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*To*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Subject*: [Xmca-l] Re: Maths and science in Russia*From*: David Kellogg <dkellogg60@gmail.com>*Date*: Mon, 22 Dec 2014 07:50:03 +0900*In-reply-to*: <CAG1MBOH9B-yZVdu8N5BV157p4z9MpGxUsMQDtPrmgZDs2_Vyag@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*: <CABjfC8KQyGQiv=5pyRR6z8Jof0KroEdm03VwE43y_md0zzfN7Q@mail.gmail.com> <CAG1MBOH9B-yZVdu8N5BV157p4z9MpGxUsMQDtPrmgZDs2_Vyag@mail.gmail.com>*Reply-to*: "eXtended Mind, Culture, Activity" <xmca-l@mailman.ucsd.edu>*Sender*: <xmca-l-bounces@mailman.ucsd.edu>

Let me float a hypothesis, and see what Huw and Ulvi make of it. A learning activity (any learning activity) is best described not as a synoptic hierarchy of molar units like operation, action and activity. Viewed diachronically, from the point of view of psychology, a learning activity is a non-hierarchical historical sequence, such that any given "method" eventually, in time, turns out to fetter progress and must be discarded, and the end result is not an inter-mental social form of activity but instead an intramental psychological one. Take the Schmittau work that Ulvi references as a concrete example. Schmittau showed that the American curriculum (like the Korean one) introduces the notion of number by counting separate objects. This allows the child to grasp the number very concretely and quickly. Groupings are then introduced, and this corresponds once again to what we see children do naturally (see Chapter Eight of HDHMF). So at every point the American curriculum takes the line of least resistance. But that means that at a specific point, the notion of number based on concrete, separable objects becomes a fetter on the child's progress. Schmittau locates this point quite precisely: it's the moment when the child, accustomed to add known quantitites of physical objects together to obtain an unknown quantity, is asked to start with an unknown quantity, remove a known quantity, and, by obtaining a known quantity, figure out what the initial whole was (e.g. "I made a bunch of snowballs and put them in the freezer. I threw one at my big brother at a Christmas pary, and two at my friends when they teased me at New Years. Now I have only half a dozen left for April Fools Day. How many snowballs did I make?") Chapter Eight of HDHMF asks the question of whether "arithmetical figures" (that is, physical groupings of countable objects) will keep the child back from learning the symbolic manipulations afforded by the decimal system of writing digits, or whether they will naturally evolve into the decimal system (because the children will of their own will invent a physical grouping of ten objects). Interestingly, Vygotsky concludes that any experiment along these lines would be unethical (and THERE is a correspondence with Chomsky, who has often correctly noted how one of the things that keeps linguistics in a "paper and pencil" era corresponding to sixteenth century physics is the immorality of experimentation on human subjects). But, like Chomsky, he resolves the question with paper and pencil (in Chapter Thirteen) with a very amusing MIS-reading of Thorndike's "Psychology of Arithmetic". Thorndike is criticizing the way in which our parents and grandparents were taught arithmetic as a symbolic system akin to language. Vygotsky apparently doesn't get Thorndike's irony, and thinks that Thorndike is lauding this culturally approved method over Lay's newfangled system based on "arithmetical figures" (dominos, in fact). See the attachment: it involves analyzing a picture where there is one girl on a swing and another on the ground ("How many girls are there?") a kitten on a stump and another on the ground (which Vygotsky misremembers as dogs). And so, by a process of misreading and misremembering, Vygotsky turns Thorndike into a cognitivist. Thorndike would probably rather be a dog. Interestingly, the way Vygotsky resolves the whole dispute is similar--that is, the child triumphs not through the adequacy of his or her own method or through seeing the superiority of the adult method, but rather through the inadequacies of both. For example (and this is my example), a child with a notion of number based entirely on separable objects has a very hard time measuring how old he is in precise terms. On the other hand, the adult method of measuring years out in months is NOT a decimal method. The child therefore has to grasp and perfect the adult system just in order to answer the simple question--how old are you in years EXACTLY? David Kellogg Hankuk University of Foreign Studies On 22 December 2014 at 07:01, Huw Lloyd <huw.softdesigns@gmail.com> wrote: > Ulvi, > > The essential 'method' is to facilitate students' own experimentation with > methods. This is called learning activity. > > Huw > > On 21 December 2014 at 12:15, Ulvi İçil <ulvi.icil@gmail.com> wrote: > > > > Hello, > > > > I know there are some works comparing Russia (Davydov's curriculum) and > US, > > and even some works done in US with an application of Davydov's, e.g. by > > Schmittau. > > > > I would like to know, not in detail, but just in general, which main > > factors lie behind this success in Russia, it is Davydov, or Zarkov or > any > > other scholar's method. > > > > Thanks in advance, > > > > Ulvi > > >

**Attachment:
For Ulvi and Huw.docx**

**Follow-Ups**:**[Xmca-l] Re: Maths and science in Russia***From:*Ed Wall <ewall@umich.edu>

**[Xmca-l] Re: Maths and science in Russia***From:*Huw Lloyd <huw.softdesigns@gmail.com>

**References**:**[Xmca-l] Maths and science in Russia***From:*Ulvi İçil <ulvi.icil@gmail.com>

**[Xmca-l] Re: Maths and science in Russia***From:*Huw Lloyd <huw.softdesigns@gmail.com>

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