In a post-smokestack age, there is only one way for the United States to avoid a declining standard of living, and that is through innovation. Advancements in science and engineering have extended life, employed millions and accounted for more than half of American economic growth since World War II, but they are slowing. The nation has to enlarge its pool of the best and brightest science and math students and encourage them to pursue careers that will keep the country competitive.

But that isn’t happening. Not only do average American students perform poorly compared with those in other countries, but so do the best students, languishing in the middle of the pack as measured by the two leading tests used in international comparisons.

On the 2012 Program for International Student Assessment test, the most recent, 34 of 65 countries and school systems had a higher percentage of 15-year-olds scoring at the advanced levels in mathematics than the United States did. The Netherlands, Belgium and Switzerland all had at least twice the proportion of mathematically advanced students as the United States, and many Asian countries had far more than that.

Other tests have shown that America’s younger students fare better in global comparisons than its older students do, which suggests a disturbing failure of educators to nurture good students as they progress to higher grades. Over all, the United States is largely holding still while foreign competitors are improving rapidly.