The system highlights the difference schools make to children’s progress - whether that be positive or negative - by comparing pupils’ test results at seven and 11.

Individual pupil scores are then averaged and each school gets a value-added measure based around 100, which denotes average progress. A score of 101 means on average each of the school’s pupils made one term’s extra progress. Below 100 means that pupils have made less than average progress.

But one headteacher who took part in the pilot project said that even value-added scores were unfair. She was given a low value-added score, despite having test scores above the national average.

She said that the scores failed to reflect pupil mobility and external factors in the children’s lives.

She said: “Children at key stage 1 are interested in school, but by the time they get to Year 6 quite a few have emotional or social problems to cope with.

The new method also creates a perverse incentive to do badly in key stage 1 tests, which would then make the leap to KS2 - and the value-added score - bigger.

The headteacher said: “One key stage 1 teacher said to me that it makes her cross because she worked hard to get the children to level 3 and then that works against the school.”

Junior schools that admit pupils from high-performing infant schools could also find it particularly tough to get a good value-added score.

Borrow Wood juniors in Spondon near Derby was delighted with this summer’s national results - 78 per cent of 11-year-olds gained level 4 in English, 86 per cent in maths, and 81 per cent in science, and more than a third of pupils gained level 5s.

But the school scored just 98.1 for value-added.

Headteacher Adam Gibson said: “Our feeder infants school is a beacon school, so we are trying to add value to what is already a very valuable product - it’s a harder game for us to play.”

He remains a supporter of the value-added concept, however, as long as “high-quality” data is used to give an accurate picture of the way that schools help their pupils progress.

“We do need to look at ways of measuring what our school does beyond simple percentage scores,” he said.

“I don’t think our value-added score this year reflects the work put in by staff or the children’s attainment, but it will prompt us to look even more closely at what we are doing.

“We’ve got to be brave enough to take it on the chin.”