Bruce, it was great to read your paper the day that a math education
candidate presented Susan Pirie's model of how mathematics understanding
develops. The candidate used the model to look microanalytically at how
students shifted from their generalizations back to more concrete terms in a
recursive but progressive way. I and others were skeptical of the model, but
appreciative of the detailed observations and elaboration of the students'
conceptual develoment it made possible. I think an understanding of
materialist dialectics would be extremely useful in this research project,
which does not now, from what I can tell, take into account the social
context or make explicit the limits of the model.
I think the model worked as a lens for pedagogy insofar as it foregrounded
the dialectic between general & specific, abstraction and evidence, that
knowledge building in our modern/post modern world is necessarily about. It
reinvoked for me the Wittgenstein quote that Paul Prior posted.
Judy
Judith Diamondstone (732) 932-7496 Ext. 352
Graduate School of Education
Rutgers, the State University of New Jersey
10 Seminary Place
New Brunswick, NJ 08901-1183
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