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Mark Ellse: Here’s a maths puzzle. How to make exams harder but pass the same number of pupils?


Dear reader, assuming for the moment, that you know absolutely nothing about maths teaching and examining, may I ask a simple question? What would happen if pupils sitting GCSE maths were presented next year with papers that are harder than this year’s papers?

Even if like Education Secretary Nicky Morgan your multiplication tables are a little rusty, the answer to that question is pretty obvious. If the exams are harder, the marks will be lower. It is as simple as that.

Now, if the pass marks are the same as this year, inevitably fewer students will pass them. Instead of around 50 per cent getting grade C in maths GCSE, the number of pupils passing maths GCSE is going to drop. If the papers are as hard as those sat by pupils in the Far East, the number of pupils passing would halve to 25 per cent. The number of A and B grades would plummet and the number studying maths at A level would fall. However much universities may bleat about the poor standard of maths applicants, they’d rather have the same number of applicants than make half their maths staff redundant.

Parents, too, would scream if 75 per cent of pupils were leaving school ‘unqualified’ in maths. However much the then Secretary of State for Education spun the news, it would be an obvious political catastrophe.

But the Conservative party has wedded itself to ‘higher standards’ and therefore the papers must be harder. What will they therefore do? Simple: they will lower the pass mark!

If one looks at the video which accompanies the Ofqual press release,

one sees their spokesman, Ian Stockford, in a very calm voice, trying to conceal the total pickle that Ofqual is in about what to do. 1 minute 30 seconds in from the beginning there is a chart that shows the distribution of marks for trial foundation papers produced by each of the four exam boards.

Three exam boards, OCR, Pearson and WJEC, have done exactly what the government wants. They have made the papers harder. The result is that virtually no candidate has above 50 per cent. This is a staggering drop in marks for a foundation paper. Grade C pass marks in the past were typically 75 per cent. The trial papers produced by these boards are far too hard.

The AQA examiners, correctly discerning that the instruction to produce harder papers should be ignored as much as possible, has made the papers a bit harder than previously. Even with their papers, very few candidates get above the old 75 per cent pass mark. They’ll set a grade C boundary of a little over 60 per cent for their new exam and roughly the same number will get a grade C, as used to with the current maths exam.

Ian Stockford, in a very calm voice says: ‘Were we attempting to set grade boundaries using those distributions, it is unlikely that we would have been able to do this reliably’! (My emphasis.) What he means is that this is a total mess. At a stage where all teachers and examiners should know exactly what is going to happen, the exam boards’ trial papers span a mark average from 25 per cent up to about 55 per cent. This is a fiasco.

Mr Stockford carries on ‘…therefore we have asked these exam boards to revisit their question papers and to ensure that while they retain the demand and the rigour at the top end for the able candidates, they also have more accessible questions to facilitate candidates across the broad range of abilities of students..’ He goes on, while saying that the AQA paper is a competent exam paper they have asked AQA to ‘look again at the expected difficulty of their papers.’ All this is code. What Ofqual really mean is this: ‘Please, please, please, we know it’s impossible, but can’t you all try to produce some harder papers so that we can fulfil our promise to make exams harder without students getting lower marks?’

Ofqual is asking something that is mathematically impossible.

It is often suggested that the government should set, centrally, a single exam for the main core subjects. Such a route is most unlikely for an exam system that is so politically driven. Were the  EducationSecretary directly responsible for GCSE exams, he would be politically vulnerable. Four exam boards, with Ofqual as an intermediary, is very convenient. There is sufficient confusion to ensure that the Department of Education have plenty of others to blame for any problems.

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Mark Ellse
Mark Ellse
Mark Ellse is a physicist and author. He is a former headmaster, independent school inspector and A level chief examiner.

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