Re: Arievitch discussion

From: Peter Moxhay (
Date: Mon Jun 28 2004 - 12:16:18 PDT


The abacus example is a good one. We see the same kind of thing in
our work with Davydov's math curriculum when first graders start to
develop addition and subtraction skills for problems of the form:
(some number up to 10) plus/minus 1, 2, or 3. The curriculum includes a
structured progression from (1) a physical action (moving on the
number line through a gesture or by drawing an arc) to (2) a verbal
action (counting up in down after interpreting a symbolic expression
like 10 - 3 = ?) to (3) giving the answer directly with all actions
"folded up."

But, to what extent can we pursue this kind of folding/unfolding of
actions a la Gal'perin as "participating in a culturally organized
activity"? (Beyond the fact that abacus use and school arithmetic are
culturally derived.) How does this idea of a movement towards
"internal plane" (actions without the physical objects present) provide
some kind of breakthrough idea, as Arievitch suggests, to overcome the
he mentions in his conclusion?


> Yes, I just tripped over Eugene's article again yesterday looking for
> something else.
> Jim Wertsch goes a different direction, preferring to distinguish
> mastery and internalization -- he is thinking about Russians who
> mastered
> the version of history they were fed in Soviet times, but disbelieving
> (e.g., not internalizing) it.
> Lets take the summary of the Galperin positions you provide:
> the key feature of Gal'perin's analysis is
> the idea that
> there is a specifically human plane of action that "enables humans to
> act with
> symbolic substitutes of objects without those objects being physically
> present."
> And that this plane is what, for better or worse, is labeled by the
> somewhat misleading
> term "internal plane of action."
> Now, doesn't work of abacus experts with a "mental abacus" (Hatano et
> al,
> also summarized in a paper by me and Jan Derry on my website about
> tools
> and intelligence) fit this defintion? An abacus expert, hands folded in
> his/her lap (usually his I suspect in this case) can be given a set of
> 10 digit numbers, say, a dozen, and asked to add them as fast as the
> experimenter can pronounce them. And the expert does so with no abacus
> in site. Of course, the abacus expert is participating in a culturally
> organized activity, although a somewhat odd one. But the actions of the
> expert certainly appear to imply the ability to act with
> symbolic substitutes of objects without those objects being physically
> present."
> mike

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