Cumbria council has become the latest authority to devote extra funding to borderline pupils, in this case those on the cusp of achieving the benchmark level 4 in key stage 2 tests.
Heads say the move, in which extra cash will be targeted at selected Year 5 and 6 children, is unfair because others, notably gifted and talented or special needs pupils, are neglected. Local authorities and the Government are concentrating on improving test statistics instead of seeking to help every child reach its full potential, they say.
Last week, The TES revealed how a project run by the secondary national strategy is targeting extra support at borderline C to E grade GCSE students in English and maths.
Myron Hyrnknow, head of Askam village school in Furness, said he had been appalled to receive a letter offering the extra support from Cumbria council for pupils whose KS1 results suggested they might just miss level 5.
"It may help a small group of children, but what about the rest?" he told a conference held in Birmingham by the NASUWT.
"What about pupils who cannot achieve a level 4 and those with special educational needs?"
A Cumbria council spokesman said that 48 of its primaries were receiving around pound;100,000 between them to pay for extra support for borderline pupils in years five and six. The funding came from a government grant set up specifically for this purpose.
He said: "It's not necessarily about achieving targets. It's about giving children the support they need."