ASHINGTON, Dec. 5 — Four years after American fourth-grade students scored high on an international test of science and math, their performance declined markedly when they reached the eighth grade, a second survey shows.

The survey results, released here today, indicate that the changes some educators had suggested were responsible for the fourth graders' success were insufficient to produce results as they advanced in school.

The survey was based on the results of tests that 180,000 eighth- graders in 38 nations took last year. It showed American students, over all, performing worse in math and science than students in Singapore, Taiwan, Russia, Canada, Finland, Hungary, the Netherlands and Australia. They did better than students in some less industrialized nations, including Iran, Jordan, Chile, Indonesia, Macedonia and South Africa.

"American children continue to learn, but their peers in other countries are learning at a higher rate," said Richard W. Riley, the outgoing secretary of education.

Mr. Riley said that data showing American youngsters doing slightly better than the international average in math and science was cause for optimism, but acknowledged, "We need to work harder and better."

The report, known as the Third International Math and Science Study-Repeat, came as a letdown to a number of educators.

It confirmed the declines over time in student performances that the initial 1995 survey of students in the United States and 42 other nations indicated.

That study showed American fourth-grade students among the leaders in science and at the international average in math. In the eighth grade, though, American students hovered at less than the international average in math and at the average in science. And in the twelfth grade, they lagged far behind students in most other nations in both subjects.

In the follow-up study, which took place in 1999, the only American group that showed improvement since the 1995 survey were black students, whose achievement rose in math, but not science. White students did better than black or Hispanic Americans on both science and math, while boys did better than girls in science, but not in math.

In agreeing to repeat the test — but examining only the most promising age group — American educators had hoped to find that the students who fared well in 1995 as fourth graders would continue to do so as eighth graders. That did not happen.

The reforms on which their hopes hinged, many undertaken during the last decade, included the efforts of school districts to bring uniformity and coherence to science and math curriculums, which vary widely with each district, and to raise standards.

Other reforms included programs by the National Science Foundation to reinvigorate science and math teaching in part by drawing working scientists into classrooms.

But the report said that such efforts, while perhaps improving achievement in isolated school districts, may have had little effect on an entire nation's performance.

Rita Colwell, director of the National Science Foundation, which is conducting several pilot projects to determine the best methods to improve the teaching of science, math and engineering, said she found the results "a little depressing."

"You would like to see the U.S. a leader not just in research and Nobel prizes, but in how our little kids perform," she said.

The international test, which was administered to 9,000 United States eighth-graders, resembled standardized tests taken nationally, asking a combination of multiple choice and open-ended questions.

In math, the questions covered five areas: fractions and number sense; measurement; data analysis; geometry; and algebra.

Science questions involved earth science and life science; physics; chemistry; environmental and resource issues; and scientific inquiry.

In 1995, American fourth-grade students did better than the international average on the science exam. Of the nations participating in both the 1995 and 1999 exams, American scores were exceeded only by those of South Korea and Japan.

But the results from 1999 showed that by the eighth grade, American students fell below the international average in science, with students in Australia, the Czech Republic, Britain, Slovenia, Canada and Hungary and five other nations doing better.

In math, American fourth graders in 1995 outperformed students in Canada, Britain and Cyprus, among others. But by the eighth grade, the report showed, they were on a level with students in Latvia, while those in Canada and Australia advanced.

Several industrialized nations that took part in the 1995 study — including Switzerland, France, Austria and Germany — did not participate this time. New nations joining the study included Taiwan, which scored well, and nearly a dozen low-scoring nations, including Tunisia, Moldova, Turkey, Thailand, Chile, Malaysia and Indonesia.

International comparisons have often come under fire, with critics arguing that other countries divide students at an early age into academic and nonacademic tracks, so that only their top-ranked students ever get to take international exams.

But Michael O. Martin, a professor at Boston College who helped design and organize this year's study, said such tracking decisions typically occur after the eighth grade. His group had tried to assure that a representative sample of students in each country took last year's test, he said.

In addition to its ranking of nations, the study also offered what Gary W. Phillips, the acting United States commissioner of education statistics, termed "a treasure chest of information" on what teachers teach and students learn in the 38 participating nations.

It found that most nations tend to employ math teachers certified in math. On average, 71 percent of students internationally learned math from teachers who majored in mathematics in college, but only 41 percent of American students did.

Nations with higher rankings teach subjects like geometry, chemistry and physics before high school, giving students more time to absorb the concepts, said William H. Schmidt, executive director of the Third International Math and Science Study Research Center at Michigan State University.

"As they get to high school, students in those countries can get much more challenging mathematics or science," he said. Only 25 percent of American high school students, he added, ever take physics.

The study showed that teachers in nations whose students scored higher in math and science tended to spend more time on professional development and refining curriculums.

Lee Stiff, president of the National Council of Teachers of Mathematics, noted that while specialized degrees are more common among high school teachers, middle schools tend to prefer — or often require — teachers to have general education degrees, since that gives administrators flexibility in assigning teachers to a greater variety of classrooms.

He said that teachers in the United States, Japan and China were eager for training and professional development, "but the other countries leave more time for development and class preparation during the school day. To have the dramatic gains we'd like, we have to do something dramatic in terms of what it means to be a teacher in America."

Carol Stoel, director of Schools Around the World, which links teachers in different nations to improve teacher and student performance, called for "greater emphasis on serious work at the middle-school level."

"Teachers in middle schools are committed, but they need lots of help in content matter," she said.