Eighth-grade students across the United States showed some improvement in math and science over the past four years, but fourth-graders’ performance was stagnant and students in both groups continued to trail many of their peers in Asia, according to the results of a major international exam released Tuesday.

The Trends in International Mathematics and Science Study, or TIMSS, was administered to nearly 600,000 students in dozens of education systems across the globe in 2015. U.S. scores are likely to stoke renewed debate among politicians, educators and business leaders about why math and science achievement has not improved more quickly relative to other nations.

U.S. fourth-graders, for example, scored an average of 539 out of 1,000 possible points in math, down two points from the average in 2011.

Scores have risen at both grade levels and in both math and science since TIMSS was first given in 1995. Matt Larson, president of the National Council of Teachers of Mathematics, said the long-term trend is heartening — and means far more than the change over a four-year span.

“Certainly we have much more work to do and achievement is not as high as we would like to have it,” Larson said. “But the trajectory is positive, and it may indicate that some of the efforts we’ve made over the past two and a half decades are making a difference.”

The average score of U.S. eighth-graders rose from 509 in 2011 to 518 in 2015, painting a picture of improvement that contradicts results on another important assessment: the National Assessment of Educational Progress, often called the Nation’s Report Card. On that test, eighth-graders showed a decline in achievement from 2011 to 2015.

Peggy Carr, acting commissioner of the National Center for Education Statistics, said she did not know why the results of the two tests show such different patterns. But she said that the national exam tends toward questions that are more “complex” than the questions on TIMSS.

On TIMSS, the average score of U.S. fourth-graders in math put them behind students in 10 other systems: Singapore, Hong Kong, South Korea, Taiwan, Japan, Russia, Northern Ireland and Ireland, Norway, and the Flemish portion of Belgium.

In Singapore, for example, 50 percent of students scored high enough to be considered advanced in math, compared with just 14 percent of U.S. students who reached that benchmark.

U.S. fourth-graders’ average score was indistinguishable from nine other systems and higher than 34 systems.

U.S. students ranked comparably in science.

David Evans, executive director of the National Science Teachers Association, said the slow progress is cause for some concern but is not surprising given that Americans so often treat science and math as inscrutable fields of study that aren’t essential to becoming educated in the same way that reading and writing are.

During the two decades in which TIMSS has been administered, he said, the time devoted to science has decreased as schools under pressure to raise standardized test scores have focused their attention on math and reading. But there has been no big change in the way science has been taught in the United States.

Evans said that he is now hopeful that new science standards that have been adopted by a growing number of states — and that push students to solve problems and learn about science by doing science — will make a difference, prompting bigger gains in the coming years.

“I think we’re right now at the very beginning of what could be a very significant change in the way we teach science,” Evans said.

Also released Tuesday were the results of TIMSS Advanced, a study of the performance of high school seniors who take advanced courses in physics and math. Those students’ achievement is unchanged since 1995, the only other year in which the United States participated in that exam.

Among fourth- and eighth-grade students, the gender gap has narrowed or closed in math and science, according to TIMSS results. But there continues to be a yawning gender gap among the advanced high school seniors: Males scored 46 points higher than females in physics, and 30 points higher in math.