Has the achievement of U.S. students improved over the past half century? Have gaps between racial, ethnic, and socioeconomic groups widened or narrowed? These and similar questions provoke near-constant conversation. But answers are uncertain, partly because research to date has yielded inconsistent findings. In this article, the authors bring…

In a report issued in 2010, the authors found only 6 percent of U.S. students performing at the advanced level in mathematics, a percentage lower than those attained by 30 other countries. And the problem is not limited to top-performing students. In 2011, they showed that just 32 percent of 8th graders in the United States were proficient in…