Thanks for your comments. Building on your grocery example I'll share
one way we have tried to balance the issues in our Connecting Math to
Our Lives Global Learning Network project. Some folks on the list have
heard about this work before, so I'll be brief.
The idea of having students internationally identify staple grocery
items and their prices and to share those and make currency
conversions, etc. is not new, and has now been done fairly often. What
we tried to do to extend the concept was to have students identify
different jobs or occupations in their county as well and how much
people make, to compare/contrast differences within and across
countries and localities. Then, we asked students to describe and
calculate the amount of time and type of labor in a given job or
occupation that was required to purchase staple grocery items. So the
price became more clearly linked to differential expenditures and
experiences of time and labor to earn the same grocery items (both
within a locality, in terms of differential wages and labor locally, as
well as across localities and countries).
That opens the door potentially to examining a range of social and
economic issues within the context of math activities, no?
That is, of course, just one example. But what I had in mind and
perhaps Michael did as well is that the types of problems, examples,
choice of content, etc. in well-established math curricula seem to
seldom open the door to more critical cultural-historical-political
analyses, no? Thus, we only have isolated examples here and there and a
flood of status quo curricular content. So as innovative as a
curriculum might be in the type of pedagogical strategies it promotes,
if that same level of innovation and potential for critique, analysis
and change are not found in the choice of content and examples it falls
This is a risk we run, perhaps, if we see pedagogy and content as
relatively independent (and then underlying match concepts as, perhaps,
even more acultural or apolitical with the choice of pedagogies and
content representations of those concepts as a less important or
salient window-dressing of sorts). I'm stating this perhaps too
extremely, but you get my gist. And this is an editorial perspective
;-) not specifically related to the details of what you, Bill and
others have been discussing, per se (in other words, I'm not trying to
characterize your conversation, just to help explicate what came to
mind for me which Michael's point).
At the same time it has been edifying to read the ways in which you,
Bill and others make sense of the rich descriptions that Bill provided.
Peg Griffin wrote:
I wonder about the difference
between "rising from the abstract to the concrete" and "staying in the
I think the former means to have a
model, an analysis, an interpretive frame that enlightens/transforms
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
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
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
Original Message -----
Thursday, November 11, 2004 2:02 PM
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
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.