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[Xmca-l] Re: Objectivity of mathematics

Mike and Huw,
Something else just occurred to me. This gap. I asked Vera about creativity and simulation. She said the difference was in the creative “leap”, something not present when the mind (the subject?) “simulates” a real world event. Does the gap involve a leap? Does this have anything to do with Pierce’s abduction?
> 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.