The UK is still lagging behind leading countries at education and has made little progress in international rankings since results three years ago.
The influential Pisa rankings, run by the OECD, are based on tests taken by 15-year-olds in over 70 countries.
The UK is behind top performers such as Singapore and Finland, but also trails Vietnam, Poland and Estonia.
The OECD's education director, Andreas Schleicher, describes the UK's results as "flat in a changing world".
- In maths, the UK is ranked 27th, slipping down a place from three years ago, the lowest since it began participating in the Pisa tests in 2000
- In reading, the UK is ranked 22nd, up from 23rd, having fallen out of the top 20 in 2006
- The UK's most successful subject is science, up from 21st to 15th place - the highest placing since 2006, although the test score has declined
After the last round of rankings, published in 2013, there were warnings from ministers in England that results were "stagnating" - and reforms were promised to match international rivals.
But Russell Hobby, leader of the National Association of Head Teachers, warned that the results showed "a lost decade" in which the government had pursued an "obsession" with structural change which had "little impact on either standards or equity".
Nick Gibb, England's School Standards Minister, described the results as a "useful insight" and showed the need to "make more good school places available" in grammar schools.
He announced £12m to support professional training for science teaching.
But Professor Stephen Gorard from Durham University said the evidence of the results did not support claims that academic selection would boost overall performance.
What is Pisa? In three sentences
The Programme for International Student Assessment (Pisa) provides education rankings based on international tests taken by 15-year-olds in maths, reading and science.
The tests, run by the OECD and taken every three years, have become increasingly influential on politicians who see their countries and their policies being measured against these global school league tables.
The UK has remained among the mid-table performers, with Singapore rated at the top and most of the highest places taken by Asian education systems.
Within the devolved UK education systems, Wales had the lowest results at every subject.
Mr Schleicher said reforms in Wales had yet to make an impact and it was too early see if they would be successful.
At present Wales' performance in reading puts it only a few places above parts of the UAE, Argentina and Colombia.
Education Secretary Kirsty Williams said: "We can all agree we are not yet where we want to be."
But she said that "hard work is underway" to make improvements in Wales - and that it was important to "stay the course".
Dylan William, of the UCL Institute of Education, urged caution on the results for Wales - saying changes took a long time to filter through and it could be another decade before rankings would reflect what was happening in today's classrooms.
England had the strongest results in the UK, but compared with previous years, Mr Schleicher said "performance hasn't moved at all".
The OECD education chief highlighted concerns about the impact of teacher shortages - saying that an education system could never exceed the quality of its teachers.
"There is clearly a perceived shortage," he said, warning that head teachers saw a teacher shortage as "a major bottleneck" to raising standards.
The National Union of Teachers said the Pisa survey showed the "government is failing in one of its key responsibilities - to ensure that there are enough teachers in the system".
Scotland trails behind England and Northern Ireland - recording its worst results in these Pisa rankings.
Deputy First Minister John Swinney said the "results underline the case for radical reform of Scotland's education system".
He said he would push for reforms to improve schools "no matter how controversial".
Northern Ireland is behind England, but ahead of Scotland and Wales.
Education minister Peter Weir said "performance has not shown any significant improvement" but he wanted to understand how these results for secondary schools could be explained when another set of results had shown Northern Ireland's primary pupils among the highest achievers for maths.
But the overall highest performer is Singapore, with the Asian country coming top in science, maths and reading.
At the top of the table, Singapore has replaced Shanghai as the highest-ranked education system.
Shanghai no longer appears as a separate entry, with the city's results now part of a wider set of four Chinese regions.
This entry for China is in the top 10 for maths and science, but not in the top 20 for reading.
The education systems in Hong Kong and Macao are also among the highest achievers.
Along with regular high achievers such as Singapore, Finland, Hong Kong and Japan, there are strong performances from Estonia, Canada and Vietnam.
But the upper reaches of the rankings are dominated by East Asian countries, with Finland, Estonia, Canada and Ireland the only non-Asian countries to get into any of the top fives.
Ty Goddard, of the Education Foundation, said the results for the UK were an "important snapshot of education achievement" - and they should not be used as an "excuse to have a national 'bash a teacher' day".
Brett Wigdortz, chief executive of Teach First, said: "It's very much a 'must try harder' for the UK. We're doing slightly better than the average, but our score has hardly moved compared to three years ago."
So why is Singapore so successful at education?
Singapore only became an independent country in 1965.
And while in the UK the Beatles were singing We Can Work It Out, in Singapore they were really having to work it out, as this new nation had a poor, unskilled, mostly illiterate workforce.
The small Asian country focused relentlessly on education as a way of developing its economy and raising living standards.
And from being among the world's poorest, with a mix of ethnicities, religions and languages, Singapore has overtaken the wealthiest countries in Europe, North America and Asia to become the number one in education.
Prof Sing Kong Lee, vice-president of Nanyang Technological University, which houses Singapore's National Institute of Education, said a key factor had been the standard of teaching.
"Singapore invested heavily in a quality teaching force - to raise up the prestige and status of teaching and to attract the best graduates," said Prof Lee.
The country recruits its teachers from the top 5% of graduates in a system that is highly centralised.
All teachers are trained at the National Institute of Education, and Prof Lee said this single route ensured quality control and that all new teachers could "confidently go through to the classroom".
This had to be a consistent, long-term approach, sustained over decades, said Prof Lee. Education was an "eco-system", he said, and "you can't change one part in isolation".
Charts and interactive map produced by Ed Lowther, Joy Roxas, Joe Reed, and James Dooley.