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[Xmca-l] Re: Objectivity of mathematics



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

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*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
:-)