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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