Teachers do more to help low-achieving pupils by explaining maths in simple language than by using the numeracy strategies.
Jonathan Solity, lecturer in educational psychology at Warwick university, piloted a new early-numeracy system at five primaries over three years. The new system was based on the core skills children need in order to improve their mathematical ability: counting, mathematical language, and an understanding of how to balance an equation.
"We spend a lot of time on mathematical concepts," he said. "It gives them better understanding, because the same mathematical concepts come up again and again."
For example, Year 1 pupils are taught the difference between one and 10.
Later, they are shown that the same rules can apply to the difference between 10 and 100. All concepts are explained in uncomplicated language.
Children are not asked to add quantities of oranges and apples, because they may find the different varieties of fruit confusing. And words like "double" or "half" are only introduced after multiplication tables have been learnt. Dr Solity found that this increased children's mathematical understanding significantly. In particular, it improved the ability of the bottom 25 per cent of pupils.
"Maths teachers have got much better at teaching to the test," he said.
"Children are being taught to jump through hoops, but they don't have a theoretical understanding of what the processes are. With our method, children have all the mathematical skills they need."
About 350 pupils were monitored between September 2002, when they began their reception year, and July 2005, when they completed Year 2. Pupils at Coppins Green primary, in Essex, were among them.
Anna Conley, key stage 1 co-ordinator, said: "It's had a dramatic impact on lower achievers. They're focused, and confident in their own ability. They know it's not about right or wrong answers, but about using their knowledge to solve problems."
In 2004, 75 per cent of Coppins Green pupils achieved the expected level 2 or above at key stage 1. The following year, 92 per cent of pupils who had followed Dr Solity's method reached level 2 or higher.
Dr Solity hopes that his research will highlight problems with methods used by many primary numeracy consultants.
Tony Gardiner, reader in maths at Birmingham university, agrees that the national numeracy strategy is failing many pupils.
"The strategy provided primary teachers with a lifeline when they were floundering," he said. "But it's like a soup kitchen. When you're starving, it's excellent. But you can't spend your life in a soup kitchen."
Sue Johnston-Wilder, chair of the Association of Maths Teachers, said: "The major problem with maths is anxiety. Telling children early on that they're failing isn't good. But that's not about the strategy. That's about the assessment regime."