Botched reforms to the GCSE

When I’m not busy sounding off online about the state of British politics, I mostly spend my day teaching Maths and German to secondary school children. One thing I’ve had to spend quite a lot of time thinking about over the last couple of years is the reform of the GCSEs. This post may well be more of interest to people who work in education than anyone else, but perhaps, in some limited way, it is an interesting example of how a government reform can, in my view, go rather wrong. 

As readers may be aware, the new, reformed GCSEs have been phased in over the last few years. The new specifications were drawn up while Michael Gove was Minister of Education, but they have only fully taken effect more recently. This is partly to do with ensuring a cohort is only taught for one specification and partly due to how decentralised the whole system is (there are lots of different exam boards; independent schools largely now enter children for an equivalent exam called the IGCSE etc). In any case, by this summer more or less all exams will be in accordance with the new specifications.

The most visible difference is the grading system. The old GCSEs were graded A*-E, now the grades are 9-1. The substantial difference here is that the new grade 9 is dramatically more difficult to obtain than the old A*. To put this into context, in Maths, the old A* was given to roughly the top 7% of candidates. The new level 9 is awarded to the top 1.5-2.5%, and the 5% or so candidates who would have received an A* are now supposed to get a level 8.  The remaining grades are meant to be distributed to allow for a rough equivalence between the old and the new system. An old A is a 7, a B is a 6  and so on.

In principle, this doesn’t sound like such a bad idea. The reform could more or less keep the old grade distributions intact, but allow for an additional category for children who are exceptionally good at a particular subject. In Maths teaching, there does seem to be a qualitative difference between the top couple of students in a year and the top 7 or 8. It seems reasonable enough that those couple of students have something on paper which recognises this, and the reform also encourages teachers to give those students appropriately challenging material. This can certainly the subject more interesting to teach.

The problem is, the way in which differentiation at the top was achieved was by making the entire exam dramatically more difficult. There is a bit of a rationale for this. About 60% of the questions in the old Maths GCSE used to be what you might call procedural questions, or ones which only test fluency with a particular method. This is not to say the questions didn’t require knowledge. Solving a pair of simultaneous equations, applying trigonometric identities, using the quadratic formula etc can’t be done without some learning, but once learned they can be done in a fairly procedural manner.  Indeed, even some more advanced Maths can be learned in a procedural fashion. You could learn to solve a second order differential equation without really understanding what you are doing. By contrast, a very difficult Maths problem could be made requiring only very basic Maths to solve it. A good example of this are the Maths and logic puzzles made by the late Bob Hargrave of Balliol  College Oxford, which can be found here. He used to give these to first year Philosophy undergrads, and they are quite tricky, but  the mathematical knowledge required does not go beyond what is taught in primary school. What is hard about them is that they require keeping track of large amounts of interacting information, applying ideas in an unfamiliar context, linking previously separate concepts and making novel leaps of inference.  The new GCSE was meant to be harder in this sense. Children were meant to be taught to have ‘mastery’ over concepts, and be able apply them in what for them was a novel way. As such, the proportion of the exam which consisted of essentially procedural questions was reduced to about 25% of the exam, the rest requiring a degree of interpretation and novel* thinking to solve.

This kind of mastery is one of the things which make a higher level mathematical education interesting and exciting. The problem is, it simply does not reflect the reality of what most children can learn, or what for them a mathematical education can offer. That’s not to say there is no value in raising expectations, or trying to broaden the number of students who are trained to think this way, or to encourage a larger number of students to do so more often. As a teacher, you can often be quite surprised by a student’s improvement, and how much additional methodological fluency eventually seems to allow for more novel thinking. But the exam reforms are just unrealistic about the extent to which many students can achieve this.

The haphazard response from the government and from exam boards as they realised this would be amusing if it wasn’t so hard on so many children. When the first cohort of students were about to take the new GCSE’s in Maths and English in 2017, until a couple of months before they sat the exams, they were led to believe that a grade 5 was the equivalent to a C grade at GCSE. This base level for a pass in hugely important, as a pass in Maths and English are requirements for entry for most schools at 6^th form, any  institution of tertiary education other than the Open University, and almost any reasonably paid job. A very large number of children thought based on their mock results that they were on the verge of failing this exam, and were going to end up being put through the demoralising process of re-sitting it. When the department of education realised  this, it was decided at the last minute that a grade 4 would be, for all personal purposes, a ‘pass’, but schools would still be measured and keep statistics on the number of passes at grade 5 and above. In other words, a lot of children were totally unnecessarily put through a lot of anxiety, and now the statistics which schools publish don’t really reflect what is actually most relevant to their students.

What’s more, even with the shift to a grade 4 as the pass, the difficulty of the exam meant that the grade boundaries are now set absurdly low. In 2017, the boundary for a pass at level 4 was set by Edexcel (the most popular exam board for Maths) at 17%. This is not a good solution. For one thing, it is demoralising for children. Telling a child, who has done a mock paper, not to worry about only being able to attempt 30% of the questions and that gaining a score of 23% is in fact a pass does not leave a student feeling very confident in themselves. What’s more, it means that for candidates hovering around the pass level, the process in increasingly random, as their performance depends on a very small number of questions.

What this shows is that those behind the reforms did not have much of an idea of the reality of education and how the children who take these exams actually learn. They missed the fact that for many people mathematical education is  about fluency with a certain type of procedure in defined contexts. And that is no bad thing. It is a useful thing to be able to learn, and quite useful to have a test which shows if someone can learn how to implement certain kinds of mathematical procedures and operations. What’s more, some of the ways in which the exams have been made more difficult don’t even have lofty, albeit misplaced justifications. They just make no sense. It is now a requirement that all students learn all formulae by heart, as they are not given a formula sheet. This simply does not test anything interesting. Apart from the very rare student who is perhaps able to derive the cosine rule or the quadratic formula from first principles, all this really tests is rote learning.

The worst thing about all of this is that the genuine benefits of the reforms at the higher end could have been achieved quite easily without demoralising everyone else. It would have been quite easy to simply add in an extra few very challenging questions at the end of each GCSE paper which require the kind of novel, highly abstract mathematical thinking that only a small number of candidates are likely to be able to consistently do. But instead, we created an exam that only caters really well for these students. 

* By novel I mean novel for that particular person, i.e taking an approach they have never been taught before. This might be compared with Chomsky's idea of 'novel' uses of language.