# [Xmca-l] Re: Objectivity of mathematics

```Andy,
the symbols are not governed by *natural laws* but by *rules*

I am returning to the themes of activity and meaning.

In the beginning is material substance AS object
material substance
becomes
the means of *figuring* [out] the symbols [as figures or as interpretations
or meaning or?]
*symbols* which ARE no longer means BUT OBJECT.
Symbols AS object ARE no longer governed by *natural laws* but are now
governed by rules
[like]
when a child is playing a rule-governed game.

QUESTION?
Where is *meaning* located? Is meaning inherent in ALL these trans
[across?] actions
or
is meaning an aspect of this unit?
larry

On Mon, Nov 3, 2014 at 10:07 PM, Andy Blunden <ablunden@mira.net> wrote:

> 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
>>>> :-)
>>>>
>>>>
>>>>
>>>>
>>>
>>
>>
>>
>>
>
>

```