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The National Union of Teachers wants stricter guidelines to stop parents exploiting a system giving children more time and extra marks in exams.
GCSE and A-level pupils in England can get extra marks on appeal, for issues ranging from a headache or hayfever, to suffering a family bereavement.
But there are fears the system is being abused after a huge increase in the numbers appealing for more marks.
In 2005, there were 250,000 appeals but there were more than 300,000 last year.
The head of education at the NUT, John Bangs, told BBC Breakfast teachers needed more defined guidelines to deter pushy parents.
He said: "The occasional pushy parent will put teachers under pressure. I think actually having a proper code of practice which teachers can actually show to parents and say, this is the guidance, this has been worked out with schools, we have been consulted on it, it's entirely reasonable, and that's as far as I can go".
While Chris Howard from the National Association of Head Teachers said the rules need to be tightened to ensure fairness.
He said: "It's the system that needs looking at.
"One of the things that concerns me is that the reward in size, in terms of marks that can be gained for a very substantial problem such as a terminal illness, isn't hugely different from that awarded for a headache, or indeed a temporary bout of hayfever."
'Harsh'
However John Dunford, the General Secretary of the Association of School and College Leaders, defended the system, saying only "very small number of marks" were awarded.
He also said the exam system could be harsh, and he argued for the individual circumstances of students to be considered.
Mr Dunford said: "Somebody can work really hard for two years and be forecast to do really well by the teacher and then something goes wrong in their lives which really, really affects them.
"We're talking about adding just a very small number of marks on to their score to at least go someway to compensate for what they're going through," he said.
The Qualifications and Curriculum Authority, the examinations watchdog, reported a 9% increase in successful claims last year.
Under official guidelines, students are given a week after their last exam in a subject to make a plea for extra marks.
Among the fiercest critics of the system is the Campaign for Real Education, which wants pupils to be judged on their performance on the day.
The campaign's Katie Ivens said: "It's very easy to make a case for your child being disadvantaged by something, not feeling well that day, maybe the goldfish died the day before, or whatever.
"And clearly it favours the parents who are articulate and literate against those who are not perhaps so quick on the uptake or so well able to make a case for the child.
"But if we want to restore fairness exams should be fair, because what they should test is the children's knowledge and their ability actually to do the exams under exam conditions, which are designed to ensure fairness for all."
The country's exams regulator said it was now looking closely at the reasons students give for lodging appeals for special consideration.
Chief Executive Isobel Nisbett said: "We're working with the awarding bodies, the exam boards who run the exams, to try to look more closely this year into the reasons for these candidates asking for extra time, and particularly, what's going on in the schools and the colleges".
The exam guidelines are set out by the Joint Council for Qualifications (JCQ), which represents England's three main exam authorities, including the AQA.
Type of trauma and % added
Recent death of parent or close relative - 5%
Recent death of distant family member - 4%
Witness to distressing event on day of exam - 3%
Hay fever - 2%
Broken limb on the mend - 2%
Stress or anxiety - 1%
Headache - 1%