There are two measures in a GCSE exam - your raw score (the actual amount of marks you got on the paper) and your grade (a 1-9 scoring). The idea is that the raw score tells you how far you walked, but the grade takes into account the steepness of the hill. If the exam was easier than standard then you will need more marks to achieve a grade. While in a harder exam, you will need fewer marks to achieve a grade.
However, after reading various news articles and talking with multiple parents, it appears that few people truly understand how these grade boundaries are determined and how they affect a student's ability to pass.
Around 40% of students failed their GCSE maths this year and are required by law to resit. I have seen news coverage questioning whether schools and maths teachers are failing our students - but is it really a reform in maths teaching that is necessary to tackle the high failure rate?
The answer to that question lies in understanding the exam system, and the role of the grade boundaries.
There are two main ways assess people...
Norm-referenced assessments are a type of standardized test that compares students’ performances to one another. It ranks students on a “bell curve” to determine the highest and lowest-performing students. This method is used to understand how students’ scores compare to a predefined population with similar experiences.
Criterion-referenced assessments are designed to measure student performance against a fixed set of predetermined criteria or learning standards. This method means every student taking the exam could theoretically fail if they don’t meet the expected standard; alternatively, every student could earn the highest possible score.
Our exam system is norm-referenced. The standardisation of exams is based on the population pass rate. The aim is that roughly the same proportion of students receive each grade from one exam series to the next. This makes results comparable across years. The standard is that roughly 67% of students get a passing grade of 4 or higher, around 20% get a grade of 7 or higher, and about 5% get a grade 9.
These pass rates are fixed by the system. When there were increased pass rates over Covid this was seen as a negative as it hindered cross-year comparability and ran the risk of making the grade worth less. There has therefore been a conscious effort by exam officials to bring the pass rate back down to pre-covid levels.
In maths these rates are slightly lower: about 60% of students get a passing grade of 4 or higher, and around 15% get a grade of 7 or higher.
That is to say, in GCSE maths, 40% of students have to fail! The system is set up to ensure that that happens. Grade boundaries are set after the exams have been sat, and towards the end of the marking process. The marked exams are then used to set the grade boundaries and they are set with the purpose of ensuring 60% of students achieve at least a Grade 4, and 15% achieve at least a Grade 7.
Students can demonstrate the proficiency they need to overcome any everyday adult maths problems - such as adding a 10% tip to a bill - and still fail their GCSE maths.
This graph is for illustrative purposes, showing a theoretical possibility, and does not represent a past cohort of students or a data-backed proficiency score.
But, in our norm-referenced system, getting 100% of a cohort to pass their GCSE maths is impossible. Everyone cannot be better than average.
It does not directly matter how well a student does in their exam in terms of marks, if they are not in the top 60% of the cohort they will fail! A limited number of passing grades are to be awarded and students are competing to get them. For a student to go from failing to passing they have to move up into the top 60%, which is only possible if another student moves down into the bottom 40%.
Now this is not necessarily a bad thing, as long as you understand that that is the system. After all, in the job market we are preparing students for, there are only a limited number of vacancies, and applicants must compete for those positions. Why should school be any different?
However, students are also working towards a goal that is moving away from them! Passing is based on them being in the top 60%, but that is largely out of the individual's hands. All that the individual can control is the raw score that they get, and how many questions they get correct on the exam in front of them. But, if you look at the AQA grade boundaries, the raw scores needed for each grade are overall rising.
AQA is the most popular exam board for GCSE maths.
The raw score needed to pass the foundation paper in 2024 was 33 marks higher than was needed in 2017.
I had a student who improved from a raw score of 140 to 159 in the last six months of Year 11, and for the first time that was not enough to get her a Grade 7.
It does not matter how well maths teachers teach. It does not matter how well the students do on their exams. 40% will still fail. That is the system, and if you want to change it - to increase the pass rate - you need to look to the exam officials, not the schools.
To me, the increasing AQA grade boundaries indicate that we maths teachers are improving how we are teaching, and we are helping our students pick up more marks in the exams. Across the entire cohort. But that does not change the fact that 40% failed. And no amount of improvement in maths teaching will change that.
Comments