In science, Massachusetts was behind the top scorer, Singapore. Taiwan was next, followed by Vermont. The top 10 also included South Korea and Japan -- and New Hampshire, North Dakota, Maine and Minnesota.
Mark Schneider, vice president at the American Institutes for Research and a former commissioner for the National Center for Education Statistics, said one of the most disturbing results from the study is the low number of "advanced" achievers in the United States compared with other countries.
Even in high-scoring Massachusetts, where 19 percent of students reached the "advanced benchmark" in math and 24 reached it in science, there were fewer higher achievers than in some other countries. About half the students in Taiwan, South Korea and Singapore reached the high benchmark in math, and 40 percent of students in Singapore did so.
On the other end, for example, Alabama had a lower percent of "advanced" achievers in math than did Romania and Turkey -- two countries it scored higher than overall.
"In a world in which we need the best, it's pretty clear many states are empty on the best," Schneider said.
Tom Loveless, a senior fellow at the Brookings Institution, said one thing that's hidden in the results of this study is that even in high-achieving states, there are low performers who need to be brought up from the bottom.
"If we as Americans want to get all of our kids achieving at the highest level, in terms of worldwide academic achievement, we have a lot of work, and it's not just the low-scoring states where it's obvious," Loveless said.
The scores were ranked on a scale of 1,000.
In math, the average state scores ranged from 561 for Massachusetts to 466 for Alabama.
In science, the average state scores ranged from 567 for Massachusetts to 453 for the District of Columbia.