Devlin's Angle

January 1998

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 opposite.

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@stmarys-ca.edu) 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.