American eighth-grade students have made significant gains in math and science compared with their worldwide counterparts, but performance at the fourth-grade level appears to have reached a plateau, according to a major international study released yesterday.

Educators described the results of the Trends in International Mathematics and Science Study, given every four years, as a "good news, bad news" picture for the United States. The gap between minority students and white students here has narrowed, but American students continue to lag behind their peers in Asian countries such as Singapore and Hong Kong.

The study, known as TIMSS, shows that "we need to do an even better job of exciting our young people in math and science," Deputy Education Secretary Eugene W. Hickok said at a news conference presenting the results.

Together with another study, known as the Program for International Student Assessment or PISA, whose results were released last week, TIMSS offers the most authoritative available insight into how U.S. students compare with students in other countries. The PISA study suggested that American 15-year-olds lag behind their counterparts in most other leading industrialized nations in the ability to solve real-life math problems.

Researchers said that varying results in the two studies -- PISA offers a somewhat bleaker picture of the state of American math and science education than TIMSS does -- can be explained by their different focus. The TIMSS test is more closely aligned with the curriculum in most U.S. schools than is the PISA study, which looks at students' ability to apply the math they have learned in practical situations.

"Both sets of tests are valid. They merely measure the attainment of knowledge in different ways," said Jack Jennings, president of the Center on Education Policy, which provided technical expertise for both studies.

Even so, the strong showing of American eighth-graders in contrast to that of fourth-graders on TIMSS surprised some experts. It has long been thought that U.S. elementary schools are doing a better job than middle schools or high schools in boosting academic performance by putting better accountability systems in place.

Since 1995, the United States has climbed several places in the international math rankings among eighth-grade students, to 15th out of 45 countries. American eighth-graders registered an average score in math of 504 out of a possible 1000, below their counterparts' scores in Singapore (605), South Korea (589) and Russia (508), but above those in Sweden (499), New Zealand (494) and Saudi Arabia (332).

During the same period, the achievement gap between white students and black students in the United States has narrowed from 97 to 77 points. The achievement gap between white and Hispanic students narrowed from 73 to 60 points.

At the fourth-grade level, U.S. students scored the same in 2003 as in 1995 on math, while slipping back six points in science. Because students in other countries have improved their performances, the United States dropped to 12th out of 25 in the ranking, below traditionally strong Asian countries such as Singapore and Japan but also some European countries such as Lithuania and Hungary.

Various researchers favor different explanations for the weak performance of the United States in math and science, particularly relative to Asian countries. Some blame the lack of a nationwide curriculum: In contrast to countries such as Japan and Singapore, each U.S. state has broad autonomy to shape its own math and science programs. Others point to the shortage of qualified teachers.

"We don't have enough mathematically trained people training the kids, and it is getting worse every year," said James H. Simons, a Wall Street investor who founded a nonprofit group called Math for America in an effort to train more qualified mathematicians. "The problem feeds on itself."

Simons, who runs the hedge firm Renaissance Technologies Corp., said he must recruit more than half of his staff from abroad every year because of the lack of U.S. citizens skilled in math. He said schools have even greater difficulty recruiting qualified math teachers because school salaries are low and there are greater opportunities elsewhere.

Focusing first on New York, Math for America is trying to train more math teachers and pay them bonuses.

One indication that the U.S. math curriculum is not sufficiently challenging came from responses to a question in the PISA study, which asked students whether they thought they were good at math. U.S. students had much higher confidence that they were doing well in math than did students in South Korea and Japan, even though their performance was significantly weaker.