Math Made Interesting

Perhaps the happiest of Stanford's new captives is Yale's Edward G. Begle, 46, a math professor and father of seven who once spent his days hammering topology into graduate students and his nights wrestling with juvenile homework. The nights were worse than the days. When Daughter Sally bogged down in percentages, Papa Begle blew up. Sally's math book explained percentages three ways without touching on the common principle. "It was dull, terrible, uninteresting," growls Begle. "It was so revolting that I had to do something."

What sad-eyed Professor Begle (pronounced beagle) did was to become the foremost disseminator of math reforms in U.S. schools. As director of Yale's School Mathematics Study Group. Begle, in 1958, began a rewriting of textbooks that has since enlightened Sallys across the nation. As one consequence, Stanford stole Sally's father from Yale. Stanford now aims to Beglize itself as "a national center in mathematics education."

Math Cookery. The son of a clothespin manufacturer, Begle graduated from the University of Michigan ('36), took his doctorate at Princeton in topology (thesis title: "Locally Connected Spaces and Generalized Manifolds"), began teaching at Yale in 1942. As secretary of the American Mathematical Society, Begle was in a key spot when Sputnik-stirred mathematicians began to worry about U.S. high schools. They were shocked at "cook book" courses stuffed with unrelated rules, appalled at teachers who themselves hated math. With grants ($4,000,000 so far) from the National Science Foundation, Begle organized top mathematicians and teaching experts into five teams, each covering a year of junior or senior high school math. Purpose: to create teachable courses.

Begle's group admired the exciting experiments of Mathematician Max Beberman at the University of Illinois (TIME, July 25, 1960)--superb classroom artistry that lures children into discovering math concepts for themselves. But to make every teacher into a Beberman was clearly impossible. Begle aimed to write courses that most teachers could handle with only an hour a week of extra study.

The result is a series of texts for students and manuals for teachers that Yale University Press publishes at $1.80 per copy, wholesale. Last year 140,000 copies were used in test cities from Seattle to Westport; this year sales will hit 300,000. To spread the word even further, Random House and Yale last week published the first six volumes of a Begle-sparked series of paperbacks ($1.95) called the New Mathematical Library, with such titles as The Lore of Large Numbers and What Is Calculus About?

Seeing Fractions. Reversing the old order of math learning, Begle's books start with particular examples that awaken students to axioms or generalizations. The chief aim is a firm grasp of "real numbers," which form the central number system of mathematics. One early discovery is the semantic difference between a number and a numeral. The first is a permanent concept, the other, one of its many aliases. The idea of 9, for example, can be expressed equally well as 4+5, 63 7 or 100-91.

Real numbers include rational numbers, meaning whole numbers that can be expressed exactly as ratios or fractions. To visualize this structure, Begle presents a rulerlike "number line"; rational numbers are fractional lengths along the line. They have a beautiful unity that can be shown by dividing a segment of the number line into four equal parts. When the student subdivides three of the four parts into thirds, he discovers that two of these thirds make exactly one-half of the full unit. He thus "sees" fractional multiplication, which he can use to check the fact, quite abstruse to math beginners, that 2/3 times 3/4 equals 1/2.

Later he learns that rational numbers can be negative (as in below-zero temperatures) as well as positive; he also finds that the number line includes some other odd units, e.g., the square root of 2. Thus the novitiate is led to the interesting discovery of irrational numbers, another class of real numbers.

With the high school books out, Begle plans new texts for kindergarten through sixth grade. But the job ahead is measuring the results on a mass scale, which is why Begle came to California, a state so ripe for experiment that its schools this year will buy about one-third of Begle's books. The state is paying part of his salary at Stanford, supplying computer facilities and even putting a fulltime staffer at his disposal. "You'd never hear of that in Connecticut," laughs Begle.

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