Pupils at independent schools in England have the highest results in the world at age 15, an analysis has found.
And the gap between private and state schools is wider than anywhere else, according to Professor Alan Smithers of Liverpool university.
Professor Smithers has analysed an international comparison of reading, maths and science results. Published in 2001, the Programme for International Student Assessment (Pisa) study is the work of the Organisation for Economic Co-operation and Development.
The study found England did well when compared to other countries, coming fourth in science, seventh in literacy and eighth in maths.
Professor Smithers said: "I think the gap between the independent and maintained sector is an interesting finding. There are at least five possible reasons: it could be the nature of the intake, the degree of parental support, the ability to attract the best teachers, extra money or being free of government interference."
He said that England's "long tail of underachievement" is similar to those in other countries. The greater spread of achievement is because the top performers in England do so much better than their foreign counterparts.
Ministers have claimed the Pisa ratings show proof of progress and achievement among English students. However, Professor Smithers' analysis found that although England did well in reading and science, the maths result is based on flawed evidence and is over-optimistic.
"You cannot infer an improvement, because the nature of the tests is very different," he said. The Pisa maths test took a maximum of 30 minutes and consisted of wordy questions.
Professor Smithers said: "It is hard to pin down what Pisa was measuring.
The test is about retrieving and interpreting information and is not so different from an intelligence test. I do not think it taps mathematical understanding and skills, it is more about tapping into a kind of common sense."
The national maths inquiry set up in 2002, found serious concerns about the standard of GCSE, AS and A-levels. Professor Adrian Smith, who reported his findings in February 2004, has recommended that maths teachers should be paid more to counter the shortages in schools.