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[Xmca-l] Re: Objectivity of mathematics


> On Nov 5, 2014, at 7:26 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.