Newly-published research reveals that 10-year-olds this side of the Channel are two years behind those across the water. They are still using their fingers to count while pupils in Germany and Switzerland are able to do relatively sophisticated sums in their head, according to a paper prepared for the National Institute of Economic and Social Research.

English children spend less than two thirds of the time that their continental counterparts spend on number work, says the paper which studied teaching methods and maths textbooks in Britain Germany and Switzerland.

In a speech to the North of England conference earlier this month Geoffrey Holland, vice-chancellor of Exeter University, noted that 16-year-olds in the UK were achieving badly in mathematics when compared with children of the same age in Germany and France.

Previous work by Professor Sig Prais for the institute had shown the average 14-year-old in France, Germany, Switzerland and the Netherlands was a year ahead.

Laying the foundations of numeracy by institute researcher Helvia Bierhoff is the first systematic comparison of primary maths textbooks, and it traces the roots of the disparity to a very early age.

Children in Germany and Switzerland tend to work from the one book. The stress is on consolidating the learning of each step, so that an eight-year-old in these countries will have six times the number of exercises on a topic as an English child.

The national curriculum in England and Wales has five attainment targets for this age group: using and applying mathematics, number, algebra, shape and space. This, says the paper, means children have less time to do basic number work and often have to shift to new topics before mastering the last.

Calculators are introduced much later in German and Swiss classrooms because educators fear “retarding pupils’ development of mental calculating-strategies”.

“In English textbooks mental calculation plays a negligible role; vertical written addition is the predominant method adopted for adding two digit numbers,” says the paper. Continental children are taught to add up simple sums, including three digit ones, mentally before going on to add up more complicated sums on paper.

Teaching methods also come under scrutiny. The paper says continental teachers rely more on their textbook, whereas English teachers are often expected to “re-invent the wheel by working out almost from first principles what to teach”.

Teachers on the continent are also more likely to suggest ways children can calculate sums whereas in England young children are expected to develop their own methods, for example using fingers, counters or bottle tops.

The London borough of Barking and Dagenham has set up a numeracy project based on teaching in Germany and Switzerland. Graham Last, the senior inspector behind the project for Years 4 and 5, said preliminary findings after a year are encouraging.

Teachers use material based upon the continental textbooks. Children are discouraged from using their fingers and only practice what they have been learning in written exercises in the last third of the lesson.

“We are getting rid of the long tail of low attainment typical in most British mathematics classes,” said Mr Last.

Laying the foundations of numeracy by Helvia Bierhoff. Available from the NIESR, 2 Dean Trench St, London SW1