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Re: math for reproduction and domination

Dear Peg,

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 short, imho. 

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.

In Peace,

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. 
----- 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,

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:
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
	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
that claim!
I'm going to step back and look at our own conversation.  This is not
kind of troublemaking i'm interested in.