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[Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]
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- Subject: [Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]
- From: Peg Griffin <Peg.Griffin@att.net>
- Date: Thu, 23 Oct 2014 11:25:45 -0400
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And thus the importance of finding a good germ cell for mathematics pedagogy
-- because a germ cell can "grow with" and "grow" the current "social
practice of mathematics." Whether someone agrees with the choice of germ
cell made by Davidov (or anyone else), a germ cell needs to be identified,
justified and relied on to generate curriculum content and practice, right?
[mailto:firstname.lastname@example.org] On Behalf Of Andy Blunden
Sent: Thursday, October 23, 2014 10:35 AM
To: eXtended Mind, Culture, Activity
Subject: [Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]
The claim that the ideal exists in the social environment from the beginning
is quite consistent, indeed relies upon, the claim that the ideal is being
continuously subject to transformation, that is, that mathematicians are
active developing the content of mathematics in the context of the problems
and resources the community is generating. Were this not the case, it would
be very difficult (though not impossible) for kids to acquire a mathematical
I think the basic ontogenetic principle fully applies to mathematics.
But the ideal is certainly not the absolute truths of arithmetic taught in
South African elementary schools. The ideal is the *social practice of
mathematics*. That is, of course, by its very nature, continually evolving
and transforming. The ideal is a pair of shifting goal posts.
Julian Williams wrote:
> I would like to expand a bit on Andy's point -
> First, I have often had very interesting discussions with children who
work out that 7+4 = 10 ... this is usually accomplished by a 'counting on'
method, which begins with the 7 ("1") and goes 7 ("1"),8 ("2") ,9 ("3") ,10
"4- there we are, 10!" ...
> 7 -- 8 --- 9 -- 10
> 1 ... 2 ... 3 ... 4
> Similarly 10 - 4 = 7 etc.
> (It doesn't really matter whether the teacher accepts the answer or
> not - the kids keep getting the answer 10... and we have data to prove
> it; until one day they are told they are hopeless and its time for
> them to leave and go down the mines/factory. See Billy Connolly's
> youtube hit on 'algebra'..)
> Second: Im pleased to say that the best arithmetic I am seeing in schools
now bears almost no relation to that I experienced 50 odd years ago as a
learner, and that I taught as a teacher 30 years ago... although there
seems still to be a lot that hasn't changed as much as Id like. Im thinking
of a lesson wherein different groups of children modelled their 'proofs'
that 3x28 = 84 using various methods, tools, etc.
> So Im afraid the story that arithmetic already exists in some ideal
> form in the social - cultural plane (eg in adult practices?), and so
> can/has to be somehow made present for the youngster in their earlier
> stages of development (if that's what Vygotsky really meant) is far
> too simple for me, and at its worst leads to terrible schooling
> practices, where there is no room for a child's intelligent argument
> that 7 + 4 really equals 10
> Andy: my sleight of hand here is that I translate your formulation of what
leontiev says "there is one true object/ive and the kids should come to know
it" into Vygotsky's " ideal form of arithmetic" where child development must
end up... thus your critique of Leontiev becomes my complaint about
Vygtosky's perezhivanie paper. Im sure you will say "not fair"?
> -----Original Message-----
> From: email@example.com
> [mailto:firstname.lastname@example.org] On Behalf Of Andy Blunden
> Sent: 23 October 2014 14:50
> To: eXtended Mind, Culture, Activity
> Subject: [Xmca-l] Re: In defense of Vygotsky [[The fallacy of
> Mathematics today is nothing like it was 300 years ago, Carol, even if
> it is in a South African elementary school. And the teacher wouldn't
> accept it if Johnny said that apes had evolved from human either or
> that gravity went clockwise. The ability to correctly reproduce
> things like
> 4+7=11 is not in my experience any evidence that a child has grasped
> what + or = means, and certainly no evidence that they have any grasp of
mathematics or even number. Of course, we might take the view that they
never will anyway, so being able to add is good enough for them.
> But if we take the view that it is worthwhile that a child learn what
science is and what mathematics is about, then in my view, the problems are
essentially the same whichever science it is.
> Of course, in general, the attitude a teacher takes to their material is
that it is objectively true and the kids should come to know it. But this
stance or attitude to knowledge, or science, is a very poor preparation for
adult life and citizenship. I don't see mathematics in principle as being an
exception. Perhaps a little teaching of the history of mathematics would
help? I don't know.
> *Andy Blunden*
> Carol Macdonald wrote:
>> I realise that, but it much more robust than orthodox science; i.e.
>> we are still doing the same maths as 300 years ago, where normal
>> science is very different indeed.
>> If Johnny said that 4+7=10, the teacher is not going to accept that,
>> is she?
>> On 23 October 2014 10:02, Andy Blunden <email@example.com
>> <mailto:firstname.lastname@example.org>> wrote:
>> Carol, mathematics is a natural science like any other.
>> It is neither the absolute truth nor merely social convention.
>> *Andy Blunden*
>> Carol Macdonald wrote:
>> Julian, Andy
>> I think arithmetic is something of a test case. Just as word
>> changes over time in a dynamic way, as recognised by
>> linguists, maths
>> truths don't. It would be difficult to argue that maths truths
>> of basic
>> arithmetic have changed over the centuries. I don't know about
>> maths truths
>> of a higher order.
>> Sorry if I use the terms arithmetic and maths interchangeably;
>> it's a South
>> African usage here in basic education.
>> On 23 October 2014 08:33, Julian Williams
>> Yes, just so, this is why I go to social theory eg Marx
>> and Bourdieu to
>> find political-economic contradictions within and between
>> But before we go there have we finally dispensed with the
>> notion in
>> Vygotsky's Perezhivanie paper that the situation or
>> environment is given
>> and the same for all, and the final form of development is
>> given in a
>> final, given 'ideal' form right from the beginning ( being
>> then associated
>> with an already given social plane).
>> I'm happy enough to accept that this is a false and
>> undialectical reading
>> of Vygotsky (after all who knows how the concept of
>> perezhivanie might have
>> matured in his hands)...
>> To return to my case - arithmetic. Many will say this
>> exists in ideal form
>> in the culture and all that needs to be done by
>> development is to bring the
>> child into the culture... Then the child is 'schooled'...
>> Passive, lacking
>> in agency, often failed, and at best made obedient to the
>> cultural legacy.
>> AsBourdieu says, through processes in school the class
>> system is
>> reproduced, and this is enculturation into the cultural
>> On 23 Oct 2014, at 07:08, "Andy Blunden"
>> <email@example.com <mailto:firstname.lastname@example.org>> wrote:
>> No, the point is that for ANL "meaning" refers to the
>> one true meaning
>> of something. He does not allow that the meaning of
>> something may be
>> contested, and that a meaning may be contested because of
>> heterogeneity in
>> society, different social classes, genders, ethnic groups,
>> social movements
>> and so on. For ANL there is only the one true meaning of
>> something which
>> "everyone knows" or individual, personal meanings, which
>> are therefore
>> taken to be subjective.
>> *Andy Blunden*
>> Annalisa Aguilar wrote:
>> This continues and extends from my original post
>> concerning Andy's
>> breakdown of ANL vs. LSV. There are about 8 points
>> total... [copypasta is a
>> starch of art]
>> --------------------------------------------------- 6. [The
>> fallacy of word-meaning] (see original post below)
>> --------------------------------------------------- You
>> say: "ANL believes
>> that motivation determines perception. The norm of
>> perception, the "true"
>> meaning of an object, is therefore the meaning it has for
>> the community as
>> a whole. I am questioning the validity of this concept of
>> "community as a
>> whole" in this context." So is it the case that
>> word-meaning is denied by
>> ANL because meaning and symbols "must be" cohesive across
>> the culture and
>> cannot have personal or spontaneous meaning? I can see the
>> politically to emphasize this, if the State is sanctioned
>> as the sole
>> arbiter of meaning. --- clip from previous post below Wed,
>> 22 Oct 2014
>> 06:28:48 +0000 Annalisa wrote:
>> _6th charge_: The fallacy of word-meaning
>> ---------- ANL believes that
>> the mental representation in a child's awareness must
>> _correspond_ directly
>> to the object in reality, and not just perceptually, but
>> also how the
>> object may relate and associate to other objects and their
>> meanings. The
>> example is a table. Because of this definition of, what I
>> will call here
>> for convenience (i.e., my laziness) "object-awareness",
>> ANL takes exception
>> with LSV's rendering of a _single word_ to stand as a
>> generalization to
>> reference the meaning of the word and as an independent unit
>> (word-meaning). Furthermore, ANL disagrees with the
>> existence of these
>> word-meanings, _as units_, but he also disagrees that they
>> are what
>> construct consciousness as a whole. ANL can say this
>> because he considers
>> consciousness and intellect to be synonymous. ----------
>> Andy's reply to #6 above: ANL believes
>> that motivation determines
>> perception. The norm of perception, the "true" meaning of
>> an object, is
>> therefore the meaning it has for the community as a whole.
>> I am questioning
>> the validity of this concept of "community as a whole" in
>> this context.
>> Carol A Macdonald Ph D (Edin)
>> Developmental psycholinguist
>> Academic, Researcher, and Editor
>> Honorary Research Fellow: Department of Linguistics, Unisa