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[Xmca-l] Re: Objectivity of mathematics



No Huw, I am not saying "there is no outside to discourse." On the contrary. I am saying that a properly developed discourse theory allows that the world has constraints which cannot be altered by discourse. Activity Theory, properly developed, also recognises that there are relations which are objective and cannot be changed by activity. And Vygotsky warned us against pitting act against word. My objections is only to those elaborations of Activity Theory or Discourse Theory which claim that there is nothing outside the Activity/Discourse. So *obviously* children learn mathematics by learning to participate in mathematical discourse according to social conventions applying to that specific discourse. But my point is only that that discourse is constrained by objective relations (and can therefore be rationally reconstructed), and social conventions can turn out to be wrong. Mathematics is not *just* a social convention. Interesting isn't it, that Leibniz and Newton each discovered calculus at the same time, but each gave it a completely different form.

Andy
------------------------------------------------------------------------
*Andy Blunden*
http://home.pacific.net.au/~andy/


Huw Lloyd wrote:
The simple problem here, Anna, is that actions require memory.  To act is
to exercise memory.  This may be why Andy is saying there's no outside to
discourse and is the reason why I proffered a way of construing discourse
that included action.

Best,
Huw

On 8 November 2014 07:16, anna sfard <sfard@netvision.net.il> wrote:

Hi Huw,

I really like your metaphor of discourse as a plane with "kinds of
mathematical knowledge ... traversing through that plane". It is for such
metaphors, if anything, and for the kind of imagery that generates it that
one should learn mathematics!

This metaphor shows me very clearly, however, that you and I are not at
the same page when it comes to the use of the word discourse. I am
insisting on this point because, unlike you, I think that "the distinction
between when something is or isn't discursive" IS "a big deal". See, for
me, discursive is tantamount to communicational. If so, when you say
"memories derived from non-discursive actions ... are not discursive", I
cannot agree. Having memories, no matter about what, is always a
communicational act. The fact that memory is about something non-discursive
cannot change this. When you say it does, you "collapse" the talk with what
is being talked about (we commit  such "ontological collapses" all the
time, so you're definitely not alone :-)).

And since Andy's post is coming just as I am about to send this email, let
me add that while I agree with Andy that activity theory and the discursive
framework are doing similar jobs in similar, but mostly parallel ways, I am
wondering about why Andy thinks that the equation 'math = discourse'
implies that 'there is no "outside" to discourse'. But this, probably, is a
different story, and since I do have life beyond [this] discourse, I think
I must leave it here :-)

anna

-----Original Message-----
From: xmca-l-bounces@mailman.ucsd.edu [mailto:
xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Huw Lloyd
Sent: Friday, November 07, 2014 10:27 PM
To: eXtended Mind, Culture, Activity
Subject: [Xmca-l] Re: Objectivity of mathematics

Hi Anna,

I think with that clarification about how you're referring to discourse
the point may be put more simply.  That is, that memories derived from
non-discursive actions contribute towards thinking and these memories are
not discursive (although they could be made to be discursive in a limited
manner).

For me, the distinction between when something is or isn't discursive
isn't a big deal.  But if you're presenting a sense of mathematical
competence upon discourse, then it becomes more important to demonstrate
that discourse offers a sufficient explanation.  Personally, I would see
discourse as a plane, and the kinds of mathematical knowledge being
referred to as often traversing through that plane.  That would mean that
discourse contributes to specific links in that genetic development, but
that discourse was not the source of that genesis, but that, however, the
social situations established through discourse may promote such
development and that interesting event that are non-discursive may be
reported discursively.  Those circumstances could give the illusion that it
was all happening discursively.

Best,
Huw



On 7 November 2014 17:01, anna sfard <sfard@netvision.net.il> wrote:

Hi Huw,



You say:



Well, I think I pointed to the source of the issue with respect to the
fabric of actions.  If you say that the entirety of actions are
discursive, rather than mediated by discursive means, that's fine.
But it means you're introducing phenomena typically inaccessible to
the analysis of discourse into this terminology.  Actions communicate,
but they also interact with the world of objects.



I didn't mean to say that "the entirety of actions are discursive",
this would be strange. There are non-discursive actions, of course.
Sometimes, they may be mediate by discourses. But it is important to
remember that discourses are not just talking – there is also
gesturing, drawing etc. But including those in discourse
(communication) does not mean putting there "phenomena inaccessible to
analysis within this terminology". I think your tacit assumption was
that discourse is exclusively a language thing, and can thus be analyzed
only with the methods used by linguists?

You also say:



Particular important points with respect to competence include notions
of independently solving tasks.  You can call that an inner discourse,
but note that in a developed form there may not actually be any
internal discourse but rather simply a memory, a knowing about
consequences of a considered action and what is required.  And this
memory is not only derived from participants but from our interactions
with objects -- things going on beneath the stratum of communication.
The use of discourse can be a rather coarse medium.  A toddler
learning to put a jumper on does not do it through talking, though
talking may help organise it a little.

Is there a contradiction between the claims "this person is recalling
things" and "this person is involved in a discourse (communication
with herself)"? I don’t think so. Recall may be not (always) the kind
of inner discourse the teacher would like to see, but it is a
discourse nevertheless. Learning to walk or dress, in itself, is not
discursive, so it doesn't belong to the debate what is and what is not
inner discourse (thinking). By the way, we may do this learning of
walking or dressing a bit more "discursive" by talking or gesturing to
the kid, thus giving her advice.



You say:



Re reductionism.  I think its often the case that people will reduce
whenever there is opportunity to.  I don't know whether the adjective
"acquisitionist" applies, though I do know of one mathematics
professor communicating some rather negative gestures about
mathematics as communication.  Personally, I thought that was rather
interesting, because the wide use of one of this professor's books
helped me to realise that there was a problem with generalisation in the
way mathematics is taught.

Hmmm, I don't know what to say. I'm afraid I'm not clear enough about
what you meant.



But anyway, this is helpful, so thanks, Huw. Hope my response is
helpful too J



anna













-----Original Message-----
From: xmca-l-bounces@mailman.ucsd.edu [mailto:
xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Huw Lloyd
Sent: Friday, November 07, 2014 5:57 PM
To: eXtended Mind, Culture, Activity
Subject: [Xmca-l] Re: Objectivity of mathematics



Hi Anna,



Well, I think I pointed to the source of the issue with respect to the
fabric of actions.  If you say that the entirety of actions are
discursive, rather than mediated by discursive means, that's fine.
But it means you're introducing phenomena typically inaccessible to
the analysis of discourse into this terminology.  Actions communicate,
but they also interact with the world of objects.



Particular important points with respect to competence include notions
of independently solving tasks.  You can call that an inner discourse,
but note that in a developed form there may not actually be any
internal discourse but rather simply a memory, a knowing about
consequences of a considered action and what is required.  And this
memory is not only derived from participants but from our interactions
with objects -- things going on beneath the stratum of communication.
The use of discourse can be a rather coarse medium.  A toddler
learning to put a jumper on does not do it through talking, though
talking may help organise it a little.

Re reductionism.  I think its often the case that people will reduce
whenever there is opportunity to.  I don't know whether the adjective
"acquisitionist" applies, though I do know of one mathematics
professor communicating some rather negative gestures about
mathematics as communication.  Personally, I thought that was rather
interesting, because the wide use of one of this professor's books
helped me to realise that there was a problem with generalisation in the
way mathematics is taught.
As far as I can tell, if you spell out the details of "internalised
discourse" then I expect you won't get the same kind of reaction...



Is that any clearer?



Best,

Huw







On 7 November 2014 10:57, anna sfard < <mailto:sfard@netvision.net.il>
sfard@netvision.net.il> wrote:



Hi Huw,
Thanks for your thoughts. I agree with much of what you say. I would like to know more, though, about why you think that if you talked about problem solving in discursive terms, "you'd quickly end up
with
linguists reducing it to wording, and various kinds of "acquisitionists" thinking that this is where you're going." I do think about these processes in discursive terms and feel, on the contrary, that this is what guards me against objectification and
acquisitionism. So why?

And on this occasion, to the other debate, the one about "objective".
If you assume the discursive stance, this word becomes an oxymoron. Objective, as I understand it, means "mind independent", bound have
a
given form independently of one's tastes, values and judgments. But this adjective ("objective") refers to narratives, to what people say/think ("facts" are subcategory of narratives). So... anna -----Original Message----- From: <mailto:xmca-l-bounces@mailman.ucsd.edu>
xmca-l-bounces@mailman.ucsd.edu [mailto:

 <mailto:xmca-l-bounces@mailman.ucsd.edu>
xmca-l-bounces@mailman.ucsd.edu] On Behalf Of Huw Lloyd

Sent: Friday, November 07, 2014 3:24 AM
To: eXtended Mind, Culture, Activity Subject: [Xmca-l] Re: Objectivity of mathematics Hi Anna, Perhaps you could also assert that quantitative choices, predicated upon social commitments, offer a means to go beyond those tentative bonds formed in numerical rituals. Commitments, such as commitment to a task that makes it a problem, seem to be important. Also, it seems to me that problem solving (mental searching etc) is something that should have a first class status in a theory about mathematics. The problem I'd have with referring to these processes as discourse is that I think you'd quickly end up with linguists reducing it to wording, and various kinds of "acquisitionists" thinking that this is where you're going. A second problem, for me, with fusing communication and cognition is the distinct role that communication has in mediating actions,
rather
than comprising the fabric of actions. For me, the act of
exercising
that fabric, whether mentally or in relation to a present object, induces transformations. I don't think these issues conflict with your account, but perhaps there's quite a bit that is skimmed over (such as the bit about individualized discourse, perhaps). I enjoyed your paper. :) Best, Huw On 6 November 2014 06:10, anna sfard <
<mailto:sfard@netvision.net.il>
sfard@netvision.net.il> wrote:

Hi,
I have not been aware of this super-interesting (for me) thread,
and
now, when I eventually noticed it, I cannot chime in properly. So
I
am doing this improperly, simply by attaching my own paper. Those who are interested enough to open the attachment will see the relevance of its theme to the present conversation. And although I mention Davydov only in an endnote, he is very much present. The theses I'm arguing for seem to substantiate his request for taking the quantitative discourse, rather than the numerical, as a point
of
departure for the process of developing child's mathematical thinking (we cannot help it, but in our society, these two discourses appear in the child's life separately and more or less
in
parallel, with the quantitative discourse free from numbers and
the
numerical one innocent of any connection to quantities; at a
certain
point, these two discourses coalescence, thus giving rise to the incipient mathematical discourse; but at the pre-mathematical
stage,
quantitative discourse is meaningful to the child on its own, as
it
supports the activity of
choosing, whereas numerical discourse is but a way to bond with
grownups).

anna