U.S. students continue to perform poorly on international tests, with 15-year-olds scoring in the middle of the global pack on the latest math, reading and science tests administered by the Organization for Economic Cooperation and Development.

In a familiar hierarchy, Asian countries and regions such as Hong Kong, Japan, Shanghai, Singapore and South Korea topped the rankings for the 2012 Programme for International Student Assessment, according to results released Tuesday morning.

Average American scores on PISA tests haven’t budged in a decade, despite bipartisan efforts to shake up the status quo through reforms such as mandating more frequent testing, publicizing student proficiency rates and opening public schools to competition from charter and private schools.

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Education Secretary Arne Duncan called the U.S. performance “a picture of educational stagnation.”

Top-line takeaways from the volumes of data released Tuesday:

• In math, the U.S. ranked 26th in the world, on par with nations such as Hungary, Russia and the Slovak Republic. American students had particular trouble with geometry, modeling and real-world applications of mathematical concepts.
• In science, the U.S. came in 21st, ahead of Russia and at the same level as Italy, Latvia and Portugal.
• In reading, the U.S. posted its best showing, with a rank of 17th in the world, on equal footing with the United Kingdom, France and Austria.
• Countries on the ascent in PISA rankings include Poland and Russia. Those slipping include Sweden and the once widely envied Finland, which has lost considerable ground in math. Canada remains a very strong performer on all three exams, as do the Netherlands and Germany.

The OECD cautioned that the rankings are approximate, due to margins of error.

For the first time, three U.S. states paid to have the PISA test administered to additional students, beyond the numbers needed for the national sample, so they could receive their own ratings. Massachusetts posted outstanding results in reading and science and very solid scores in math; Connecticut was not far behind.

Florida, however, scored significantly below the U.S. average in science and math and at the average in reading. The poor results in Florida, which has been at the epicenter of the education reform movement for more than a decade, were a surprise, since the state matched the U.S. average in math and science for both fourth and eighth graders on a different international test, the TIMSS, in 2011.

Joe Follick, a spokesman for the Florida Department of Education, responded by focusing on the benefits of taking such snapshots of student achievement. “By continuing to measure our performance, our students will meet the challenges necessary to succeed in college and career,” he said.

Nationally, meanwhile, advocates and analysts rushed to extract meaning from the results.

The OECD has analyzed global scores for years and has found that two popular proposals — reducing class size and expanding school choice — don’t seem to be correlated with better performance on the PISA.

Duncan has advocated both in the past, but in responding to PISA, he focused on other reforms, including investing in preschool, raising academic standards and recruiting more “top-notch educators.”

Union leaders support all those goals, but they emphasized other priorities.

Randi Weingarten, president of the American Federation of Teachers, said the flat PISA scores make it “abundantly clear” that a decades-long focus on “hyper-testing students, sanctioning teachers and closing schools has failed to improve the quality of American public education.” She called for better teacher training, a more robust curriculum and efforts to distribute more resources to the neediest schools.

Dennis Van Roekel, president of the National Education Association, emphasized the corrosive effects of poverty. The U.S. has one of the highest child poverty rates in the world, double or triple the rate in PISA powerhouses such as South Korea, Germany, Finland, Estonia and the Netherlands. Van Roekel called poverty “the main cause of our mediocre PISA performance.”

Indeed, high-poverty schools in the U.S. posted dismal scores on the PISA tests, akin to countries such as Kazakhstan, Romania and Cyprus.

Wealthy schools, by contrast, did very well on all three tests. Students in the most affluent U.S. schools — where fewer than 10 percent of children are eligible for subsidized lunches — scored so highly that if treated as a separate jurisdiction, they would have placed second only to Shanghai in science and reading and would have ranked sixth in the world in math.

Schools where low-income teens made up 10 percent to 25 percent of the student body also turned in a very solid performance; ranked on their own, they would have placed in the top eight in the world in reading and science and 17th in math.

But poverty alone does not explain the lagging results in the U.S. Vietnam is a poor nation, yet it outscored the U.S. significantly in math and science. And on all three tests, students from the U.S. were far less likely to score advanced than their peers in high-flying countries such as Shanghai, Finland and Canada.

In math, for instance, fewer than 9 percent of U.S. students scored advanced, compared to a whopping 55 percent of students in Shanghai, 40 percent in Singapore and more than 16 percent in Canada. In science, just 7 percent of U.S. students reached the top two levels of performance, compared with 27 percent in Shanghai and 17 percent in Finland. The U.S. also had significantly higher proportions of students scoring at the lowest levels than most of its international rivals.

One possible explanation: Unlike the state standardized tests most American teens are accustomed to, the PISA tests include open-response questions designed to measure critical thinking and problem-solving.

“These deeper learning skills… are the skills most in demand in today’s global economy,” said former West Virginia Gov. Bob Wise, president of the Alliance for Excellent Education. “They are also the skills that far too many U.S. students lack.”

The Common Core academic standards that are rolling out nationwide this year are meant to push students toward that “deeper learning” but have stirred considerable opposition on both left and right.

Amid the chorus of suggestions on how to raise PISA scores in the U.S., a few contrarian voices suggested it may be almost impossible, absent a fundamental change in American culture. Martin Carnoy, a professor of education at Stanford, said he was struck by how Estonian educators approached the PISA: They told each 15-year-old who had been randomly chosen to take the test that it was a great honor for them to represent their country and emphasized how crucial it was that they do their very best on the arduous exam.

“Whereas American kids, they could care less,” Carnoy said. “It’s just one more test.”