Date: Mar 13, 1997 2:57 PM
Author: Michael Paul Goldenberg
Subject: Re: Plausibility Arguments

I think Andre has raised some interesting, if not completely
unproblematic, points. I'd suggest that one issue is how fully we should
generalize from personal experience about what kids can know, should know,
or want to know (each of these is a huge quagmire). As I observe students
in middle- and high-school math classes each week, I never cease to be
amazed at the connections and (perhaps unknowingly) deep questions that
emerge in classrooms full of "low-track" students. And I'm equally amazed
at the hatred of mathematics, effort, learning, proof, giving plausible
reasons, etc., that are present in classrooms at many points on the
spectrum of difficulty. My sense is that there are important messages from
both kinds of observations about what and how to teach mathematics.
Responsibility for the less-satisfactory attitudes our students display is
not theirs alone, however (any more than it is their teachers' alone).

What we need more of, perhaps, is empathy and respect. David Hawkins
speaks in his essay "I, Thou, and It" about the need for respect between
students, between students and teachers, and between students and subject
matter. Andre clearly had a great deal of respect for mathematical issues
at an early age. Many of the students we teach don't. If we choose to
disrespect them simply because they haven't learned the same things as we
have and at the same points in development, I think we're unlikely to
improve matters very much.

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Michael Paul Goldenberg
University of Michigan 310 E. Cross St.
4002 School of Education Ypsilanti, MI 48198
Ann Arbor, MI 48109-1259 (313) 482-9585
(313) 763-9683 email: mikegold@umich.edu

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