What is 256 times 98? Can you do the multiplication without using a calculator? Two thirds of Massachusetts fourth-graders could not when they were asked this question on the statewide MCAS assessment test last year.

Math education reformers have a prescription for raising the mathematical knowledge of schoolchildren. Do not teach the standard algorithms of arithmetic, such as long addition and multiplication, they say; let the children find their own methods for adding and multiplying two-digit numbers, and for larger numbers, let them use calculators. One determined reformer puts it decisively: "It's time to acknowledge that continuing to teach these skills (i.e., pencil-and-paper computational algorithms) to our students is not only unnecessary, but counterproductive and downright dangerous."

Mathematicians are perplexed, and the proverbial man on the street, when hearing the argument, appears to be perplexed as well: improve mathematical literacy by downgrading computational skills?

Yes, precisely, say the reformers. The old ways of teaching mathematics have failed. Too many children are scared of mathematics for life. Let's teach them mathematical thinking, not routine skills. Understanding is the key, not computations.

Mathematicians are not convinced. By all means, liven up the textbooks, make the subject engaging and include interesting problems. But don't give up on basic skills! Conceptual understanding can and must coexist with computational facility--we do not need to choose between them.

The disagreement extends over the entire mathematics curriculum, kindergarten through high school. It runs right through the National Council of Teachers of Mathematics (NCTM), the professional organization of mathematics teachers. The new NCTM curriculum guidelines, presented with great fanfare on April 12, represent an earnest effort at finding common ground, but barely manage to paper-over the differences.

Among teachers and mathematics educators, the avant-garde reformers are the most energetic, and their voices drown out those skeptical of extreme reforms. On the other side, among academic mathematicians and scientists who have reflected on these questions, a clear majority oppose the new trends in math education. The academics, mostly unfamiliar with education issues, have been reluctant to join the debate. But finally, some of them are speaking up.

Parents, for the most part, have also been silent, trusting the experts--the teachers' organizations and math educators. Several reform curricula do not provide textbooks in the usual sense, and this deprives parents of one important source of information. Yet, also among parents, attitudes may be changing. A recent front-page headline in the New York Times declares that "The New, Flexible Math Meets Parental Rebellion."