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.
Computation is what computers do best. There's so much more to mathematics than computation. Computers aren't anywhere near humans at discovering properties and proving them (in other words, proving theorems).
I'm pretty sure a computer could be used to solve most International Mathematical Olympiad problems quicker and more reliably. Its not an argument that computers are better at creating the theory that is used to solve the problems.
In essence, I'm saying the International Mathematical Olympiad is not a competition about forming or proving theorems. Correct me if I'm wrong, but isn't the competition essentially determining who makes a better computer? I'm arguing the utility of such skills is limited by the existence of computers.
Although I admit formulating and modeling problems would be a useful skill set not easily replicated by a computer, I'm not sure this is what most testing regimes actually test for.
I'm saying the International Mathematical Olympiad is not a competition about forming or proving theorems.
This statement shows you have utterly no familiarity with the content of most International Mathematical Olympiad problems, which are typically posed as open-ended problems for which the contestants must provide written solutions with proof.
Correct me if I'm wrong
This is one of the rare cases where I can recommend a Wikipedia article for more reading on the topic.
> A1. Determine all functions f : R -> R such that the equality f([x]y) = f(x)[f(y)] holds for all x,y in R. Here, by [x] we denote the greatest integer not exceeding x.
Can Mathematica or another computer program solve that? I am betting it can. And very quickly. And I also reject that such a problem is open ended.
The most that the Wikipedia article speaks on the topic related to the above mentioned partial quote is
> extensive knowledge of theorems
Which does not mention actually proving any theorems. Although I may misunderstand the difference between proving a theorem and proving a solution to a given problem.
Perhaps it suffices to say that persons who know the item content of the IMO contests intimately are very happy to hire (or recruit as students) young people who have demonstrated ability to solve the contest problems. They don't think they are gaining access to people who can be replaced by a computer program.
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/