Singapore has the highest-achieving primary and secondary pupils in international education tests in maths and science.
But primary school pupils in Northern Ireland were ranked sixth at maths, the highest of any in Europe.
England's performance has not advanced since tests four years ago.
The top places in these rankings are dominated by East Asian countries, such as South Korea and Japan, which are pulling away from their competitors.
These international rankings - Trends in International Mathematics and Science Study (TIMSS) - are published every four years, based on tests taken by more than 600,000 students, aged nine to 10 and 13 to 14 in 57 countries.
International competition has been a major focus for changes to England's school system - and researchers say the "most surprising feature of England's 2015 results is how little they've changed since 2011".
"The period between 2011 and 2015, under Michael Gove, saw major changes to school structures, the curriculum, teacher training, and assessment, and so one might have expected to see some impact from these changes," said Ben Durbin at the National Foundation for Educational Research.
Secondary maths top 10
- South Korea
- Hong Kong
- United States
England is above average - and ahead of many European countries - but it has not made any significant progress in rankings, despite the ambitions of ministers that overhauling the school system...Read more...