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*To*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Subject*: [Xmca-l] Re: Objectivity of mathematics*From*: HENRY SHONERD <hshonerd@gmail.com>*Date*: Wed, 5 Nov 2014 21:17:01 -0700*In-reply-to*: <E7B63AAD-A65A-4F8A-A0CE-1FD88D6BE187@umich.edu>*List-archive*: <https://mailman.ucsd.edu/mailman/private/xmca-l>*List-help*: <mailto:xmca-l-request@mailman.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca-l.mailman.ucsd.edu>*List-post*: <mailto:xmca-l@mailman.ucsd.edu>*List-subscribe*: <https://mailman.ucsd.edu/mailman/listinfo/xmca-l>, <mailto:xmca-l-request@mailman.ucsd.edu?subject=subscribe>*List-unsubscribe*: <https://mailman.ucsd.edu/mailman/listinfo/xmca-l>, <mailto:xmca-l-request@mailman.ucsd.edu?subject=unsubscribe>*References*: <CAGVMwbUV9Jdf2XpAshWE0dCNcT1kHRTrpxGy=Ci2M3xR9N3rhQ@mail.gmail.com> <9A0CD8DC-7A92-4561-A550-EF5900B9B1CE@umich.edu> <CAGVMwbUcnDxvMbpfha4QVHKtU6mi+igRvxZhzFFj8hyynkDiwg@mail.gmail.com> <5883D78B-B4BC-4EB7-987E-06C3C2D22EB1@umich.edu> <CAGVMwbVugt4Mqh_jLosUdHNyRmg19dEaULa7weLj8y7jHSXn6g@mail.gmail.com> <5451DB76.7010007@mira.net> <CAGVMwbWSmg+0X=VvUQMojAtX911Hg6jmfYqkx3a2EoTjCq2OxA@mail.gmail.com> <54520634.9080302@mira.net> <CD06F23C-D0F7-4169-AB99-E025679FDA4A@umich.edu> <5452C9B0.70505@mira.net> <32EF9A39-CDDA-4258-BBDE-7D7658C85A03@umich.edu> <5455DA75.9040906@mira.net> <8EB7C6A3-BA03-469A-A2A5-94274633BE10@umich.edu> <CAHCnM0CGp_qJU5mVEt0ieiK8r-A7qvg0N=5-Fd5eqjOkaTqWqA@mail.gmail.com> <54585A04.8020708@mira.net> <AE980414-2565-49C5-881F-C1A33995A1D6@umich.edu> <3B024BCD-D68E-474C-A83A-35864F9C3027@gmail.com> <CAHCnM0B_PT6OhbYHwuw3+3XLvxTN6KAJ91KWjrT8ArkFz6RTPw@mail.gmail.com> <E7B63AAD-A65A-4F8A-A0CE-1FD88D6BE187@umich.edu>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Sender*: <xmca-l-bounces@mailman.ucsd.edu>

Ugh! > 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. > >

**References**:**[Xmca-l] Re: Apologies***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Objectivity of mathematics***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: Objectivity of mathematics***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: Objectivity of mathematics***From:*mike cole <mcole@ucsd.edu>

**[Xmca-l] Re: Objectivity of mathematics***From:*Andy Blunden <ablunden@mira.net>

**[Xmca-l] Re: Objectivity of mathematics***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: Objectivity of mathematics***From:*HENRY SHONERD <hshonerd@gmail.com>

**[Xmca-l] Re: Objectivity of mathematics***From:*mike cole <mcole@ucsd.edu>

**[Xmca-l] Re: Objectivity of mathematics***From:*Ed Wall <ewall@umich.edu>

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