Ofqual is refusing to say how many students entered into foundation tier GCSEs were given higher tier grades by its model that would have been “impossible” if they had actually sat their exams.

The phenomenon emerged yesterday when schools found that not only were some centre-assessed grades (CAGs) worked out by teachers replaced by higher moderated grades, but they were also not in the correct tier. 

Melanie Muldowney, who teaches maths at North Bromsgrove High School, in Worcestershire, said: “I am aware that the algorithm threw out some grade 6‘s for foundation tier students. Foundation only goes up to grade 5, so this should never have happened.”

Critics have warned that this could set “unrealistic expectations” and allow students to get on to A-level courses that would not be appropriate for them.

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Today Ofqual has confirmed that some students who were entered into foundation exams had their final GCSE grades adjusted up from the CAG and above the maximum grade 5 that should have been available to them.

GCSE results: Why some students got ‘impossible’ grades

The regulator sometimes needed to do this to ensure that schools’ results met the profile set by its statistical model.

But Ofqual declined to say, when asked, how many students entered into foundation tier exams were awarded a grade 6 or above. It said it would publish “further insight” in the weeks ahead.

Sam Freedman, a former Department for Education adviser, said the “impossible” grades were needed for Ofqual’s algorithm.

“In the guidance given to schools, Ofqual said they were going to grade outside the tier if the ranking of pupils implied that they needed to because the ranking needed to be king in order for this algorithm to work,” Mr Freedman, chief executive of Education Partnerships Group said.

“It is an example of a known problem with the algorithm because in a normal year these grades would have been impossible.”

Sir Jon Coles, chief executive of United Learning multi-academy trust, has called for an independent inquiry into the way grades have been awarded and said the decision of Ofqual to uplift grades above the CAG seemed irrational.

An Ofqual spokesperson said: “We have always been clear that calculated grades would include some that are ‘off-tier’.

“This is part of our commitment to take decisions that work in students’ favour in such unprecedented and challenging circumstances, and has helped to ensure fairness where some teachers’ predictions may have been slightly more severe than those at other centres.”

This flexibility also prevented students who entered a higher tier failing to get a grade at all if the calculated grade was below a 4.

However, the discovery that foundation students were awarded grades of 6 was highlighted as a problem on results day.

In a post on Twitter, Mr Freedman highlighted the issue and added: “Safe to say if they hadn’t already U-turned they would have had to.”

In a research and analysis report into the awarding of A levels, AS levels and GCSE, Ofqual says that it might be necessary to lift a student in a foundation tier above a grade 5 if it was decided that the school needed an overall uplift in its grades and this could not be achieved through just lifting the higher tier students.

The report also says that limiting foundation tier students to no more than a grade 5 might result in the ranking of students provided by a school changing.