THIS IS MATH?

It is math time for the fifth-graders at Fernangeles Elementary School in Sun Valley, Calif., and everyone is stumped. The students have spent close to an hour puzzling over the question at hand: "What if everybody here had to shake hands with everyone else? How many handshakes would that take?" While the children, seated in small groups, debate and frown and scribble notes--and devise alternatives to the dread act of actually touching classmates of the opposite sex--their teacher, Kathy Pullman, roams the room. When the hour ends, no group has an answer. "This happens to be a particularly difficult lesson," Pullman says, unfazed. The class will dive in again after lunch.

To peer into Pullman's classroom is to glimpse why math has once again become a battleground in America's education wars. This school year, nearly half of all American elementary students are expected to learn math the way children do at Fernangeles Elementary: not in neat rows of desks, repeating times tables and memorizing theorems, but through trial-and-error problem solving, often in groups with little direct instruction and almost always with a calculator nearby. Advocates call it "interactive" or "inventive" math and insist that it sets American schoolchildren on the way to becoming "mathematically powerful."

When opponents of these currents are being polite, they call that kind of talk nonsense. And they have labels of their own. One is "whole math," a pejorative reference to "whole language," the controversial method of reading that emphasizes learning entire words and phrases over mastering phonics. Another is "new-new math," recalling the ill-fated New Math fad of the 1960s and '70s, which introduced millions of students to math arcana like set theory and congruences. (Remember those? Didn't think so.)

Resistance has resulted in pitched battles at school-board hearings and within academia over the future of U.S. math education. Educational scholar E.D. Hirsch Jr. says opposition to the newest math is "suddenly making people wake up and say, It doesn't work, it doesn't comport with reliable theories, and we're making a mistake."

It all started in 1989, when the National Council of Teachers of Mathematics, in response to the consistently poor math scores of U.S. children, issued new standards overhauling math education. Out went the stalwarts of traditional math: the rote memorization drills, the droning chalkboard lectures. In came the cool stuff: calculators and geoboards, hands-on, open-ended problems, exercises that encourage kids to discover their own route to the right answer. "The standards emphasized that you had to pay attention to how kids think," says Gail Burrill, president of the council.

Eight years later, 40 states have instituted some "standards-based" math programs in their schools, and the National Science Foundation spends $10 million a year on development of comprehensive instructional materials. California has become a leader: one cutting-edge curriculum called MathLand is used, its publishers claim, in 60% of the state's K-6 classrooms--including those in Fernangeles, where MathLand is taught in both English and Spanish. It even has its own Website: 192.216.191.114/. "These kids will be better problem solvers," says Pullman. "They will think more."