Junior school mathematics, they believe, is probably to blame for the problems they have so far identified in secondary maths teaching. They now intend to administer maths tests to trainee teachers in pursuit of their theory.

Professor David Reynolds, head of the International School Effectiveness Project, and Professor David Burghes from the Kassel research programme plan to rate the mathematical ability of British primary school teachers in comparison with their peers abroad.

Professor Reynolds, from Newcastle University, hit the headlines with his Worlds Apart analysis of Taiwanese teaching earlier this year. This suggested that British classrooms could benefit from the whole-class methods used in Pacific Rim countries.

Professor David Burghes, from Exeter University, produced figures last March that showed British pupils lagging behind a range of countries in Europe and the far east. He concluded that modern teaching methods and the failure to concentrate on the basics of numerical understanding were damaging British maths lessons.

His Kassel project was funded by the Gatsby charitable foundation. Burghes and Reynolds have now approached Gatsby for financial help with their proposed study of trainee primary teachers.

The latest findings from Professor Burghes’s on-going research make worrying reading. They seem to demonstrate that not only do British 13-year-olds start from a lower base than their Hungarian counterparts, but that they then make less progress over the next three years.

“We must be wary of simplistic answers, or even of assuming that high attainment is preferable to the social cohesion gained by the Scandinavian countries, who use mixed ability throughout,” said Professor Burghes.

“Our data certainly indicate that we do not organise our education sufficiently well to achieve high success but, equally, we do not achieve the social cohesion that Scandinavian countries clearly place at a higher level of importance than basic attainment.”