|
Hi, Kevin,
Thanks for word of the project you have worked on
-- "Some folks on the list have heard about
this work before, so I'll be brief." Can you give more about
where/how I might find more in the xmca archives or
elsewhere?
It is also iMho that "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." The mathematics we are
talking about is content, right, not pedagocical strategies, and it is
subject to critique, analysis and change? It's not just common cause
we have about the status quo curricula, it's the same
cause.
I go further
than you in the following: ""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?" AND, I add, they
seldom open the door for mathematics development for most of us.
Many miss the mathematics by a mile or set up for later sabotage of
it. Those fifth graders (and the rest that NAEP shows have weird ideas
about fractions) and their teacher that Phillip White described? I grit my
teeth as I see them as younger students being set up for a massive muddle
because of inadequate critique, analysis and change of the mathematics content
in their early education.
I think we
agree that mathematics concepts are not ahistorical, apolitical,
or acultural. Think back to those jars with rattling tokens inside;
think of the number words (beyond the ones to 9) in Chinese; think
of "lowest prices" advertisements and the mathematics of the
fight against them; think of the connection to the mathematics Nancy
Ares and colleagues are developing to living wage, health care, and
taxes.
Peg
----- Original Message -----
Sent: Friday, November 12, 2004 10:07
AM
Subject: 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,
K.
Peg Griffin wrote:
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
|