[Xmca-l] Re: Objectivity of mathematics

[anna sfard]

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
>
>
>
>