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Re: Manifesto on IMP
Posted:
May 8, 1997 5:03 AM
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On Wed, 7 May 1997, Dan Fendel wrote:
> Datta asserts that "IMP cannot satisfy the academic requirements . . ."
> The fact is that the IMP curriculum was thoroughly examined several times
> by a group of mathematicians from the University of California, appointed
> by the University specifically to determine its mathematical soundness.
> They certified the first three years of the program as fully meeting
> entrance requirements to U.C., and certified the fourth year as
> satisfying requirements for an additional year of college-preparatory
> mathematics.
Why just entrance requirements to U.C.? In some sense the IMP curriculum
may well satisfy the entrance requirements to the National Academy of
Sciences. Let me explain. The IMP book which I have read contains the
well-known unsolved problem about the iteration X_n+1 = X_n/2 if X_n
is even and X_n+1 = 3 X_n if X_n is odd. This problen has been unsolved
for 30 years although many competent mathematicians tried to solve it.
It may turn out to be as difficult as Fermat's Last Theorem which
Wiles solved and was elected to the National Academy of Sciences.
Several pages further your book contains exercises on addition and
subtraction of small integer numbers and a nice story which can help
pre-school children to understand this. However, nothing is done to
further this: no training with adding more than two numbers, no
training with multiplication or division, no training with greater
numbers etc.
Both pieces look strange in a high school textbook, but for opposite
reasons. People who are examining your book may choose this or that
or some other piece to base their judgement. Hence such a diversity
of judgements. The final judgement will be made by the actual practice.
Perhaps, students of IMP will become as competent in number theory
as Wiles and perhaps some of them will solve the iteration problem.
But it seems more probable to me that most students of IMP will
suffer from inadequate arithmetical skills.
Andre Toom
Department of Mathematics toom@universe.iwctx.edu
University of the Incarnate Word Tel. 210-646-0500 (h)
4301 Broadway 210-829-3170 (o)
San Antonio, Texas 78209-6318 Fax 210-829-3153
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