[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[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 disposition.

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.

*Andy Blunden*

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: xmca-l-bounces@mailman.ucsd.edu [mailto:xmca-l-bounces@mailman.ucsd.edu] 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 word-meaning]

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 <ablunden@mira.net <mailto:ablunden@mira.net>> 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"
            <ablunden@mira.net <mailto:ablunden@mira.net>> 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