Nearly 200 top mathematicians and scientists, including four Nobel laureates, are urging U.S. Secretary of Education Richard W. Riley to withdraw the government's endorsement of math programs that experiment with nontraditional teaching methods.

The strongly worded letter expresses outrage that some of the 10 widely used programs leave out such basic skills as multiplying two-digit numbers and dividing fractions.

"These curricula are among the worst in existence," said David Klein, a Cal State Northridge math professor who was one of the letter's authors. "To recommend these books as exemplary and promising would be a joke if it weren't so damaging."

Those signing the letter fear that a government endorsement of the programs will be a powerful force pushing teachers and school districts to use "dumbed down" instructional materials and methods. Several said they see the letter, which is to be publicized widely today, as providing a countervailing argument.

Klein was joined by math professors and physicists from UC Berkeley, Stanford University, Harvard University, the University of Chicago and elsewhere. The signers also include two winners of the Field Medal, which is the top honor in the field of mathematics, and Nobel laureates in physics Steven Chu (1997), Sheldon Lee Glashow (1997), Leon M. Lederman (1988), and Steven Weinberg (1979).

"I'm hoping to provide ammunition for teachers who are under pressure to adopt some of these programs," said Richard Askey, who holds an endowed chair in math at the University of Wisconsin.

More broadly, those signing the highly unusual letter want the federal government to refrain from taking sides in the continuing national education debate that some have dubbed the "math wars."

Linda P. Rosen, Riley's top math advisor, said the endorsements are not likely to be withdrawn. She said Congress directed the department to create the panel of experts that made the recommendations and that the intent was to help school districts make informed choices when purchasing math programs.

But, she said, such decisions remain "absolutely locally based" and that school districts must take local opinions into account.

Steven Leinwand, a member of the federal panel that judged the books, defended the selection process.

"Every one of the programs designated as exemplary had real, clean data that showed test scores going up," said Leinwand, a consultant to the Connecticut Department of Education.

But he acknowledged a difference of opinion among mathematicians as to what constitutes good mathematics. "These programs do not teach kids to do five-digit by three-digit long division problems," he said. "Instead, they teach all kids, not just a few kids, when and why people need to divide."

Rosen and others said the letter represents an escalation in the back-and-forth rhetorical struggle over how to promote mathematical understanding without sacrificing the ability to compute accurately.

As a result of the controversy, the nation's leading mathematics education group and the leading proponent of nontraditional methods, the National Council of Teachers of Mathematics, has sought input from professional mathematicians. Some fear that this letter will hamper those efforts.

"I have an uncomfortable sense that everyone is talking past one another," Rosen said. "What's missing in the whole darn thing are the students . . . and that's very unfortunate and just devastating to all of us who care deeply about young people."

Hung-Hsi Wu, a UC Berkeley math professor and a co-author of the letter, acknowledged that not all mathematicians agree with it. But, he said, he wrote it out of a sense of "social obligation" to improve math instruction.

The use of nontraditional instructional materials by schools has sparked protests in communities across the nation. Usually, those who complain are parents who are concerned that their children are failing to learn fundamental skills, that solving algebraic equations is being de-emphasized and that math class has been downgraded to math appreciation class, leaving high school graduates unprepared for college-level courses.

In California, at least, the traditionalists have gained the upper hand. The state adopted standards for math classes that stress memorization of multiplication tables and only limited use of calculators, as well as an understanding of concepts such as place value.

As a result, the state rejected, or did not consider, all of the math programs recommended by the federal government except for a part of one, so school districts are prevented from using state textbook funds to buy them.

Still, the materials on the federal recommended list remain in widespread use across the state and have been the focus of protests by parents in Palo Alto, Escondido, Torrance, Simi Valley, Los Angeles and many other cities around the state.

Similar battles have occurred nationally.