Re: CMU and situated cognition

Jay Lemke (JLLBC who-is-at CUNYVM.CUNY.EDU)
Mon, 20 May 96 13:45:49 EDT

I have just been reading a very interesting new PhD dissertation
(which must remain anonymous as I am an Examiner and it's not
yet passed), on mathematics education. It analyzes the discourses
(including the mathematical register and symbolic algebras and
graphical representations) of classrooms in private boys-only
and girls-only socially elite schools and in a working class,
mixed-sex school. Most of the work is a linguistic analysis, and
quite valuable as basic research, but there is also some
consideration of the gender and social class differences. The
author's view is that insofar as teachers make accomodations to
the dispositions of their students from non-dominant groups (i.e.
not male and upper-middle class), they wind up not modeling for
them the most powerful discourses, registers, and genres of
mathematics -- offering instead something much less valuable as
cultural capital. And to the extent that teachers do model
these discourses in their 'pure' forms, the result tends maximally
toward reproduction of the dominant forms.

So far as I could see, the accomodations made by the teachers
of the less-dominant students were either reasonable or necessary
under the conditions under which they were teaching. Some of them
might even be desirable in my view for all teaching. Most of them
were of two kinds: a greater attention to the interpersonal and
social-relations aspects of the human situation of teaching (as
opposed to a no-nonsense, lets-just-do-math attitude), and efforts
to make the content easier to learn by simplifying the language,
using alternative representations, etc. What the research here
shows, however, is that when this is done there is a concommitant
tendency to elide the corresponding formal representations (i.e.
a substitution instead of a scaffolding), and to in effect expect
less of students. While this is not necessary, and only a few
classrooms were included in this very detailed analysis, I think
it probably generalizes pretty well across my own experience
as an observer in science classes.

One factor contributing here is time, or pacing. There is time
to present the material once, not twice. It can either be presented
formally or less formally, not first less and then more formally.
There is time to build the scaffold, but not the building itself.

Another factor, more difficult to imagine solutions for, is that
dominant discourses are spoken from dominant social positions, and
this feature is built into their linguistic registers as well as
their distribution of use in the population. Lacking the habitus
to speak from a dominant position (lack of confidence/arrogance,
disinclination to the style of abstraction/assertion, etc.), these
discourses in their pure forms (even in their diluted forms) feel
not-right in the ears/mouths of many students. But their value as
cultural capital comes the combination of who speaks them, how they
are spoken, and what can be done technically with them. (Bourdieu
gets the first two, which many others miss, but misses the third,
which others may exaggerate and over-ideologize, but which is still
the basis for the other two).

So to Fritz Mosher's question about whether we do or do not do
students a favor by efforts to reproduce dominant genres, I have
at this point only very ambivalent answers. JAY.

JAY LEMKE.
City University of New York.
BITNET: JLLBC who-is-at CUNYVM
INTERNET: JLLBC who-is-at CUNYVM.CUNY.EDU