Pam Sorooshian

I love Keith Devlin's writing and his radio program - I take a lot of
what I talk about at conferences from him.

I thought you all might enjoy his ideas, even though you're not doing a


Math + Rigor = College
According to the recent US Department of Education Report Mathematics
Equals Opportunity, completion of a rigorous program of mathematics at
high school pays huge dividends when it comes time to enter college,
regardless of the course of study pursued at college level.
Does this provide support for the back-to-basics movement? Not at all.
At least, not at all if by "basics" you mean the ability to perform
mental arithmetic or do long division. The message in the DOE report is
that, for most people, when it comes to high school math, it's not what
you learn that counts, it's the mental skills you develop.

When the automobile became widely available, skill at riding a horse
was replaced by skill at driving a car. Likewise, in the age of the
pocket calculator and the electronic computer, computational skill is
no longer necessary. We need other abilities. Training students to be a
poor imitation of a $30 calculator is a waste of time for both teacher
and students.

Whenever I say this kind of thing, I am invariably bombarded with
accusations that I am advocating a lowering of standards. Not at all.

Using -- I mean using properly -- calculators and computers does not
represent a reduction in skill or the need for accuracy. On the
contrary, successful use of today's computational aids requires far
greater mathematical skill, and much more mathematical insight, than we
old timers had to master to get our sums right.

Those who claim that use of computational aids and an increased
emphasis on conceptual understanding lead to lower standards are way
off target. In my experience, the only thing that leads to lower
standards is a lowering of standards. And you can lower standards just
as easily with an abacus as with the latest Pentium computer.

Today we live in a society that is largely shaped by mathematics --
though by one of life's paradoxes, the more important mathematics has
become in our lives, the more it has disappeared into the background.
You would not know it unless you looked closely, but large parts of
modern communications, transport, medicine, entertainment, sport,
financial trading, and even law enforcement, all make heavy use of,
often sophisticated mathematics. In the industrial age, we burned
fossil fuels to drive the engines of society. In the information age,
the fuel we burn is mathematics. The mathematics involved is so
specialized that we cannot hope to teach it in our schools. What we can
-- and should -- do is make sure our children are prepared to acquire,
quickly and efficiently, what particular math skills they require when
the time comes.

The bulk of that basic skill set on which each individual can build in
later life has little to do with numbers or arithmetic. The industrial
age was an age of number and arithmetic. The information age is quite
different. The mathematics used today is the mathematics of abstract
patterns, relationships, and structures. As we continue to revise our
curriculum for the high school math class of the next millennium, we
have to accept the fact that the mathematics we teach today's students
will not be (at least, should not be) the same as their parents
learned. But that does not make it easier or less rigorous. Quite the

In terms of arithmetic, getting the right answer to a long division
problem using pencil and paper is no more important to today's new
citizen than being able to use a horse-drawn plow. On the other hand,
getting the right answer to a problem using a powerful calculator or a
computer can be crucially important. It's also much harder. It's not
the same problem the student is solving, of course. That's why the math
curriculum has to change. The need for accurate, rigorous, precise
logical thinking is more important to more people today than at any
time in history. To try to achieve that ability by harking back to the
mathematics taught a half century ago, as continues to happen in states
across the nation, will surely fail with today's students. They -- and
we -- deserve better.

- Keith Devlin

Devlin's Angle is updated at the beginning of each month.
Keith Devlin ( devlin@...) is Dean of Science at Saint
Mary's College of California, in Moraga, California, and a Senior
Researcher at Stanford University. A regular commentator on mathematics
issues for National Public Radio, he has just finished work on a
six-part television series and accompanying book called Life By the
Numbers, which set out to show how mathematics is used in sports,
entertainment, communications, transport, business, in fact, in all
walks of life, both work and play. Hosted by movie star Danny Glover,
Life By the Numbers will air nationwide on PBS in April. The book will
be published at the same time.