UK 15-year-olds lag behind teenagers in other developed countries when it comes to their understanding of key mathematical concepts, a new report has found.

The study from the Programme for International Student Assessment (Pisa) found that less than one in five UK 15-year-olds (18.6 per cent) understand the concept of the "arithmetic mean", compared with the average of 29.4 per cent across 34 developed countries. Four out of ten UK teenagers said they had never heard of the concept.

In Shanghai, China, 68.3 per cent of pupils said they understood the concept well.

The report also reveals that nearly 36 per cent of UK 15-year-olds understood the concept of a linear equation well, compared with an average of 41.8 per cent across the 34 Organisation for Economic Cooperation and Development (OECD) countries.

More than 11 per cent of the UK pupils said they had never heard of the concept, the report "Equations and Inequalities – Making Mathematics Accessible to All" said.

Earlier this year another OECD report revealed that one in five UK 15-year-olds was a “low performer” in maths.

Professor Alan Smithers, director of the Centre for Education and Employment Research at the University of Buckingham, blamed the poor performance on a “progressive” approach to maths developed in the UK in the 1960s.

The new approach to maths in classrooms, focusing on the basics, however, should lead to improvements, he said.

“It is early days for the new approach to show through but hopefully we will be catching up", he said.

He added that efforts to learn effective teaching techniques from successful Asian countries should also have some impact in the future.

Mike Ellicock, chief executive of the charity National Numeracy, said that the relatively poor performance of the UK was due to a “cultural problem” where people had a fixed mindset about their abilities in maths.

It was essential, he said, for making good decisions in adult life, that people understood basic concepts well and could apply them.

Schools Minister Nick Gibb said: "This report is based on 15-year-olds tested in 2012 and reflects the deep concern we had about the previous curriculum, particularly in maths. It does not take into account our reforms since 2010.

“Since then we have reformed the maths curriculum in primary schools, as well as maths GCSE - raising expectations and bringing it closer to the academic standard expected in the highest performing countries and jurisdictions.”