Hi Peg,
I don't have a copy of this special issue either at hand. Thanks for your
appreciative comments about the introduction--I agree with your assessment
of its value (I had a limited role in writing it). The issue is not really
about generalization/abstraction as a theme but you might want to look at
the commentary by Hoyles since she has developed her own view of this theme
which she (and Richard Noss) called situated abstraction (!). There was an
interesting session at AERA this year with Celia Hoyles and Anna Sfard and
others on the topic of abstraction in mathematics education.
I mentioned this source because it is an example of the changing paradigms
within math education--some of it directed by people from CHAT. There was a
very critical review of this special issue that shows how unhappy some
people in math ed are about this change in theory. It began as a panel
discussion at a meeting (Psychology of Math Education) which also generated
quite a bit of heat.
Ellice
--On Thursday, June 02, 2005 11:56 AM -0500 Peg Griffin
<Peg.Griffin@worldnet.att.net> wrote:r
> 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. Peg
>
>
> ----- Original Message ----- From: "Ellice Forman" <ellice+ who-is-at pitt.edu>
> To: <xmca@weber.ucsd.edu>
> 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
>> <Peg.Griffin@worldnet.att.net> 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: xmca@weber.ucsd.edu
>>> 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 <Peg.Griffin@worldnet.att.net> 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
>>
>>
>
>
Ellice Ann Forman
Department of Instruction and Learning
University of Pittsburgh
5M38 WWPH
Pittsburgh, PA 15260
(412) 648-7022
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