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[Xmca-l] Re: Maths and science in Russia
This is quite interesting. Let me give some different takes on some of what you write (I, by the way, am still unsure)
Some say part of the fetters you refer to are in the manner in which the equal sign is used (e.g. as compute) and the propensity for vertical addition in the early grades. I have seen a US 3rd grade teacher complicate things somewhat (she and the children were definitely working with countable objects) in starting with an unknown quantity, remove a known quantity, and, by obtaining a known quantity, figure out what the initial whole was without too much trouble. That isn't too say that things might not have proceeded more efficiently with another curricular starting point.
There is an interesting different between Korean students and US students in the early grades. US students have something called eleven and twelve and Korean students have something translated, in effect, as ten-one and ten-two. There has been speculation by some that these can be fetters of a sort on the way to decimal number (there are also things called nickel and quarter and five dollars not to mention inches, etc. which can also be somewhat un-helpful).
On a different note, what is the adult system of determining how old one is in years, exactly? I know how young children do this correctly, but inexactly.
On Dec 21, 2014, at 4:50 PM, David Kellogg wrote:
> 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 <email@example.com> wrote:
>> The essential 'method' is to facilitate students' own experimentation with
>> methods. This is called learning activity.
>> On 21 December 2014 at 12:15, Ulvi İçil <firstname.lastname@example.org> wrote:
>>> I know there are some works comparing Russia (Davydov's curriculum) and
>>> and even some works done in US with an application of Davydov's, e.g. by
>>> 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
>>> other scholar's method.
>>> Thanks in advance,
> <For Ulvi and Huw.docx>