What are the ‘right’ grade boundaries for GCSE Maths?

By Andrew Taylor
Published 28 September 2022

On results day this year, I wrote a short blog about why AQA’s grade boundaries were higher than most people anticipated. Since then, there have been lots of comments and questions about the boundaries and a definite difference of opinion about whether higher boundaries are a good or bad thing. This got me thinking about where ‘ideal’ grade boundaries for GCSE maths would be.

As always, my first instinct is to look for clues in the history of the qualification and that usually means starting with the Cockcroft report ‘Mathematics counts’ from 40 years ago. The report set out an approach to assessment that became the three tier GCSE and Cockcroft had this to say about boundaries.

We cannot believe that it can be educationally desirable that a pupil of average ability should be required to attempt an examination paper on which they are able to obtain only about one third of the available marks.

The report argued that there were two fundamental principles that should be applied to any examination in mathematics:

• Candidates are enabled to demonstrate what they do know rather than what they don’t.
• Examinations should not undermine the confidence of those that take them.

A lot has changed since those words were written but I think the principles hold true. We want all students to be able to show positive achievement and to be confident enough to go into the next exam and to continue learning and doing maths.

But, is that even possible with the number of grades each tier has to cover and with the distorting effect of the standard pass at grade 4? It’s certainly not easy and the requirements we have to work to were actively intended to increase challenge at the upper end of the attainment scale. This has to mean that the lowest available grades will always be compromised. Remember, 50% of marks in any paper have to focus on the upper available grades and, on Higher tier, no marks can be focussed below a grade 4 standard. Hence, a student achieving grade 4 from the Higher tier is never going to show what they can do because most of what they can do is on the Foundation paper!

However, that should not stop us trying to get papers as accessible as possible within the requirements and, hence, get more students gaining more marks. If I stopped there, most teachers would, I think, nod in agreement. Our comparable outcomes / no grade inflation model means that an inevitable consequence of this is that grade boundaries go up because the proportions of students achieving each grade is tightly controlled.

So, is higher always better when it comes to boundaries? Not really. If a paper is too easy, or too hard, it becomes difficult to reliably differentiate across the range of attainment. Grade widths are narrow and, as a result, grades are less reliable because every student is close to a borderline. Further, if the boundary for the top grade is very high, are we ‘sorting’ students on their mathematical ability or on their ability not to get bored by the lack of challenge and avoid silly errors?

Right now, in GCSE Maths, we don’t have a problem with boundaries being too high. This year grade 9 was set at 89% and, whilst I would not want it too much higher, it feels reasonable for a top grade that’s only reached by a small proportion of students. Nor do we have an issue with grade widths. These are 25-35 marks wide so grading can be highly reliable.

So, how close is our ‘average pupil’ to Cockcroft’s ideals? The median grade at age 16 is a 5 so, in the Foundation tier, a boundary of 70+% suggests positive achievement and being able to show what they know. In the Higher tier, even with the constraint of meeting the requirements for demand mentioned above, they are still achieving something more than a third of the marks so I’d say we’re moving in the right direction.