[Xmca-l] Re: Objectivity of mathematics

[Larry Purss]

Natalia and Henry
Vygotsky's understanding the place of abstraction in this quote
"So abstraction is incorporated into the process of imagination as an
indispensable constituent part, but it does not form its centre. The
movement from the concrete through the abstract to the construction of a
new form of a concrete image, is the path which describes imagination in
the adolescent age."

If this is the movement of imagination "in the adolescent age" is that
different from Mike's nonlinear [spontaneous] imaginal groking.

Henry, yes Peirce was fascinated with this topic and his engaging with
abduction as spontaneous has a family resemblance with groking.
Larry



On Wed, Nov 5, 2014 at 9:02 PM, Natalia Gajdamaschko <nataliag@sfu.ca>
wrote:

>
> And connection of imagination to thinking?
> As per LSV (1931):
> " From our point of view, imagination is a creative transforming activity
> which moves from one form of concreteness to another. But the mere movement
> from a given concrete form to a newly created form of it and the very
> feasibility of a creative construction, is only possible with the help of
> abstraction. So abstraction is incorporated into the process of imagination
> as an indispensable constituent part, but it does not form its centre. The
> movement from the concrete through the abstract to the construction of a
> new form of a concrete image, is the path which describes imagination in
> the adolescent age."
>
> ----- Original Message -----
> From: "HENRY SHONERD" <hshonerd@gmail.com>
> To: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>
> Sent: Wednesday, November 5, 2014 8:50:34 PM
> Subject: [Xmca-l] Re: Objectivity of mathematics
>
> 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.
> >>
>
>
>