Full equation sheets are bad for learning but good for helping students to pretend to understand
With the grim inevitability of the managed decline this country knows too well, full equation sheets in GCSE Mathematics, Physics, and Combined Science are now confirmed to be here to stay. The Minister for Schools Standards, Georgia Gould, has requested that Ofqual continue to require exam boards to provide these exam supplements for the remainder of the current GCSE cycle.
In the distant world of the 2010s, blissfully untouched by pandemics — and lockdowns — Physics and Combined Science students received short equation sheets in exams with well under half of the full set of equations they were expected to be familiar with, while no equivalents existed for GCSE Mathematics. Full equation sheets were introduced as a temporary measure in recognition of the effects of the pandemic (the exact reasoning being somewhat unclear, but of course with “strong support from all stakeholder groups”). The pretence that this was going to be only temporary has doomed these equation sheets to premature obsolescence for the last few years by disclaimers of touching naivety: “For use in June 2025 only”.
The problem is not exactly that this is a symptom of decline — that students should memorise equations and should be tested on their recall. Rather, Gould and other supporters of this move have got the wrong end of the pedagogical stick.
Equation sheets are presented as liberating students from the tyranny of rote memory, which is one of the main bogeymen in the progressive educationalist’s imagination. It is of course possible, especially in the era of short-form media, to argue for a place for rote memorisation in education. But this is not the point either.
As a secondary science teacher, two things are abundantly obvious. Firstly, equations are not random sequences of symbols: they encode information which pertains to models, and a good mental model is hard to achieve without being able to recall the relevant equations. In many cases, the equation is in fact a definition. It is simply not possible to have an understanding of power, for instance, and not be able to state that P=E/t and know what this means. Even when equations do not encode a definition, they still carry highly significant meaning. If you can’t work out, for instance, that the power developed in a component increases when either the current through it and the potential difference across it does — which is enough to remember that P=IV – you do not have a good mental model of how circuits work.
The second obvious thing is that students who cannot recall equations usually have not practiced doing calculations with them to the level that they could be confident of getting questions right in an exam. It’s true that the factor of ½ in the equation for kinetic energy is not obvious to a GCSE student. But a student who has prepared well for their exams will in almost all cases have it in their memory. The triplet of trigonometric equations on the Mathematics formula sheet referred to as SOHCAHTOA is literally named by a memory aid. With even the most cursory acquaintance a student should be able to recall these equations. Even the rather unwieldy quadratic formula should, with good practice, become familiar.
These two straightforward observations mean that it is poor pedagogy to encourage students to devote specific attention to memorising equations — it focuses on the appearance of understanding rather than understanding itself. My heart sinks when students assure me that they have broken out the equation flashcards for revision. But this misunderstanding of equations’ place in science and maths, the idea that equation recall is orthogonal to understanding and calculational fluency, is implicit in Gould’s decision. It is the other side of the same bad coin as promoting the learning of equations by rote.
Predictably, told that they will receive additional support, some students get complacent
On top of this are the perverse incentives that full equation sheets present to students, which teachers have already been seeing in the last few years. Predictably, told that they will receive additional support, some students get complacent, thinking that looking at the equation sheet in the exam can replace the hard work of building understanding over years of learning.
Lurking beneath this debate lies something more troubling. Most commentators and even many teachers make the mistake of assuming that school education is basically successful in academic terms. Exam results tell a different story. In science, around a quarter of students are entered for separate qualifications in Biology, Chemistry, and Physics, generally academically selected either by school type or within their school. In 2025, the median grade in Physics with AQA, the largest exam board in science, was grade 6, which required 54 per cent of the marks available. Not a disaster. But among the other three quarters, who were entered for Combined Science (which leads to the award of two grades), the median grade was two 4s. Depending on the tier of exam entry, this required either 23 per cent on a harder exam or 55 per cent on an easier exam capped at two grade 5s (nationally, slightly more students take the easier exam). The median grade in GCSE Mathematics in 2025 with Edexcel was 4, requiring 22 per cent or 60 per cent in the same way. There’s no way to convey simply what these percentages mean in practice, but readers are welcome to consult past exam papers. The upshot is that these statistics just barely hint at thousands of stories of mis- and incomprehension that play out in classrooms across the country.
The strongest argument for full equation sheets, in spite of the case against sketched here, is that understanding and calculational fluency — the development of which should achieve memorisation as a byproduct — is simply not on the table for most students sitting these exams. Instead, they should focus on picking up as many scraps of marks here and there in the attempt to perform a simulacrum of understanding. Full equation sheets can certainly help them in this. Somehow, however, I suspect nobody, from the government down to teachers, really wants to go there.
