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[Xmca-l] Re: Objectivity of mathematics
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.
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.
> On Wed, Nov 5, 2014 at 5:11 PM, HENRY SHONERD <email@example.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.
>>> On Nov 3, 2014, at 10:51 PM, Ed Wall <firstname.lastname@example.org> wrote:
>>> 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.
>>> 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 Blunden*
>>>> 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.
>>>>> 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?
> It is the dilemma of psychology to deal with a natural science with an
> object that creates history. Ernst Boesch.