The following was published under the Letters to the Editor in the March 1997 edition of the American Mathematics Society's Notices, Volume 44, Number 3

Dear Letters-To-The Editor:

Professors Wu [*Forum*, December 1996] and MacLane [*Letters to the
Editor*, December 1996] express criticisms of the current wave of "reforms''
in the teaching of mathematics. We feel that such criticisms are long overdue
and wish to congratulate both authors for expressing their opinions.

Wu and MacLane may not have a first--hand experience of the status of the "calculus reform" at second (and third) tier four-year institutions (as we do). At these institutions the "reforms" hold greater sway than at institutions where scholarship is more highly valued. At such institutions, in our experience, political activists from the administration, from the school of education, from those with a financial stake in the "reform movement", and from governmental "politically correct" funding organizations, promote such reforms (and are sometimes joined by a contingent of resident activist mathematicians). In the process, all distinctions between "proof", "explanation", and "observation" are often lost. In such schools, mathematics programs are often extremely starved for resources, even when compared to other programs at the same schools. In such a situation, a little seed money from cynical or ignorant book publishers, calculator salesmen and Washington bureaucrats can have an immense impact. Official looking flyers from commercial interests too often impress administrators (who are frequently more versed in "cooperative learning" than mathematics). Occasional letters critical of the "reforms" from famous mathematicians (famous, that is to other mathematicians) are printed in journals outside the reading circle of ordinary administrators.

In many such mathematics departments, Ph.D mathematicians are outnumbered by those with degrees from the school of education or those who lack advanced degrees. One can easily guess the effect this situation has on the current employment opportunities for new Ph.D.'s in our field. It is not uncommon to observe students, in class, circled in groups of four or five with their graphing calculators and four-colored, expensive and faddish calculus books attempting, in a few hours, to empirically rediscover the great insights of Newton, Leibniz and Gauss. Their "discoveries", expressed on poster boards or on group tests, are recorded frequently in "collective grades". These "educational" procedures differ in essential ways from the more successful methods used to teach mathematics in the past. Instead of developing deep insights, and a love for the beauty of mathematics, our students make observations with their calculators and look for patterns (much as our colleagues in experimental psychology). Theory makes such students positively uncomfortable.

The "reform" movement, in its religious fever and intolerance declares that the
teaching of mathematics must change to reflect modern technology, the demands of
the employment market and the increasingly fickle taste of our students (with
their abysmal algebraic skills). Ironically, these untested "reforms" forced
on second-tier colleges and public high schools, have coincided with students
*less* enthusiastic about mathematics, *less* able to apply what
they have learned (even to easy, artificial problems, much less to "real
world'' problems), and in general, *less* familiar and knowledgable about
mathematics. Lost in all the sloganeering is the fact that *real*
mathematics, as taught by *real* mathematicians, is becoming a rarer and
rarer experience at American second and third tier universities and colleges.
Mathematics without precision, rigor and proof, while not totally lacking in
value, is simply not mathematics!

In endorsing *NCTM Standards*, the AMS implied it was speaking for its
members. This is not so for the undersigned (both members of the AMS). Our
deep appreciation to Drs. Wu and MacLane for sounding the alarm on this threat
to our profession and to our students.

Boris A. Kushner

Marc H. Mehlman

**Last revised: 15 November 1998
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