[Xmca-l] Re: Objectivity of mathematics

[Andy Blunden]

On pre-concepts, see p. 16 of 
https://www.academia.edu/6262583/Vygotsky_on_the_Development_of_Concepts 
, Ed.
The interesting thing with the unit, for me, is how the triangle 
rotates, so that the material things which were once the substance of 
the object, become the means of figuring out the symbols, which are no 
longer means, but object. The symbols are not governed by "natural 
laws", but by rules, like when a child is playing a rule-governed game, 
like chess, which has its own rules, different from the rules of war.
How is learning elementary mathematics related to playing rule-governed 
games?
Andy
------------------------------------------------------------------------
*Andy Blunden*
http://home.pacific.net.au/~andy/


Ed Wall wrote:
> Andy
>
>       What you say here fits somewhat with some of the thinking I've been doing, but, in part, it is at the point of symbol manipulation that things seem get complicated for me. Also, I find myself wondering whether teaching mathematics, in effect, as mathematics or even Davydov-style is just the things you list. There seems to be more that is needed (and I could be wrong about this) and I have yet to factor in something  like those pre-concepts you mentioned earlier. So I need to do a little reading/rereading on the symbolic question, think a bit more about the space the teacher opens up for studying mathematics, and factor in those 'pre-concepts' before I can reply reasonably to what you are saying here. 
>      I admit that I tend to complicate things too much (smile), but that may come from thinking about them too much. 
>
> Thanks
>
> Ed
>
> On Nov 3, 2014, at  10:45 PM, Andy Blunden wrote:
>
>   
>> 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
>>> :-)
>>>
>>>
>>>       
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