Those who believe all is well in America's public schools are pointing to the 10 percentage-point gain in high school graduation rates over the past decade, with 80 percent of high schoolers now completing high school.

To the extent there is any problem, they attribute flagging standards of American education to the rising numbers of children from immigrant and other disadvantaged backgrounds. But a just-released report from the Education Department reveals that high school seniors have shown no signs of improvement in either math and reading between 2009 and 2013.

If one digs even deeper into the numbers and test scores and compares them with students around the world, they tell an even bleaker story. With a few notable exceptions in states like Massachusetts, public schools are underperforming across the board. They are failing even children from families where a parent has a college degree and in more affluent districts. According to our new research, these U.S. students from more advantaged backgrounds are not doing nearly as well as similarly-situated students in other industrialized nations.

Among this privileged group of students, the United States trails 27 of 34 other industrialized countries in math proficiency. In a just-released report, my colleagues Eric Hanushek and Ludger Woessmann and I find on the latest international tests that less than half of the 15-year-old students from homes where parents are well-educated are proficient in either math, science or reading. The tests were administered to 15-year-old students in the 34 countries that are members of the Organization for Economic Co-operation and Development by its Program on International Student Assessment.

Our study places all 15-year-olds into one of three categories according to the education background of their parents: 1) those with a parent who had a college degree; 2) those with a parent who had a high school diploma but no college degree; and 3) those without a high school diploma. For each parental-education category, we identified the percentage of students who were proficient in math, science and reading as well as the percentage of students who performed at or above the advanced level in math.

Not surprisingly, students who come from highly educated families are more likely to do well than those from families in which no parent has a high school diploma. The percentage who are proficient among U.S. students from high-education families are 43 percent in math, 42 percent in reading and 40 percent in science, as compared to 18 percent, 17 percent and 12 percent in the three subjects, respectively, among those coming from families with low education levels.

But that 43-percent math proficiency rate among the 15-year-old students from families with strong educational backgrounds does not come close to the levels achieved by students in many other countries. Countries with higher proficiency rates among students from better-educated families include South Korea (73 percent), Poland (71 percent), Japan (68 percent), and Germany (64 percent). Other major countries that score much higher than the United States include Canada (57 percent), France (55 percent) and Australia (55 percent). The United States outperforms only Italy, Turkey, Sweden, Greece, Chile and Mexico.

The U.S. economic strength has been built in large part through its record of technological invention, which is dependent upon the pool of students who have developed advanced skill in math and science. To see whether there is evidence of excellence at the very top of the American school system, we also checked out the share of the population in the United States that scores at or above the advanced level of performance in mathematics.

Among students from well-educated families, the United States once again comes in 28th among the 34 OECD nations. As compared to the 12 percent performing at the advanced level in the United States, the eight world leaders post percentages that are at least twice as high: Korea (30 percent), Japan (23 percent), Belgium (19 percent), the Netherlands (18 percent), Germany (17 percent) and Poland (16 percent). Canada, our neighbor to the north, also turns out twice as high a percentage of students at the advanced level in math as does the United States.

There are pockets of excellence in the United States: Massachusetts, Minnesota and a few other states on the northern tier of the country perform up to the Canadian standard. But these relatively small states are more than offset by scandalously low achievement levels registered in such large states as New York, California, Illinois and Florida.

The United States has two achievement gaps to be bridged — the one between the advantaged and the disadvantaged, and the one between itself and its peers abroad. Neither goal needs be sacrificed to attain the other.

Paul E. Peterson, a professor of government at director of the Program on Education Policy and Governance at Harvard University, is also a senior fellow at the Hoover Institution. Thinking of submitting an op-ed to the Washington Examiner? Be sure to read our guidelines on submissions for editorials, available at this link.