WASHINGTON — It's common in an American school to hear maxims such as these: "To succeed, you must believe in yourself" and "To teach, you must relate the subject to the lives of students."

But the Brookings Institution is reporting this week that countries such as the United States that embrace self-esteem, joy and real-world relevance in learning mathematics are lagging behind others that don't promote all that self-regard.

Consider South Korea and Japan.

According to the Washington think tank's annual Brown Center report on education, 6 percent of South Korean eighth-graders surveyed expressed confidence in their math skills, compared with 39 percent of U.S. eighth-graders. But a respected international math assessment showed South Koreans scoring far ahead of their peers in the United States, raising questions about the effectiveness of self-esteem.

In Japan, the report found, 14 percent of math teachers surveyed said they aim to connect lessons to students' lives, compared with 66 percent of U.S. math teachers. Yet the U.S. scores in eighth-grade math trail those of the Japanese, raising similar questions about the importance of practical relevance.

Tom Loveless, the report's author, said the findings do not mean that student happiness causes low achievement. But he wrote that his analysis of the international math assessment, the 2003 Trends in International Mathematics and Science Study, found that U.S. schools should not be too quick to assume that happiness is what matters in the classroom.

"It is interesting that people grasp this notion in other areas of self-improvement — eating healthy foods, getting exercise, saving for retirement — but when it comes to education, for some reason, the limitations of happiness are forgotten," Loveless wrote.

Several countries in Asia and some in Europe routinely beat the United States in math scores, even though their students show less satisfaction with performance and less love of math, and even though the lessons they receive are less "relevant," the report found.

The report is likely to stoke a debate over teaching math and other subjects that has divided the United States for at least a century. Progressives say that what students choose to study and how they feel about education should matter as much, or more, in the classroom than test results; traditionalists say that gain requires some pain and that tests matter.

Alfie Kohn, a progressive author and lecturer, questioned the findings. "Let me get this straight," Kohn said. "Kids who get higher scores on standardized tests are unhappy and self-doubting, so that means we should question the importance of happiness and self-confidence, rather than the importance of these tests?"

Gerald W. Bracey, an educational psychologist and columnist for the education journal Phi Delta Kappan, said the report overlooked countervailing trends in Japan, Singapore and other countries that do better than the United States on eighth-grade math tests. Officials in those countries say their education systems are not yielding graduates who have the same level of creativity as American graduates. Some Asian nations have begun to copy aspects of U.S. education, including the emphasis on letting students search for answers rather than memorize them.

The Brookings report notes that in most countries, including South Korea and the United States, students who like math and think they are good at it have higher math scores than those who don't.

Perspective matters, Loveless wrote: Japanese students who would be considered good at the subject if they were in the United States think that they are not so good when compared with their peers in Japan.

Chester E. Finn Jr., president of the D.C.-based Thomas B. Fordham Foundation, said the report shows that schools need not be fun to be effective. "Schools should work on academics, not feelings," Finn said. "True self-esteem, self-confidence and happiness are born of true achievement."