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[Xmca-l] Re: Objectivity of mathematics



*spontaneously* [bracketed]
 In the nonlinear way that meaning develops, I groked it
[and THIS PROCESS this *groking* is possibly abductive, rather than
deductive or inductive] - LP]

and I could have, at that  moment, explained why on xmca.

Mike, this process [groking] emerging prior to explaining IS *imaginal* and
has qualities which are central to composing meaning - *spontaneously*
Larry


On Wed, Nov 5, 2014 at 8:50 PM, HENRY SHONERD <hshonerd@gmail.com> wrote:

> Huw,
> You’re making me think about the connection between imagination and
> memory. Is it in the intentionality of these two “acts”? I think sometimes
> memories come unbidden, sometimes unwanted. But you’re talking about using
> the imagination with memory?
> Henry
>
> > On Nov 5, 2014, at 8:41 PM, Huw Lloyd <huw.softdesigns@gmail.com> wrote:
> >
> > The way I like to think about it is how experienced problems structure
> > memory.  That is, how the awareness of the problem in getting the right
> > length strip can move to the beginning of subsequent attempts.  I think
> of
> > it as a process of exchange.  How memories are moved upstream through the
> > right kinds of action.
> >
> > Those kind of effects are what I'd call "concrete generalisation", rather
> > than, say, "notational generalisation" which would be based upon patterns
> > perceived in the notation.  I'm guessing that its this latter sort of
> thing
> > that is often filling up that seemingly necessary gap.
> >
> > Huw
> >
> >
> >
> >
> >
> > On 6 November 2014 03:15, mike cole <mcole@ucsd.edu> wrote:
> >
> >> 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.
> >>
>
>
>