Scores in math, reading and science posted by 15-year-olds in the United States were flat while their counterparts elsewhere — particularly in Shanghai, Singapore and other Asian provinces or countries — soared, according to the results of a well-regarded international exam released Tuesday.

While U.S. teenagers were average in reading and science, their scores were below average in math, compared to 64 other countries and economies that participated in the 2012 Program for International Student Assessment, or PISA. That pattern has not changed much since the PISA test was first given in 2000.

“Our scores are stagnant. We’re not seeing any improvement for our 15-year-olds,” said Jack Buckley, commissioner at the National Center for Education Statistics, the research arm of the Education Department. “But our ranking is slipping because a lot of these other countries are improving.”

Education Secretary Arne Duncan called the scores a “brutal truth” that “must serve as a wake-up call” for the country.

The test scores offer fresh evidence for those who argue that the United States is losing ground to global competitors and others who say a decade’s worth of school reform has done little to improve educational outcomes.

How U.S. students compare internationally

“While the intentions may have been good, a decade of top-down, test-based schooling created by No Child Left Behind and Race to the Top — focused on hyper-testing students, sanctioning teachers and closing schools — has failed to improve the quality of American public education,” said Randi Weingarten, president of the American Federation of Teachers.

Some observers, including education historian Diane Ravitch, noted that American students have never been top performers on international tests dating back to the 1960s, but that has not prevented the country from becoming one of the most successful and innovative in the world. Ravitch accused Duncan of trying to “whip up a national hysteria”over the PISA scores.

Shanghai dominated the PISA exam, taking the top slot in all three subjects. The Chinese province catapulted to the top after focusing on teacher preparation and investing in its most challenging classrooms, among other things.

Germany, Poland and Italy were among several countries that made significant improvements in scores while Finland, which had been a top scorer in the past several exams, recorded a drop.

Overall, 40 of the 65 countries and economies made some progress, said Andreas Schleicher, deputy director for education and skills at the Organization for Economic Cooperation and Development. “In general, we’ve seen remarkable progress in education over the decade in the industrialized world,” he said.

China, the world’s most populous country and a fast-growing economy, did not participate in PISA, although several of its provinces did.

The test, administered every three years by the OECD, is designed to measure whether students can apply what they’ve learned in school to real-life problems. Approximately 510,000 15-year-olds in public and private schools took the paper-and-pencil exam in the fall of 2012.

On the math portion, 29 countries tested better than the United States. Aside from the Asia powerhouses of Shanghai, Singapore, Hong Kong, Taipei, Korea and Japan, the United States was outscored by European countries including Latvia, Britain, Poland, France, Germany and Slovenia.

In science, 22 countries posted better results than the United States, including Vietnam, Canada and Poland. In reading, 19 countries had higher scores than U.S. students, including Estonia and Liechtenstein.

Three states — Massachusetts, Connecticut and Florida — had students take the test to see how they compared internationally.

Students in Massachusetts and Connecticut scored above both the national and PISA average in math, while Florida scored below those averages. Massachusetts also beat the U.S. and OECD averages in science while Connecticut scored above the U.S. average and below the OECD average. Florida scored below both the U.S. average and OECD average in science. In reading, Massachusetts and Connecticut scored above the U.S. and OECD averages while Florida teenagers scored about the same as the U.S. and OECD average.

Not only did the United States score below average in math, it had fewer top performers. These are students who can develop “models for complex situations, and work strategically using broad, well- developed thinking and reasoning skills,” according to the OECD. While just 2 percent of U.S. teenagers reached that level in math, 31 percent of Shanghai students achieved it. The OECD average was 3 percent.

Even the top-performing U.S. state — Massachusetts — was outperformed by Shanghai. In math, 19 percent of Massachusetts students who took the exam placed in the top two levels of proficiency, while 55 percent of students in Shanghai reached those tiers. That difference is equivalent to more than two additional years of formal schooling, the OECD said.

At the other end of the spectrum, about 25 percent of U.S. students tested in the lowest levels of math proficiency — more than the OECD average. That statistic has not changed since 2003.

U.S. students are particularly weak in performing math tasks with higher cognitive demands, such as taking real-world situations and translating them into mathematical terms, according to the OECD report.

Despite their tepid math scores, U.S. teenagers were more confident about their math skills than their international counterparts, the report found.

Some observers say the United States does not perform well in international competitions because it is a large, diverse country, with the highest child poverty rate among industrialized countries.

But countries like Vietnam, where 79 percent of students are economically disadvantaged, outscored U.S. students in math.

“So it’s not demography itself. Those demographics are a factor, not the only factor,” Buckley said.

A weak curriculum could be the culprit, the report suggested.

“Perhaps the application problems that most students encounter today are the worst of all worlds: fake applications that strive to make the mathematics curriculum more palatable, yet do no justice either to modeling or to the pure mathematics involved,” the OECD said. Providing students with better opportunities to learn will help them develop skills to make frequent and productive use of math in their work and daily life, it said.

The new Common Core academic standards in math and reading, which have been fully adopted by 45 states and the District of Columbia, could help pull up the nation’s PISA scores, according to the OECD. While the standards are now being implemented in most U.S. classrooms, there has been growing political opposition from the right, left and center.

One clear finding from the PISA test was the impact of preschool education. Across countries, students who were enrolled in preschool consistently performed better on the test, Schleicher said.

Dennis Van Roekel, president of the National Education Association, said the country should end divisive debates about policies and adopt methods that are working in top-scoring nations. “We need to say we know what works, take it out of the political arena and do what’s right for kids,” he said.

Shocked by its moderate PISA results in 2000, Germany adopted national education standards and has taken steps to improve teacher education and establish a common test for final high school exams in all 16 German states. Germany’s 2012 PISA scores improved in math, reading and science.

The United States should also take several actions simultaneously, Duncan said. The country must “invest in early education, raise academic standards, make college affordable, and do more to recruit and retain top-notch educators,” he said.

Buckley cautioned against using the PISA results to draw conclusions about whether education policies are working.

“People like to take international results like this and focus on high performers and pick out areas of policy that support the policies that they support,” he said. “I never expect tests like these to tell us what works in education. That’s like taking a thermometer to explain why it’s cold outside.”