GCSE Mathematics - charting grades, participation by age and tiering
Stephen Lee & David Sirl, Senior Research Fellows
The first half-term of the academic year has now passed, and with it the start of November marks when examinations in GCSE English and Mathematics can be (re-)taken under certain circumstances, i.e. restricted to students aged 16 and over. In recent years around 55-65,000 students take GCSE Mathematics in the November sitting. Almost all are examined on the foundation tier (95%) and overall 55% are from Year 12 and 45% from Years 13 and above (see Ofqual). This is a small number compared to the summer examination series, which generally has around 700-800,000 GCSE Mathematics awards.
The chart below shows GCSE Mathematics awards data in England for Summer 2023 by grade and age – this is data from a recent Ofqual Freedom of Information release of summer GCSE Mathematics examination awards for England by grade, age and tier, rounded to the nearest 5. The awards data was available for sixteen-year-olds, and for all ages. A whole vertical bar therefore represents the total awards for a given GCSE Mathematics grade for all ages. This can be separated into aged sixteen (light shade) and ‘not sixteen’ (dark shade).
[Note. From this data release it is not possible to tell the ages of the not sixteen group. However, the vast majority of the not sixteen candidates obtaining lower grades are likely to be over sixteen – the relatively few not sixteen awards for higher grades are likely to comprise mainly of those taking GCSE Mathematics at an age less than sixteen. This is supported by JCQ GCSE data for summer 2023 for 15/16/17-year-olds.]
The distribution seen for overall awards is as might be expected. However, the feature that really stands out from the chart is the large proportion of not sixteen-year-old candidates who are awarded grades 1, 2 and 3. This will be the substantial group of resit students, who, having had to take the examination for a second or third time still obtain in most cases a grade below 4. This was the subject of an Observatory blog post earlier this term - GCSE revisioned.
Tiering and grade boundaries
When GCSEs were redeveloped in 2015, many things changed, including the grading system. A 2017 Ofqual blog on GCSE Mathematics grade boundaries discussed multiple areas of interest on this topic. It specifically noted the concern about low grade boundaries for the redeveloped qualifications – on GCSE Mathematics higher tier 20% of maximum marks may be needed to get a ‘pass’ grade 4, whereas on foundation tier this would usually be over 50%.
A key question that arises, is – for those that get a grade 4 or a grade 5, which tier did they study?
Recent Ofqual data provide the opportunity to investigate some of the relationships in GCSE Mathematics between awarded grade, tiers and age. An important element of this is that sixteen-year-olds make up the large majority of awards (around 80%), so headline statistics about the whole cohort largely capture what’s happening to the sixteen-year-olds. Focussing on foundation tier, a few key insights include:
- For all ages, 56% of overall GCSE Mathematics awards in 2023 were from foundation tier, but when broken down by age
- for sixteen-year-olds, 46% of awards were from foundation tier
- for the not sixteen-year-old group, 94% of awards were from foundation tier
- For all ages, 33% of GCSE Mathematics grade 5 awards in 2023 were from foundation tier, but 70% of GCSE Mathematics grade 4 awards in 2023 were from foundation tier.
The data can also be visualised through a pyramid plot. This visualisation is typically used to explore the age and sex/gender distribution of a population, but has potential here to show and suggest insights from this grade and tier distribution of GCSE Mathematics awards. In the following chart, awards made via the foundation tier are to the left of the centre line, and awards through the higher tier are to the right.
The key question posed earlier – ‘for those that get a grade 4 or a grade 5, which tier did they study?’ – can easily be answered when looking at the chart. Given 4 and 5 are the two main grades that can be obtained on both tiers, understanding that the majority obtaining a grade 4 do so from the foundation tier (70%) is helpful. These students will likely have scored 50-75% of the marks to get that grade for a given awarding organisation, e.g. see Edexcel 2023, page 10. However, this does mean that in 2023 around 40,000 students with a grade 4 from the higher tier will likely have scored 20-33% of the marks to obtain that grade.
This short post has given a brief insight into GCSE Mathematics awards by grade, age and tier for 2023. We are currently looking into whether these patterns are stable over time, or if not, then how they’re changing. However, discussion of that will have to wait for another blog!
If you have any observations from these visualisations then do get in touch.
Author information
Stephen and David are both Senior Research Fellows in the Observatory.
Observatory for Mathematical Education team
Observatory for Mathematical Education on LinkedIn.