Devlin's Angle

March 1998

Forget "Back to Basics." It's Time for "Forward to (the New) Basics."

The report card for US secondary school math education came in at the end of February, in the form of a report based on the Third International Mathematics and Science Study (TIMSS). In tests of mathematics general knowledge and advanced mathematics, the results obtained by US 12th-graders were among the lowest of the participating countries.

Secretary of Education Richard Riley called the results "entirely unacceptable." It is hard not to agree. The question is, what is the best response? It is tempting to look for ways to simply improve our rankings on the international league tables. But math education is not an Olympic sport. Topping the league tables might make us feel good. But as the nation that leads the world in science and technology, the question we should be asking is: How can we lead the world in math education? And since school education is supposed to be a preparation for adult life, that means: What is the best way to prepare our children for life in the twenty-first century?

The first thing to realize is that the nation needs only 3 or 4 percent of the population to be highly skilled in mathematics. Of the remainder, hardly any will ever need or make real use of any appreciable knowledge of, or skill in, mathematics. What mathematics they need and use they have probably already met by the time they are fourteen years old.

But that does not mean we should filter out the top 3 percent and then drop math from the high schools for the others. According to a Department of Education white paper, "Math Equals Opportunity," released in fall of last year, completion of a rigorous program of mathematics at high school pays huge dividends when any student enters the work force or goes to college, regardless of what profession or course of study the individual chooses. This effect is even greater for low-income students.

Using data from several long-term studies, the report found that 83 percent of high school students who took algebra and geometry courses went on to college. That's more than double the rate (36 percent) of students who did not take these courses.

Low-income students who took algebra and geometry were almost three times as likely to attend college as those who did not. While 71 percent of low income students who took algebra I and geometry went to college, only 27 percent who did not take those courses went on to college. By way of comparison, 94 percent of students from high-income families, and 84 percent of students from middle-income families who took algebra I and geometry in high school went on to college. Sixty percent of students from high-income families and 44 percent of students from middle-income families who did not take algebra I and geometry went to college.

The study also found that mathematics achievement depends on the courses a student takes, not the type of school the student attends. Students in public and private schools who took the same rigorous mathematics courses were equally likely to score at the highest level on the NELS 12th grade mathematics achievement test.

How do we reconcile these data with my observation about most people never using any math beyond the 8th Grade? Easily. The message 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. That gives us considerable freedom in what we teach in the math class. Let's use it.

Today, we live in an invisible universe of mathematics. We burned fossil fuels to power the engines of the industrial age. The fuel we burn to drive the information age is mathematics. Mathematics is used in modern communications, transport, medicine, entertainment, sport, financial trading, law enforcement, science, engineering, and many other areas of life. Most of that mathematics 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 if and when the time comes in later life.

Much 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. Today's information age is quite different. The mathematics used now involves abstract patterns, relationships, and structures (as well as numbers). Consequently, the mathematics we teach today's students should not be the same as their parents learned. That does not make it easier or less rigorous. Quite the opposite.

For example, 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.

In addition to ensuring that our students can get the right answer using modern technology, we should also try to interest them in mathematics as a human creation, developed over the centuries to improve the quality of our lives. To do that, we need to show them some of the many different ways that mathematics plays a major role in today's society, including some of the mathematics developed during our own lifetime.

In my view, those who cry "Back to basics" have got it wrong. The call should be "Forward to (the new) basics."

Who knows, if we answer that call, we might even produce a generation that is not math phobic or paralyzed by math anxiety.

- Keith Devlin

Devlin's Angle is updated at the beginning of each month.
Keith Devlin ( [email protected]) is Dean of Science at Saint Mary's College of California, in Moraga, California, and a Senior Researcher at Stanford University. He has just finished work on a book to accompany a six-part television series, Life By the Numbers, which will be broadcast nationwide on PBS in early April. The book, which has the same title as the television series, will be published at the same time by John Wiley and Sons.