New qualification needed to improve England’s poor participation in mathematics post-16

14 January 2013

The solution to England’s poor participation rate in post-16 mathematics education could lie in a new qualification that provides a clear and attractive alternative for students who don’t currently go on to study AS or A level Mathematics, according to a comparative study of mathematics education in seven countries, published by the Nuffield Foundation today. The study was led by Professor Jeremy Hodgen at King’s College London.

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.

In addition, 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.

These recommendations are made in order to address the fact that 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%.

The study, Towards universal participation in post-16 mathematics: lessons from high-performing countries, aims to identify the factors that drive participation in upper secondary mathematics (known as ‘post-16’ in England). It is a follow-up study to Is the UK an outlier?, a study of mathematics education in 24 countries, which was also led by Professor Hodgen and published by the Nuffield Foundation in 2010.

What drives increased participation?

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. Where mathematics is compulsory, it is never the only compulsory subject, suggesting that mathematics and the question of compulsion need to be considered within the wider curriculum and qualification framework both pre- and post-16.

Mathematics is compulsory in Germany and Hong Kong, leading to near universal participation in at least basic mathematics. However, New Zealand and Singapore have the highest levels of participation in advanced mathematics (equivalent to AS level) of the countries surveyed, without making it compulsory at this level.

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.

Can we learn from policy in other countries?

Education systems are embedded within the specific cultural and political context of each country, and the report highlights the risks of trying to transfer ideas from one country to another, particularly as the education system in England is unusually complex. However, some key features of successful policies could usefully be considered as part of the reform process in England.

Professor Jeremy Hodgen said:

“Our study shows the importance of a consensual approach to policy development and implementation. Higher education and employers will need to be involved in the development of a new qualification if they are to value it and to make it an entry requirement. Schools and colleges may need to be incentivised to offer the new qualification to students, as well as to ensure that existing advanced qualifications maintain their levels of participation. And it’s important not to underestimate the timescale necessary for change, particularly if we are to address the critical shortage of mathematics teachers.”

Josh Hillman, Director of Education at the Nuffield Foundation said:

“While we should be careful of the danger of ‘cherry-picking’ policies from other countries, the evidence from New Zealand shows that it is possible to increase participation by providing an alternative pathway, focused on statistics, that is widely recognised and valued by higher education and employers. We believe there is much to learn from New Zealand and other models overseas, and hope they will inform the development of an attractive and valued qualification in this country.”


Towards universal participation in post-16 mathematics: lessons from high-performing countries will be published online on 15 January at

Contact: Frances Bright, Communications Manager (Nuffield Foundation)
Tel: 020 7681 9586


1. The countries included in the study are England, Germany, Hong Kong, New Zealand, Scotland, Singapore and the USA. For the USA and Germany, only one state was analysed in detail. These are Massachusetts (USA) and Rhineland-Palatine (Germany).

2.‘Upper secondary’ refers to a period of education usually between two and four years in duration and intended for 16 to 18/19 year olds or for 15 to 17/18/19 year olds. It is generally referred to as ‘post-16’ in the UK.

3.This study is a follow-up to Is the UK an Outlier? An international comparison of upper secondary mathematics, Jeremy Hodgen and David Pepper, King’s College London; and Linda Sturman and Graham Ruddock, NFER (Nuffield Foundation 2010). See

4.The Nuffield Foundation is an endowed charitable trust that aims to improve social well-being in the widest sense. It funds research and innovation in education and social policy and also works to build capacity in education, science and social science research. The Nuffield Foundation has funded this project, but the views expressed are those of the authors and not necessarily those of the Foundation. More information is available at

5.King’s College London is one of the top 25 universities in the world (2010 QS international world rankings), The Sunday Times ‘University of the Year 2010/11’ and the fourth oldest in England. A research-led university based in the heart of London, King’s has nearly 23,000 students (of whom more than 8,600 are graduate students) from nearly 140 countries, and some 5,500 employees. More information is available at