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Re: math for reproduction and domination
the trouble with language is that it can be used differently. So the abstract in classical western philosophy and the abstract in dialectical materialism are different things, the first one corresponding to the ideal in idealism, the second one always being a concrete abstract, which Il'enkov nicely explains in terms of genetic linkages from parent to filial generations, the parent corresponding to the abstract, concretizing itself in different widely differing forms in the filial generations. Generalization in the western sense might not find similarities within the filial generation, because it looks for common features, whereas materialist dialectic looks for the history of the filial generation, which leads to the same common origin.
On 12-Nov-04, at 7:46 AM, Peg Griffin wrote:
I wonder about the difference between "rising from the abstract to the concrete" and "staying in the concrete."
I think the former means to have a model, an analysis, an interpretive frame that enlightens/transforms the "concrete."
The latter could mean having all that continuing to work with it OR being bound by physical and socio-historical forces, being an objective subject without a subjective object.
I think the former notion of concrete would ward off Kevin's concerns about "reified artifacts [that] reflect the cultural-historical-political status quo" except as they were exactly what one wanted to challenge.
For many US kids, "=" in "2+3=" concretely means something like "having counted to 2 and then counting on 3, write the final count number to the right." It is sort of a synonym for "2+3?" The mathematician's concrete = (and concrete 2 and 3) is something else altogether, and a good mathematics education allows student to rise to it.
(A four cell representation --abstract/concrete one dimension, general/specific the other -- is important here, not conflating the two dimensions.)
Has anyone heard of mathematics activities for middle school that take on Wal Mart as provisioner, employer, and taxed entity? I think it could rise to the concrete to address Michael's point about a mathematics curriculum that fails to educate students about how "every time you buy something at a bargain, or cheap, you actually take from someone else."
I remember being in a huge apartment complex in the southwest corner of Moscow. It had a huge food store. As was normal, then, people complained everyday about the empty shelves. One day we walked in and found the manager had taken down all the shelves -- pitiful little piles of the few available and unwanted commodities set out here and there over the floor like a strange droppings from some consumer beast. But the shelves were no longer empty.
It was a good joke and brightened many a person's conversation that day.
The manager purposefully stayed in the concrete and doing so made sly evaluation of the abstract perestroika.
<x-tad-bigger>----- Original Message -----</x-tad-bigger>
<x-tad-bigger> </x-tad-bigger><x-tad-bigger>From:</x-tad-bigger><x-tad-bigger> </x-tad-bigger><x-tad-bigger>Kevin Rocap</x-tad-bigger><x-tad-bigger> </x-tad-bigger>
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<x-tad-bigger>Sent:</x-tad-bigger><x-tad-bigger> Thursday, November 11, 2004 2:02 PM</x-tad-bigger>
<x-tad-bigger>Subject:</x-tad-bigger><x-tad-bigger> Re: math for reproduction and domination</x-tad-bigger>
Dear Bill, et al,
I think I appreciate your point Bill, and have also appreciated Michael raising the issues he has raised.
I just have to quickly comment on the concrete versus "philosophical path". I think that anyone advocating for disrupting hegemony is in part marginalized automatically by the fact that the "concrete" is more likely to include reified artifacts of the dominant ideology. So staying in the "concrete" arguably means valuing the reified dominant ideology over any alternatives and considering alternatives can always be seen as "abstract" or "philosophical" or "non-concrete" precisely because reified artifacts reflect the cultural-historical-political status quo one may seek to challenge.
My, no doubt inflation-ridden, two cents. Not meaning/intending to push the analysis of the notes and the rich discussion of what was observed and noted into a more ideological discussion at this juncture, however. ;-) I just wanted to weigh in one quick perspective from the sidelines.
Bill Barowy wrote:
What I meant was, I'm simply trying to cook some notes, and while that does
not preclude a cultural historical analysis at some later time, the analysis
at this moment centers on some kids learning some math. The analysis will
surely and eventually broaden, as yrjo's expansive methodolgy demands. Peg's
questions concerning NCTM content has already been moving things toward
cultural historical analysis.
And then, I have the impression of some history of xmca conversations going
down the dialectical philosophical path and then, paradoxically, failing to
rise back up again to the concrete. I'd like to stay concrete as long as
On Thursday 11 November 2004 12:19 pm, Wolff-Michael Roth wrote:
I am not one of those editors who imposes his/her view of the world on
others. I recognize the work in itself, even though I might disagree
with the content. You notice that my own paper dealt with the
production and reproduction of identity in the context of urban
science, and the fragility of "success" to be and become a student or
You may not be interested in this kind of trouble making, but in this
you make a choice as to the nature of the society you live in. I think
a dose of social analysis of the kind Dorothy Smith, who argues for a
feminist sociology, is required to interrogate our ideologies so that
we can bring about a rupture. Bourdieu, too, asks us, as social
analysts, to break with the gaze through radical analysis of our own
On 11-Nov-04, at 8:52 AM, Bill Barowy wrote:
On Thursday 11 November 2004 11:24 am, Wolff-Michael Roth wrote:
historical situation of the activity system. You seem to advocate that
we can understand children's and their teachers' actions just by
looking at a classroom.
I just can't believe YOU edited MY paper in MCA and can still make
I'm going to step back and look at our own conversation. This is not
kind of troublemaking i'm interested in.