# [Xmca-l] Re: In defense of Vygotsky [[The fallacy of word-meaning]

```I've been listening to this conversation and thought I might make a few observations (not absolute truths - smile)

As a person who does mathematics, I agree with what Andy writes here although the relevant social is, in a practical sense, often somewhat narrowly restricted. The mathematical problems that interest me are more than often those that interest my colleagues or currently in vogue (especially if by current one means 100 years or so - smile). It might be of interest to note that many mathematicians do not consider 'school arithmetic' mathematics although they consider it a necessary warm up.

In my observations and teaching of young children, I note that counting seems to be somewhat foundation to what they latter do in school mathematics. There is a progression through the beginnings  of ordinal arithmetic (rather like what happens with the alphabet - I am, by the way, leaving some early beginnings out) where number names predominate, a move into matching objects with names (i.e. 1-1 mappings) and a leap into cardinality with the numeric naming of a collection of objects. The very idea of addition seems to trigger - possibly because of the way we teachers stress fingers  - the act of counting on with, at times, the results Julian has noted. Usually, in my experience, the problem is more counting back (i.e. a form of subtraction). That is, the social practice that I see early on in US classrooms is

7    8-9-10-11               (i.e. one is counting on from 7)

11  10-9-8-6                  (i.e. one is counting back from 11)

Note the consistency as with Julian's example. The key operations (and it is mathematical as well as pedagogical) here (keeping in mind that there are some problems with the notion of subtraction) is not 7 + 4 or 11 - 4, but 7 + 1 and 11 - 1.
Children are often quite aware of the social conventions of counting, counting on, and counting back and will correct one another; however, they most often - although they trust us somewhat - do not seem to see these as absolute truths (an observation with which I agree). This trust seems to fade a bit by the time children hit fractions and signed numbers which, unfortunately, are taught as absolute truths or, even worse, meaningful models of objective reality.
Anyway, the problem as I see it, is helping kids make sense - within a social grouping (and they are often well aware that adults may see things in a very different and overly complicated way) - of the operations and objects of arithmetic, not getting them to reproduce over and over again some algorithm (as 'counting on' can be). I am not saying 'accuracy' is not important, but one needs to be in the ball park first. I had a horse once who, when reasonably distrustful of some notion of mine, balked; children are a lot smarter.

Oh, the problem with 'equality' seems mostly teacher and parent induced. Adult social practices involving mathematics are often quite problematic.

Ed

On Oct 23, 2014, at  9:34 AM, Andy Blunden wrote:

> Julian,
> 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
> ------------------------------------------------------------------------
> *Andy Blunden*
> http://home.pacific.net.au/~andy/
>
>
> Julian Williams wrote:
>> Andy/Carol
>>
>> 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
>>
>> :-)
>>
>> Julian
>>
>> 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
>> ------------------------------------------------------------------------
>> *Andy Blunden*
>> http://home.pacific.net.au/~andy/
>>
>>
>> Carol Macdonald wrote:
>>
>>> Andy
>>>
>>> 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?
>>>
>>> Carol
>>>
>>> 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
>>>    ------------------------------------------------------------------------
>>>    *Andy Blunden*
>>>    http://home.pacific.net.au/~andy/
>>>    <http://home.pacific.net.au/%7Eandy/>
>>>
>>>
>>>    Carol Macdonald wrote:
>>>
>>>        Julian, Andy
>>>
>>>        I think arithmetic is something of a test case. Just as word
>>>        meaning
>>>        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.
>>>
>>>        Carol
>>>
>>>        On 23 October 2014 08:33, Julian Williams
>>>        <julian.williams@manchester.ac.uk
>>>        <mailto:julian.williams@manchester.ac.uk>>
>>>        wrote:
>>>
>>>
>>>            Andy
>>>
>>>            Yes, just so,  this is why I go to social theory eg Marx
>>>            and Bourdieu to
>>>            find political-economic contradictions within and between
>>>            activities.
>>>
>>>            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
>>>            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
>>>            arbitrary.
>>>
>>>            Julian
>>>
>>>
>>>
>>>
>>>            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
>>>                ------------------------------------------------------------------------
>>>                *Andy Blunden*
>>>                http://home.pacific.net.au/~andy/
>>>                <http://home.pacific.net.au/%7Eandy/>
>>>
>>>
>>>                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
>>>            reason
>>>            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.
>>>
>>>                --end
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> --
>>> Carol A  Macdonald Ph D (Edin)
>>> Developmental psycholinguist
>>> Academic, Researcher,  and Editor Honorary Research Fellow: Department of Linguistics, Unisa
>>>
>>>
>>>
>>>
>>
>>
>>
>>
>

```