WASHINGTON — Students in the U.S. perform better than the global average, but still lag behind many of their peers in Asia and Europe, an international study found.

Fourth-graders have improved their scores in reading and math over the past four years, according to a study released Tuesday. But progress seems to fall off by eighth grade, where math and science scores are stagnant.

Meanwhile, kids in countries like Finland and Singapore are outperforming American fourth-graders in science and reading. By eighth grade, American students have fallen behind their Russian, Japanese and Taiwanese counterparts in math, and trail students from Hong Kong, Slovenia and South Korea in science.

“These 2011 international assessments provide both encouraging news about our students’ progress and some sobering cautionary notes,” said Education Secretary Arne Duncan, who applauded gains among fourth-graders but warned those gains aren’t being sustained in later grades. “That is unacceptable if our schools are to live up to the American promise of giving all children a world-class education.”

The results of the study, conducted every four years in nations around the world, show mixed prospects for delivering on that promise. A nation that once took pride in being at the top of its game can no longer credibly call itself the global leader in student performance. Wringing their hands about what that reality portends for broader U.S. influence, policymakers worry it could have ripple effects on the economy down the line, with Americans increasingly at a competitive disadvantage in the international marketplace.

Elevating the skills needed to compete with emerging countries has been a priority for President Barack Obama, who has pledged to train 100,000 new math and science teachers over the next decade. “Think about the America within our reach: a country that leads the world in educating its people. An America that attracts a new generation of high-tech manufacturing and high-paying jobs,” he said this year in his State of the Union address.

The U.S. has a long way to go to reach those goals. In the meantime, other countries are making significant strides. Russian eighth-graders were about tied in math with their American peers in 2007, the last time the study was conducted. Four years later, Russia’s scores have surged and now surpass the U.S. by a significant margin.

Reading skills are a major strength for American students. Only a few points separate American students from the top-scoring students in the world. In Florida, which took part in the study separately, reading scores are second only to Hong Kong.

Asia continues to dominate the top echelon of scores across subject fields. The tiny city-state of Singapore takes first place in eighth-grade science and fourth-grade math, with South Korea scoring nearly as high. Singapore takes second place to South Korea in eighth-grade math, with Taiwan in third.

The results also lean toward Asian nations when it comes to advanced levels of learning. In Singapore, 4 in 10 eighth-graders achieved the “advanced benchmark” in science, which requires an understanding of complex and abstract concepts in physics, chemistry, biology and other sciences. About 2 in 10 make the grade in Japan, South Korea and Taiwan. In the U.S., it’s about 1 in 10.

“There are a small handful of countries or systems that are managing to get a much larger percentage of their students over the advanced benchmark,” said Jack Buckley, commissioner of the National Center for Education Statistics. “There’s clearly some room for improvement.”

The Trends in International Mathematics and Science Study and its sister test, the Progress in International Reading Literacy Study, are used to measure knowledge, skills and mastery of curricula by elementary and middle school students around the world. Students in rich, industrialized nations and poor, developing countries alike are tested. In 2011, 56 educational systems — mostly countries, but some states and subnational entities like Hong Kong — took part in math and science exams. Fifty-three systems participated in the reading exam, which included almost 13,000 American fourth-graders.

“These kinds of tests are very good at telling us who’s ahead in the race. They don’t have a lot to say about causes or why countries are where they are,” said Brookings Institution senior fellow Tom Loveless, who in previous years represented the U.S. in the international group that administers the test.

Other findings released Tuesday:

— Some U.S. states that were measured separately were clear standouts, performing on par with or better than some top-performing Asian countries. Eighth-graders in Massachusetts and Minnesota score far better in math and science than the U.S. average. But in California and Alabama, eighth-graders fell short of the national average.

— Racial and class disparities are all too real. In eighth grade, Americans in the schools with the highest poverty — those with 75 percent or more of students on free or reduced-price lunch — performed below both the U.S. average and the lower international average. Students at schools with fewer poor kids performed better. In fourth-grade reading, all ethnic groups outperformed the international average, but white and Asian students did better than their black and Hispanic classmates.

— Boys in the U.S. do better than girls in fourth-grade science and eighth-grade math. But girls rule when it comes to reading.

— On a global level, the gender gap appears to be closing. About half of the countries showed no statistically meaningful gap between boys and girls in math and science.

The tests are carried out by the International Association for Evaluation of Educational Achievement, a coalition of research institutions. The U.S. portion of the exams is coordinated by the Education Department’s National Center for Education Statistics.

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Online:

Trends in International Mathematics and Science Study: http://nces.ed.gov/timss/

Progress in International Reading Literacy Study: http://nces.ed.gov/surveys/pirls/