If the technique is successful at primary level, researchers say, it could have a dramatic impact on the National Numeracy Strategy, which begins in September.
"We are confident we will see an increase in children's ability to handle number, and that schools running the programme alongside the numeracy hour will see better results," said Professor Philip Adey, director of the Centre for the Advancement of Thinking at King's College, London, who co-devised the CASE - cognitive acceleration through science - programme.
Pupils in 10 schools in the White City area of Hammersmith, west London - an area of high deprivation - will receive weekly half-hour "think" lessons. They will work out the basic thought processes behind science and maths. Typical lessons include arranging different-sized sticks in a sequence or posing the question "does a cup of tea taste different if you put the milk in first or last?" Professor Adey said: "Children respond to slightly challenging tasks. It's like crosswords. If they are dead difficult then people shut off and don't do them, if they are too easy they are boring."
Secondary pupils who took part in the programme three years ago did significantly better than their peers in English, maths and science, gaining an average of 20 per cent more A-C grades. At key stage 3, schools in the programme more than doubled the proportion of pupils reaching level 6 or above in all three subjects. At the time, critics of the programme put its apparent success down to enthusiastic teaching.
Two years ago Hammersmith introduced similar lessons in five schools. All the children involved improved, but the most dramatic results were seen in what had previously been the two lowest-performing schools, where the number of pupils reaching level 4 and above in key stage 2 tests rose by 28 per cent in science, 20 per cent in English and 18 per cent in maths.
Chief inspector Gillian Palmer said: "There were other indicators. The children were noticeably more confident, articulate and had more enthusiasm for learning."
Anne Robertson, who will advise teachers on implementing the new lessons, said although the pilot was science-based, "the ways of speaking, of questioning and listening to the children will benefit the entire curriculum". King's College and the Teacher Training Agency are currently developing a nationwide network of trainers in the technique.