of difference between ANL and LSV! Just as in all those dual 
stimulation experiments of Vygotsky, the teacher introduces a symbol 
which the student can use to solve the task they are working on.
So the unit of learning mathematics is *an artefact-mediated action*. 
The artefact is introduced by the teacher who also sets up the task. At 
first the symbols is a means of solving the material task, but later, 
the symbol is manipulated for its own sake, and the material task 
remains in the background. This is what is special about mathematics I 
think, that the symbolic operation begins as means and becomes the 
object. C.f. Capital: the unit is initially C-C' becomes C-M-C' and then 
from this arises M-C-M' - the unit of capital.

Andy

------------------------------------------------------------------------
*Andy Blunden*
http://home.pacific.net.au/~andy/


mike cole wrote:
> That is really a great addition to Andy's example, Ed. Being a total 
> duffer here i am assuming 
> that the invert v is a sign for "power of" ?
>
> You, collectively, are making thinking about "simple" mathematical 
> questions unusually interesting. 
>
> The word problem problem is really interesting too.
>
> mike
>
> PS - I assume that when you type:  There is, one might say, a 
> necessity within the integers is that 5 x -1 = -5.   you mean a SUCH 
> not is?
>  mike**2
> :-)
>
>