This month, the Organisation for Economic Co-operation and Development released its review of global educational achievement. The Program for International Student Assessment, or PISA, is one of the most comprehensive global school surveys, assessing half a million 15- and 16-year-olds every three years. This year's results contain a profoundly important insight into what works in U.S. education reform.

At the start of 2000, U.S. students were average or below average. In 2012, their scores were almost exactly the same. Meanwhile, students in China, Singapore, South Korea, Japan and Hong Kong made steady gains, particularly in math and science.

While our recent scores are quite disheartening, they don't tell the whole story. The message from education pundits has been that U.S. schools are stuck at mediocre. But had our students continued to improve in 2012 as they did in 2009, the picture of national education achievement would be much different.

In 2009, U.S. PISA scores improved notably in math and science, increasing by 13 points in each area. But they then fell back in 2012. Had U.S. students' math scores made another 13-point gain in 2012, our students would now be well above the PISA average and even with Denmark and New Zealand, having passed Norway, Luxemburg, France and the United Kingdom. The same is true for science. Had our students made the same gain in 2012 that they made in 2009, the headlines would be about improvement, not stagnation.

The National Assessment of Educational Progress (NAEP), another major evaluation of student achievement, shows similar significant gains among U.S. students in 2008 and 2009 compared with the previous decade. But as with PISA, the growth in NAEP scores has slowed dramatically since 2009. Fourth-grade math scores, for instance, climbed 14 points between 2000 and 2009 but only two points over the next four years.

Precisely identifying what accounted for improvements in the 2000s is not easy. Education data like PISA and NAEP test scores are incredibly complicated. The cause of any particular trend is usually murky and multifaceted. It's difficult to draw definitive causal relationships.

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Still, the substantial gains through 2009 coincided with states widely adopting rigorous accountability policies. Throughout the mid- to late-1990s and early 2000s, the nation embraced accountability. By 2000, more than half the country had adopted some form of consequential accountability policies, and these efforts were extended and expanded nationally through the No Child Left Behind Act (NCLB), President George W. Bush's landmark education legislation, passed in 2001.

During Bush's second term, I was charged with implementing NCLB's rigorous reporting and evaluating protocols. I witnessed firsthand how clearly defined, high-achievement standards fueled student improvement. Effective teachers and administrators were rewarded. Stagnating schools were pressed to change. Importantly, parents were empowered to hold educators accountable. The law explicitly allowed parents to send their children to other schools or utilize tutors if their children attended a school that was persistently in need of improvement.

Sadly, federal policymakers have loosened standards since 2009. A substantial number of schools have been exempted from NCLB's accountability requirements. Having been granted waivers from the law, most states and localities no longer impose consequences on many of the schools that aren't making adequate progress. Parental choice has been curtailed. This has hit disadvantaged children especially hard, since most schools that serve them inadequately are now largely off the hook.

Everyone concerned about the future of education needs to understand this lesson from PISA and NAEP. Student gains have stalled just as policymakers have scaled back the key policies that had begun to lift student achievement.

Accountability works. We either keep the policies that drive improvement in student achievement or there will be further losses ahead.

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The writer is president of the George W. Bush Foundation. She served as education secretary from 2005 to 2009.