Re: For King Beach

From: Peg Griffin (
Date: Thu Jun 02 2005 - 09:56:01 PDT

Hi, Ellice,
Thanks for the reminder about one of the most interesting collections of the
good work in mathematics education. As I recall, the intro alone sets up
for good thinking about how and how come different research approaches
relate. I don't have a copy here so I'm not sure which parts would be most
helpful to look at concerning relations among different takes on
abstractions/generalizations for thinking about development in the
mathematics domain.

----- Original Message -----
From: "Ellice Forman" <ellice+ who-is-at>
To: <>
Sent: Thursday, June 02, 2005 10:38 AM
Subject: Re: For King Beach

> Peg,
> It has happened in math ed for example: Kieran, C., Forman, E., & Sfard,
> A. (Eds.). (2001). Bridging the individual and the social: Discursive
> approaches to research in mathematics education. (Vol. 46).
> Ellice Forman
> --On Wednesday, June 01, 2005 11:15 PM -0500 Peg Griffin
> <> wrote:r
>> It's just that maybe progress is made when you go beyond (or aside) "a
>> single overarching characterization." If it can happen in linguistic
>> studies with matters somewhat similar maybe it could happen in studies of
>> mathematics pedagogy. Peg
>> ----- Original Message -----
>> From: Mike Cole
>> To:
>> Sent: Wednesday, June 01, 2005 10:51 PM
>> Subject: Re: For King Beach
>> Peg & King et al-- I am missing some important link here. how does the
>> linguistic-metalinguistic-epitlinguistic set-of-distinctions/sequence
>> relate to the question of LSV and Davydov approaches to abstraction and
>> generalizations and different takes on/orinetations to the Jurow article?
>> Dense not in New Delhi
>> mike
>> On 6/1/05, Peg Griffin <> wrote:
>> Yes, the intent about epi/meta/plain-vanilla-linguistic was really in
>> service of the point King makes so well -- Gombert shows that for his
>> work at least the three coexist and I think it is interesting to think
>> about genetic relations among them (and discontinuities within and among
>> them) , too. Plus is there a pointer to where I could learn more about
>> the New Delhi work? Peg
>> ----- Original Message -----
>> From: Mike Cole
>> To: Xmca
>> Sent: Tuesday, May 31, 2005 9:53 PM
>> Subject: For King Beach
>> Mike and others,
>> I am going to dip my oar in the water here from New Delhi where we
>> are working with organizations trying to help street and working kids
>> build connections (not necessarily similarities) between their lives
>> in slums and the government schools--certainly involving
>> generalization is a broader sense. However, two points flow from the
>> juxtaposition of our current work with this conversation.
>> One is our tendency to look for a single overarching characterization
>> of generalization, e.g. as ascending from the abstract to the
>> concrete or the expansion of local discursive practices. Those of us
>> who are psychologists by training might recognize this as our
>> discipline's historical desire for single process explanations such
>> as learning transfer. Davydov's concept of substantive
>> generalization, for example, makes far more sense to me in the
>> context of teaching and in science than it does where there are not
>> clearly generative "germ concepts." Trying to makes sense of the
>> transitions that primary-aged kids make between school and home/work
>> involves so many levels of generalization as to make single
>> process/single principle constructs problematic.
>> The other is a tendency with generalization to focus on that which
>> develops with some degree of commonality across social space and time
>> rather than on the production of disjunctions and contradictions as
>> well. Like Michael Roth here I do find Hegel and Ilyenkov (partic.
>> Dialectics of Abstract and Concrete) helpful in thinking about
>> generalization more broadly than the production of similarity. The
>> contradictions and disjunctions between what the kids must do here in
>> their daily lives and what they do in the school classrooms have far
>> greater developmental potential than do any hoped for highly
>> "abstracted" set off commonalities between studying in school and
>> working on the streets (or well-intentioned but misguided attempts to
>> "smooth" the daily transitions that these kids make between the
>> streets and the school by making "word problems" out of their
>> experiences working with their families).
>> Cheers,
>> King
> Ellice Ann Forman
> Department of Instruction and Learning
> University of Pittsburgh
> 5M38 WWPH
> Pittsburgh, PA 15260
> (412) 648-7022

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