Towards universal participation in post-16 mathematics

This study is a follow-up to the Nuffield Foundation report Is the UK an outlier? An international comparison of upper secondary mathematics education. It provides up-to-date information on participation in upper secondary (post-16) mathematics education in seven countries, and aims to identify the factors that drive participation. 

Key findings

Only about 20% of students in England study mathematics after GCSE. This is lower than other comparable countries, including Scotland, where 48% of students study mathematics post-16. In Germany and Hong Kong, this figure is over 90%, and Singapore, New Zealand and the US all have participation rates over 65%

High levels of participation are not simply driven by compulsion, particularly for advanced mathematics. Other factors, such as providing appropriate options for all students and the breadth of the post-16 curriculum in general, are associated with high levels of participation.

In Singapore, participation has increased following a requirement for students to choose a contrasting subject equivalent in size to an AS level, so arts and humanities students must take a science or mathematics option and vice versa.

New Zealand has increased participation by offering students an alternative mathematics option focused on fluency, statistics and the application of mathematics. This contrasts with England, where although other qualifications exist, the only widely available option is AS and A level mathematics, which have a significant calculus component and may not be the most appropriate route for all students, particularly those going on to study disciplines such as biosciences, geography, or business and management, where fluency and statistics may be more relevant.

Key recommendations

A new qualification should be introduced to provide a clear and attractive alternative for students who don’t currently go on to study AS or A level Mathematics. The qualification should focus on mathematical fluency, modelling and statistics and be built into requirements for higher education in order to encourage take-up. It should be developed in the context of the wider curriculum and qualification framework, with consideration given to encouraging study of a broader range of subjects post-16.

GCSE Mathematics should remain compulsory until students have achieved a satisfactory grade (as previously recommended by the Wolf report), and consideration should be given to enabling some students to prepare for GCSE for an additional year or more rather than the current tendency towards early entry.  

Project details



Dr Jeremy Hodgen, David Pepper and Rachel Marks, King's College London

Funding programme


Grant amount and duration


21 March 2012 – 20 June 2012

The report


Towards universal participation in post-16 mathematics: lessons from high-performing countries is by Jeremy Hodgen, Rachel Marks and David Pepper from King's College London. It was published by the Nuffield Foundation on 15 January 2013.

Towards universal participation in post-16 mathematics (main report)


Technical report


Germany (Rhineland-Palatinate)

Hong Kong

New Zealand



United States (Massachusetts)