# [Xmca-l] Re: Maths and science in Russia

```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
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.
> >