New courses modelled on the revolutionary secondary school CASE programme - Cognitive Acceleration through Science Education - have been tested out in secondary maths and are now being developed in secondary English and primary schools.
And with 400 schools already following the CASE curriculum, King's College and the Teacher Training Agency are developing a nationwide network of trainers to pass the technique on to the rest of the country's 3,500 secondary schools.
But there are also signs that the CASE technique - which seeks to boost children's mental development by getting them to think about the way they learn - is seeping through the teaching profession.
"I believe we're talking about a revolution, " says Professor Michael Shayer of King's College.
"We are moving towards a different way of teaching, not just of maths and science but of everything - one that is not just concerned with kids' conceptual knowledge but with the quality of their underlying thinking."
CASE was created by Professor Shayer and Dr Philip Adey to encourage the development of higher-order thinking skills in pupils - the confident handling of abstract concepts. Only around 30 per cent of the population develop these skills, which are needed to gain higher grade GCSEs.
Early evaluation of CAME, the maths follow-up, suggests similarly impressive results to CASE, which caused a sensation when its first results were published in 1991 and which last year was credited with raising pupils' GCSE science pass rate by 20 points and major improvements in maths and English scores.
Tested among 11-to-13-year -olds in 10 schools - four of them closely monitored by Professor Shayer and colleague Mundher Adhami - CAME produced a substantial boost in pupils' maths ability and thinking skills.
In one Newcastle school, which ran CAME and CASE together, the improvement in pupils' performance in a standardised maths test was even greater.
CASE and now CAME encourage cognitive development through a two-year series of challenging, fortnightly lessons for pupils in Years 7 and 8. Children collectively explore advanced concepts and then discuss and reflect on what they have learned.
The key is not so much the information they gain, but the insight into how they got there - and the fact they learn from each other, which Professor Shayer believes means the lessons are internalised by pupils much more easily.
At Hampstead School, a north London comprehensive, 12 and 13-year-olds in class A3 last week struggled to come to grips with circle area and exponential growth - something they normally would not meet for at least another year.
Teacher Su Nicolson says the lessons are challenging to run, because pupils are given so much more independence and there is so much more discussion. "You can't just tell them to turn to page six," she said.
And they are rewarding for the pupils. As he tries to work out the area of one circle, 12-year-old Arun says that hearing what other pupils have to say gives him confidence.
"If you feel you don't know something and everybody's speaking up and they're not sure either you realise you're not the only one. Everybody's probably as confused as you."
Teachers at Hampstead School are already finding they are using the CAME techniques in other lessons - and that pupils are coming to expect it. They want their chance to have their say about what they are doing.
Professor Shayer says that is a common finding in many schools which have taken part in CAME and CASE. Another is that student teachers are picking up the technique in their classroom practice. A handful of teacher-training courses have even incorporated it into their syllabus.
"PGCE students value it more than any other part of their teaching practice because there is a describable set of professional skills that go with it," he says.
CASE and CAME were designed for the start of secondary school because that is a crucial time in pupils' development - a time of major brain growth as well as social change.
The primary schemes are designed to improve pupils' concrete thinking skills so they will be more ready for abstract thought later. One trial will run in infant years - another crucial moment in children's development - while a second will run in the last years of junior, "priming" them for secondary.
For further information contact the school of education, King's College, Strand, London WC2R 2LS.