I read all the comments kindly posted here before mine, and then I read the fine submitted article. Here I will link to the study "Not Just the Problems of Other People's Children: U.S. Student Performance in Global Perspective"[1] that underlies the news report submitted here. The full study report will of course give you details that a brief news report has no space to provide. It's good to read a news report from British journalists about education issues here in the United States, as the British journalists are less likely to hand-wave away concerns about United States educational performance.
As a response to some comments here, I'll note that I have lived in east Asia (I am a proficient speaker and reader of Chinese as a second language, and have lived in Taiwan during two three-year stays since I became an adult) and can verify that the schools there generally do a better job teaching mathematics (and also second languages) than the schools in the United States, at less expense per student. That efficiency in primary and secondary education lets both students who go on to higher education and students enter the workforce after secondary education achieve more in their adult pursuits than many Americans. Children there have childhoods with play and fun, but then they get to grow up to be adults with actual skills for advancing themselves.
For comparative rankings of different countries, showing how many more students in some countries reach high levels of mathematics achievement by eighth grade, see the very well constructed data chart "Distribution of Mathematics Achievement" for eighth graders in Exhibit 1.2 of Chapter 1 of the TIMSS report from the 2011 testing round.[2]
This issue is familiar to Americans like me who have lived overseas and have learned the local language of another country and have read the math textbooks available there. Better instruction can produce better educational results--and for less money besides. The top student issue is illustrated also by results from the International Mathematical Olympiad[3] and other international academic competitions. The United States has a huge population base, and it has many families in which the children are brought up by parents who are first-generation immigrants who received their own primary and secondary educations in other countries. (Such children do conspicuously well in academic competitions in the United States.) And the United States is wealthy, a heritage from the good governance structure set up by the United States federal Constitution. But even at that, the United States national team can be beat at the International Mathematical Olympiad by countries that have many fewer people and much poorer economies. Some countries have a very impressive group of top students.
[1] http://www.hks.harvard.edu/pepg/PDF/Papers/PEPG14-01_NotJust...
[2] http://timssandpirls.bc.edu/timss2011/downloads/T11_IR_M_Cha...
[3] http://www.imo-official.org/