[Xmca-l] Re: Objectivity of mathematics

[mike cole]

Nice observation/connection Henry. I provokes the following thought.

The result of a displacement, in the way I have been thinking about it, is
to create a gap in the connectivity/continuity of the experience, and
filling that gap is a process of imagination, of seeing-as in a new way.

mike

On Wed, Nov 5, 2014 at 5:11 PM, HENRY SHONERD <hshonerd@gmail.com> wrote:

> Ed and Andy,
> Just a little while ago, while I was finishing the Moxhay paper, which
> seems to have produced an AHA! moment” regarding object-mediated action for
> Andy, I had my own AHA! moment, and it is this:
>      Some years ago, after teaching Intro to Linguistics many times, I
> decided that the most important property of human language that clearly
> sets it apart from what we know about other species’ ability to communicate
> is what is called DISPLACEMENT: the ability to use language to refer to
> things removed from the here and now, including imaginary happenings or
> things. The Davydov tasks in the Moxhay article give children the same
> problem of displacement by requiring that they figure a way to compare two
> objects removed from one another in space, and, effectively, in time. And I
> am wondering if this touches on the other threads I have been following: L2
> and the Blommmaert/Silverstein. Does the need for standardization in
> measurement of the objects in the world today find its way into L2 teaching
> and language policy? The blending of qualitative and quantitative research
> methods come to mind, to my mind at least. Moxhay’s article ended with a
> comparison of  Classroom A and B that certainly was a blend of the two
> methods, though the ways in which the dialog broke down in Classroom B (a
> qualitative issue, I would think) was only hinted at. That would have
> required a narrative. So, the interplay of narrative and dialog, objects
> mentioned by David K. I know I have bitten off more than I can chew.
> Henry
>
>
> > On Nov 3, 2014, at 10:51 PM, Ed Wall <ewall@umich.edu> 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
> >>> :-)
> >>>
> >>>
> >>
> >
> >
>
>
>


-- 
It is the dilemma of psychology to deal with a natural science with an
object that creates history. Ernst Boesch.