Teaching: The Trials of New Math

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On their first day in second grade, 200 Urbana, Ill. schoolchildren were told to add 19 and 3. None got it; a large and desperate proportion of them answered "112," apparently thinking "' plus 3 is 12, carry 1 and bring down 1." The kids were then asked how many cookies they would own if, having 19, they were given 3 more. Nearly every child said "22."

Old math is rote learning of unexplained rules ("carrying," for instance); new math tries to cut away mystery by making computation seem real, open and understandable. New math is here to stay. But, as many a baffled parent suspects, the teaching of it is in deep confusion. Max Beberman, the Illinois professor who has been urging new math on the U.S. for a decade, is now "very much disturbed."

25,000 Popsicle Sticks. "We're in danger of raising a generation of kids who can't do computational arithmetic," says Beberman. He still favors new math, when properly taught, as strongly as ever; one of his ideas is that the first purchase of equipment for elementary-school math classes should be 25,000 Popsicle sticks, to let children deal with tangible things because "enumeration systems are ways of talking about physical objects."

But the current confusion and frustration in new-math teaching do not stem from any lack of Popsicle sticks. The heart of the matter, as James Gates, executive secretary of the National Council of Teachers of Mathematics, points out, is that most of the nation's 1,600,000 elementary-school teachers are insufficiently trained to teach math —either new or old. Many teachers who spend a fifth of their workday on math have not taken any math courses themselves since the ninth grade.

The hazard in teaching new math is that its basic concepts—sets, number systems not based on ten, lattices—require profound comprehension by teachers, which usually entails plenty of upgrading study. Professor Robert Wirtz, an associate of Beberman's at the University of Illinois, visited more than 100 elementary schools all over the U.S. and reported: "The teachers I found are frightened. They don't understand the new math or why they are supposed to teach it."

The Trick: Go Slow. Some school systems have caught on to the problem and worked out ways to overcome it. A Detroit official says the trick is to go slow: "We began five years ago with only twelve schools and a handful of teachers, and have no target date for all our 225 elementary schools." Now 78 of Detroit's schools teach new math in Grades 4, 5 and 6. Of the 3,500 teachers in the system, 700 have attended new-math seminars and courses on Saturdays, encouraged by $15-a-day payments. Aggravating the shortage of new-math teachers is the fact that not enough new-math courses are offered at universities and teachers colleges.