The national numeracy strategy, introduced in 1998 as Labour tried to emphasise the 3Rs in primary schools, has succeeded partly because it includes traditional rote-learning of times tables.

However, Dr Sylvia Steel of Royal Holloway, London university, who presented the research to the British Association Festival of Science, questioned whether the strategy was doing enough for lower-ability pupils.

Earlier this year, 40 children in Year 3 at a Surrey school were given simple tests in addition and multiplication, and 41 pupils in Year 6 (11-year-olds) were tested on multiplication. The results were then compared with those of 241 youngsters in tests from 1995 to 1998.

The research confirmed that pupils who could remember the answer (known as retrieval), were quicker and more accurate than those who used other strategies, including counting on fingers.

National curriculum targets say children should be using retrieval to answer simple addition, subtraction and multiplication questions by the end of Year 3.

Among the Year 3 children tested in 2004 on addition, 13 per cent used retrieval to arrive at the answers, compared with only 2 per cent among the earlier group. Extrapolated nationally, this suggests that the numbers using retrieval may have grown from 12,000 to 78,000 pupils a year in England.

On multiplication, 8 per cent retrieved their answers compared to 4 per cent in the previous study. The proportion guessing dropped from 9 to 3 per cent.

The results for Year 6 pupils were more equivocal, with the proportion using retrieval actually falling from 31 per cent in the earlier test to 30 per cent. However, overall, pupils in the second group answered questions more quickly.

Dr Sylvia Steel said: “There have been some gains from the strategy, and my feeling is that more retrieval is going on.”

However, teachers worried that children who have the most problems with maths may have made less progress than their peers, because the strategy covered a lot of ground and there was little opportunity for extra practice for those who struggled.

That suggestion was supported by another paper presented at the festival.

Dr Chris Donlan, of University College, London, said that up to 7 per cent of pupils may be being overwhelmed by the number of subjects which are covered by the national curriculum at key stage 2.

The Government might do better, he said, to reduce the number of topics covered because many pupils lacked the memory capacity to cover a large spread of subjects effectively.