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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 22:02:27 -0700*In-reply-to*: <CAG1MBOEu-vXK9XX8d1jx+hixkYtrLz6HRDH-=yHoAuH9iT=Vog@mail.gmail.com>*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> <CAHCnM0BiOUEptT3SNrMKDGwNjyaj0nVAvi3o3UzZuvYy64p1Yg@mail.gmail.com> <CAG1MBOEu-vXK9XX8d1jx+hixkYtrLz6HRDH-=yHoAuH9iT=Vog@mail.gmail.com>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Sender*: <xmca-l-bounces@mailman.ucsd.edu>

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? 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. >>

**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>

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

**[Xmca-l] Re: Objectivity of mathematics***From:*Huw Lloyd <huw.softdesigns@gmail.com>

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