Math angles & Saxon - math educator John Saxon

National Review, Nov 25, 1988 by Chester E. Finn, Jr.

THE FACT THAT American schoolchildren perform dreadfully in mathematics is no secret. According to the National Assessment of Educational Progress testing program, just half of our 11th-graders in 1986 knew that 87 per cent of ten is less than ten. Only six in a hundred could solve a problem such as this: "Suppose you have ten coins, and have at least one each of a quarter, a dime, a nickel, and a penny. What is the least amount of money you could have?" Putting it more plainly than education analysts ordinarily do, the Assessment staff concluded that the "performance of 17-year-old students was dismal." No wonder math is one subject in which international comparisons always locate the U.S. near the back of the pack.

We've known for years that the teaching and learning of math-along with reading and writing, history and geography, science and literature-are in sore need of repair. Many would-be repairmen are now at work. Indeed, the math-education profession is a-buzz with projects intended to set matters right. At every turn there is a new study, task force, panel, or committee. The National Council of Teachers of Mathematics has in near-final form a new set of curriculum and evaluation standards meant to furnish goals and norms. A research center on math education, funded by the U.S. Department of Education, is cranking away at the University of Wisconsin. The august National Academy of Sciences has given birth to a 34-member Mathematical Sciences Education Board, complete with half a dozen subcommittees. The American Association for the Advancement of Science and the National Science Foundation are also in on the act. Interested people can attend colloquia on such topics as "Calculus for a New Century: A Pump, Not a Filter."

The pattern is familiar: A problem is found. A crisis is declared. The organizations that allowed the problem to develop commence, with ample fanfare, to unveil elaborate plans to solve it. Federal agencies and private foundations disgorge dollars. Committees are created, meetings held, draft reports circulated.

Almost as familiar is the emergence of a new "conventional wisdom" about what went awry and what needs doing. Here is how it goes in math education nowadays, as stated by a profesor with considerable stature in the field:

School mathematics in the United States today consists to far too great a degree of endless preparation for a payoff that will occur in the next course. In the past, it was important to acquire a broad array of specific manipulative skills to be prepared for that payoff. Prerequisites for problem-solving were abilities to do arithmetic, to do algebra, to perform the computational procedures of calculus and analytic geometry. Students accepted this promise of delayed gratification grudgingly, but they accepted it.

Today the situation is very different. Anyone doing the technical work that requires secondary-school algebra, geometry, trigonometry, calculus, or statistics has access to low-cost computing technology that performs all the numerical, graphic, and symbolic manipulations that we' have traditionally spent so much time training students to execute.

We have before us an opportunity to sharply diminish the time devoted to training students to become more like machines. The technology already available supports strikingly effective ways of teaching and of engaging students in realistic and attractive problem-solving activities.

To oversimplify only slightly: let the calculators handle the drudgery of multiplying fractions, calculating percentages, and finding square roots. Get the kids to engage in "problem solving"-which does not mean working out the answers to rows of long-division problems but, rather, devising tactics by which to attack "word problems," also known as "story problems." (The coin question posed above is one such.)

Certainly it's not the kids' fault, aver the experts. They shouldn't have to be bored. They don't really need to practice old-fashioned arithmetic skills or to memorize "math facts." Times have changed.

This new philosophy can be found on both sides of the Atlantic. The Maths Working Group, formed to advise the British government on the new national curriculum, declared in August that "it is unnecessary to teach penciland-paper techniques for long division and long multiplication. . . . In the age of the calculator, it is not important to drill pupils in pencil-and-paper methods." Drill and practice have become dirty words with the math avant garde, roughly equivalent to the standing of the Pledge of Allegiance among the social-studies cognoscenti.

ENTER JOHN SAXON, a renegade math educator from Norman, Oklahoma, who rarely finds himself invited to sip lime seltzer with today's busy reformers. For Saxon has had the gall to tell students (in the introduction to his 1981 algebra textbook) that

Repetition is necessary to permit all students to master all of the concepts, and then the application must be practiced for a long time to ensure retention. This practice has an element of drudgery in it, but it has been demonstrated that people who are not willing to practice fundamentals often find success elusive. Ask your favorite athletic coach for his opinion on the necessity of practicing fundamental skills.