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Topic: Reply to M. Goldenberg
Replies: 1   Last Post: Sep 9, 1995 1:34 AM

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Posts: 63
Registered: 12/6/04
Reply to M. Goldenberg
Posted: Sep 8, 1995 7:05 PM
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I would like to deal with several comments that have been
made about our critique of Rowser-Koontz article in the
Mathematics Teacher.

We have made several points, which we still stand by. The
first is that it is harmful to associate certain learning
styles with a particular racial or ethnic group. While the
authors do use the expression "many African Americans," we
wonder what "many" can mean. If it means only a small
percentage, then what's the point of making the statements; if
it means a large percentage, then we can certainly associate
the particular behavior with African Americans. One can only
assume that the authors meant the latter. In the context of the
article, and especially, in the context of its title, the word
"many" can only amount to an effective stereotype.
Furthermore, Goldenberg says nothing to enlighten us as to
what standards are used to determine who is African American.
This sort of determination would open up a discussion of race,
genetics, appearances, culture etc. Are we prepared to carry
such a discussion through all its details? And to what end?

The truly distressing thing is that all of the nonsense is
unnecessary. As we point out: "Had the authors simply stated
that various students learn and reason in various ways, and
that teachers must proceed with this knowledge and use diverse
teaching teaching techniques, they would have been merely
restating a widely proclaimed and accepted fact." Why the need
to mention African American or any other group? The same holds
for so-called "IQ." Why do research to correlate IQ with race?
Why not with eye-color or height? There is more variation
WITHIN "racial" or ethnic groups than BETWEEN these groups. We
must address the individual and the individual's needs. There
are two main reasons for the proliferation of classification
by race. The truely malignant one is to prove notions of
racial superiority (Shockley, Herrnstein, Murray, et. al.).
The other reason is to have a leg up in getting grants and
having papers published...

We agree with Judy Roitman about the use of different
teaching techniques. In addition to our statement just quoted,
we also say: "[we must] start the educational process from
where each student is situated" and "the authors are right in
asserting that this help [in sharpening reasoning and
computation skills] must come in varying formats." Goldenberg
certainly overlooked these statements.

Goldenberg chides us for failing to appreciate how Koontz
and Rowser distinguish between inferential and inductive
reasoning. In fact, they don't. Here is what they say. (1) "An
inference is a judgment made from observations or evidence."
(2) "Inductive reasoning forms generalizations from many specific
cases." This reminds me of the distinction between capitalism
and communism: "Under capitalism, man exploits man, whereas
under communism the reverse is true." If there is any
important distinction here, it escapes us. None of our
dictionaries give us any further clue. Perhaps Goldenberg can
enlighten us. We quoted Koontz and Rowser that inferential
reasoning "must not be thought of as inferior." Would
Goldenberg care to defend this statement?

When we face a student who is weak in mathematics, we must
try to find out why, and then address that student's needs.
Perhaps the student has had bad teachers, or is unduly
influenced by negative peer attitudes. Perhaps the student is
specifically math-phobic or learning disabled, or has never
reached the stage of intellectual development necessary for
abstract thought. Sometimes we can intervene intelligently, or
make a shot in the dark... or maybe just wait. For some, group
learning is helpful, for others, counterproductive. Does it
help to know that the student is African American, Nigerian,
Israeli, Chinese or rich? If the student is African American,
do we say: Aha! You probably "prefer novelty, freedom and
personal distinctiveness"? If the student is Asian, do we say:
You are obviously an underachiever? This is a very dangerous
road to go down.

Mark Bridger (

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