England is neglecting its brightest children, leaving them lagging far behind youngsters overseas, new research suggests.
It reveals that the nation's teenagers are four times less likely to score the top level in international maths tests than pupils in countries such as Switzerland and Korea, and half as likely to achieve this standard than those in places like Slovenia and the Slovak Republic.
Those pupils in England who are considered to be "high performing" are most likely to attend private or grammar schools, the report says, rather than being state educated.
The Sutton Trust, which commissioned the research, said the findings paint a "deeply troubling picture" and warned that more must be done to help able students.
Researchers at the Centre for Education and Employment Research at Buckingham University examined the proportions of pupils achieving the highest levels in Organisation for Economic Co-operation and Development (OECD) tests. The PISA tests (Programme for International Student Assessment) compare the performance of pupils in different countries in subjects such as reading and maths.
The new report found that just 1.7% of England's 15-year-olds reached the highest level, Level 6, in maths, compared to an OECD average of 3.1%.
In Switzerland and Korea, 7.8% of pupils reached this level.
Overall, England ranked 26th out of 34 OECD countries in terms of the proportion of pupils reaching the top level in maths, behind other nations like Slovenia (3.9%), the Slovak Republic (3.6%) France (3.3%) and the Czech Republic (3.2%), which were among those scoring around the OECD average.
The report adds that globally, the situation looks worse for England.
Singapore, which is not part of the OECD table analysed, saw 15.6% of its students score the top level, while in Hong Kong and Shanghai, which were also not part of the OECD table, 10.8% and 26.6% respectively got the top level.
"This is a deeply troubling picture for any us who care about our brightest pupils from non-privileged backgrounds," Sutton Trust chairman Sir Peter Lampl says in a foreword to the report.
The study also suggests that comparing the maths results of 18-year-olds would be even more stark because 90% of English pupils drop the subject after GCSE.
In many other countries, maths is compulsory up to the age of 18.
The report argues that England is falling down international tables because of successive failures to help the most able pupils.
It calls for bright children to be identified at the end of primary school, with their achievements and progress tracked from then on.
There should also be tougher questions in exams to allow bright youngsters to stretch themselves and show their abilities.
Sir Peter said: "These are shocking findings that raise profound concerns about how well we support our most academically able pupils, from non-privileged backgrounds.
"Excellence in maths is crucial in so many areas such as science, engineering, IT, economics and finance. These figures show that few bright non-privileged students reach their academic potential - which is unfair and a tragedy for them and the country as a whole."
Report author Professor Alan Smithers said: "Recent policy has been a mess and there is no proper provision. It is time to scrap the confusing and catch-all construct 'gifted and talented'. The focus should be on those capable of excellence in the major schools subjects.
"The Government should signal to schools the importance of educating the brightest through how it holds the schools to account. At present the accountability measures are pitched at the weakest and middling performers."
Mike Ellicock, chief executive of National Numeracy, said: "National Numeracy strongly welcomes this report highlighting the importance of unlocking highly able pupils' mathematical potential.
"It is vital to raise aspiration for all pupils and to challenge the all-too-common 'I can't do maths' attitude, which easily becomes self-perpetuating even for the highly able."
Education Secretary Michael Gove said: "This report underlines why the Government is determined to act decisively to restore academic rigour to schools and ensure our exams match the world's best."