Hi,
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.
Peg
----- Original Message -----
Sent: Thursday, November 11, 2004 2:02
PM
Subject: Re: math for reproduction and
domination
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.
In Peace,
K.
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
possible.
bb
On Thursday 11 November 2004 12:19 pm, Wolff-Michael Roth wrote:
Hi Bill,
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
teacher.
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
presuppositions.
Cheers,
Michael
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
that claim!
I'm going to step back and look at our own conversation. This is not
the
kind of troublemaking i'm interested in.
bb