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WASHINGTON – Eighth- graders in more than half the U.S. states did better than average on an international test in math and science, but the top students lagged behind South Korea, Singapore and Taiwan, according to a study released by the federal government Thursday.

In math, public school students in 36 states scored higher than average. The lowest scoring state was Alabama and the highest scoring was Massachusetts. U.S. students did better on the science test, with students in 47 states scoring higher than average. The District of Columbia was the lowest scoring U.S. jurisdiction while Massachusetts was again the highest scorer.

Still, while Massachusetts led the nation, only 19 percent of eighth-graders from the Bay State scored high enough to be considered “advanced” in math compared to nearly 50 percent of eighth-graders in Taiwan, South Korea and Singapore.

“It’s a good news, bad news scenario,” said Jack Buckley, the commissioner of the National Center for Education Statistics, the research arm of the Department of Education. “All of our high performing states are being outperformed significantly by these other countries.”

The report gave new fuel to policy makers who have been arguing for 30 years that the U.S. has stalled in educational attainment and that K-12 schools need a reboot to produce adults who can compete in a global economy.

The analysis released Thursday used 2011 test scores from the Trends in International Mathematics and Science Study, or TIMMS, an exam given by the United States and 46 foreign countries and provinces. India and China, frequently cited as economic competitors to the United States, were not among the test takers.