Headteachers say that "secret" guidance given to Sats markers should be made available to all schools.
The call comes after teachers took to Twitter to share their anger over numerous examples of answers in the spelling, grammar and punctuation (Spag) that they thought had been wrongly marked according to the official mark scheme.
But it emerged yesterday that markers had been given further marking guidance that was not available to schools – and that markers were told to get rid of after use.
Now Russell Hobby, general secretary of the NAHT heads' union, has called for all guidance to be published.
"All forms of marking guidance should be transparent and available to schools," he said. "You need to tell teachers this [the marking guidance] in advance, otherwise people feel the goalposts have shifted and what you are trying to do is catch children out rather than recording what has been taught."
More than 550,000 pupils took the tests in spelling, punctuation and grammar (Spag), reading and maths in May and results were returned to schools last week.
One consultant said it was “Kafkaesque” that teachers were preparing to appeal against marks they believe have been wrongly lost according to the published mark scheme – while another mark scheme existed that appeared to show that the papers were correctly marked.
In the Standards and Testing Agency's (STA) published mark scheme, teachers are told pupils will get one mark for a correctly placed semi-colon.
But another mark scheme – which Pearson, the company which runs the marking, has confirmed is official – offers extra guidance to markers asking them to take the shape and size of punctuation marks and their exact position into account.
Teachers suspect that this insistence on the correct height, depth and orientation of the semi-colon may be why some children who have correctly identified where to put it, were not given a mark.
And they are concerned that not only does the guidance exist but also markers were expected to destroy it after use.
A spokeswoman for Pearson confirmed that each year, markers were asked to dispose of all their materials once the marking was over.
But the status of "secret" guidance issued to Sats markers in the appeals process remains unclear.
Mr Hobby said: "In our view, the official STA published guidance is relatively straightforward and usable. The training and preparation of markers seems to have departed from common sense.
"We don't understand ourselves how that gap [between the published guidance and markers guidance] has emerged. We've written to STA and Ofqual for clarification.
"It seems to me the official STA guidance should be the basis for appeals."
Rosamund McNeil, head of education at the NUT teaching union, has also called for the criteria to be published. "These are urgent, systemic problems which must be addressed," she said.
"In the particular case of the semi-colon, the sensible thing to do would be for Pearson to publish its marking criteria and relax those that are causing problems."
Debra Kidd, the education consultant and former teacher, shared the "secret" guidance on Twitter. "What seems to be unusual this year is that the guidance is so detailed," she said.
"For 10- and 11-year-olds to be judged negatively on something that was not in the question seems inhumane. If teachers appeal, they have to be pretty certain they are going to be successful.
"If teachers can't be successful because of marking criteria that they didn't see, that is Kafkaesque. You are appealing against a system but you don't know the rules."
And James Bowen, director of the NAHT Edge union for middle leaders, added that the difference between the published mark scheme and the advice given to markers could "erode confidence that children's abilities are being assessed in a fair and transparent way".
Last week, the DfE revealed that 61 per cent of pupils had reached the expected standard in reading, writing and maths in the key stage 2 Sats.
The DfE has been contacted for comment.