[Xmca-l] Re: Objectivity of mathematics

[mike cole]

Exactly, Ed.

"Spontaneously" I was driving along and found myself of thinking about
number lines and
"a minus times a minus equals a plus. And for maybe the first time, sitting
on a freeway in a car, I actually could arrive easily at the conclusion,
"of course" without driving off the road or into another car. In the
nonlinear way that meaning develops, I groked it and could have, at that
moment, explained why on xmca.

All very interesting. Makes one almost wish for traffic to sit in from time
to time..... :-)
mike

On Wed, Nov 5, 2014 at 6:26 PM, Ed Wall <ewall@umich.edu> wrote:

> Henry and Mike
>
>       That displacement you mention is part of why I've been doing the
> wondering I mention below. I do think the teaching of mathematics should be
> so that the gap, in part, is filled, as Mike put it, by imagination;
> however, in many classrooms it is filled by anything but.
>
> Ed
>
> On Nov 5, 2014, at  7:21 PM, mike cole wrote:
>
> > 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.
>
>
>


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