Skip to main content

Mathematical Sciences: Contribution to Society

Volume 722: debated on Tuesday 15 November 2022

I am going to call Sir Stephen Timms to move the motion. I will then call the Minister to respond. There will not be an opportunity for the Member in charge to wind up because that is the convention in a 30-minute debate.

I beg to move,

That this House has considered the contribution of the mathematical sciences to society.

I am delighted to serve under your chairmanship, Mr Paisley, and am most grateful to Mr Speaker for selecting this subject for debate to help to mark Maths Week this week. I am pleased to see the distinguished Schools Minister in his place, and I welcome and applaud his appointment—for the third time, if I remember correctly, which surely makes him the longest-serving Schools Minister ever, and deservedly so. I am also pleased that the hon. Member for North Devon (Selaine Saxby), who I think taught maths before being elected, is in her place.

The aims of Maths Week are to raise the profile of mathematics throughout England, change the conversation about maths in the population at large to be more positive, enable children and adults from all backgrounds to access and enjoy mathematical experiences, supplement teachers and support them to plan low-cost and high-impact maths activities at their schools during the week, encourage higher education centres to invite schoolchildren to visit maths events, raise aspiration, encourage greater take-up of maths at A-level and university, and make maths accessible to and enjoyable for people who think it an elitist subject just for “clever” people.

I want to do four things in my speech: underline the value of maths in enabling us to solve the big challenges our society faces and to build our economy; press the Minister to deliver the full commitment on funding for research in the mathematical sciences pledged by the then Prime Minister, the right hon. Member for Uxbridge and South Ruislip (Boris Johnson), in January 2020; argue for ensuring that degree-level maths does not become the preserve of the well-off; and press the case for much higher take-up of maths post 16, fulfilling the promise of core maths, which we see in the higher take- up of maths in the most successful economies around the world.

I have a maths degree, so I am biased, and I know that maths can often seem a bit impenetrable to those not familiar with it, and that being “no good” at maths can almost be a boast sometimes, but maths enables the most exciting and urgent technological developments in energy generation, artificial intelligence, driverless cars, quantum computing and tackling climate change. Professor Alison Etheridge, chair of the Council for the Mathematical Sciences, points out that the maths used to design dust filters in vacuum cleaners is also used to develop filters to remove arsenic from groundwater in the Ganges-Brahmaputra delta, which benefits hundreds of thousands of people.

I appreciate the right hon. Gentleman bringing the matter forward and I concur with his comments.

At this time, many of the United Kingdom’s priorities are focused on energy supply and climate change, as well as targets for the future, and the University of Lancaster has concluded that mathematics has proven to be a basic but crucial component of building resilience in terms of flooding and understanding data fluctuations with respect to our energy supplies. With that in mind, does the right hon. Gentleman agree that further funding for mathematics must be centred on helping our students of STEM—science, technology, engineering and maths—including 53% of further education students in Northern Ireland, although I acknowledge the Minister has no responsibility for them, because they are paving the way for success with respect to environmental change in the UK?

I am grateful to the hon. Gentleman for that intervention, and I do agree with him: maths is a vital enabler of economic growth, and it underpins many technological advancements that contribute so much to UK economic growth. We need to value that.

Deloitte estimates that the mathematical sciences add more than £200 billion a year to the UK economy, that there is a significant salary premium for advanced maths skills, which is calculated to be £8,000 a year, and that the mathematical sciences are of fundamental importance to tackling all our most pressing policy challenges. The hon. Gentleman has just given a good example of that.

The maths that is most familiar to us is about certainty—a x b = c—but maths also provides the tools to quantify uncertainty, underpinning important decisions in medicine and finance, and on the environment. Furthermore, understanding uncertainty is crucial to making decisions on how to deploy limited resources, from allocating hospital beds to dividing up the bandwidth available for telecommunications.

The briefing for the debate provided by the Protect Pure Maths campaign, which I congratulate on its efforts, gives a couple of examples of the use of a mathematical theory called extreme value theory. Unfortunately, my maths course did not include extreme value theory, which has been used in the successful work of Professor Chris Dent and others on energy generation and storage, which has had a big impact on improving energy supply, as well as in the work referred to by the hon. Member for Strangford (Jim Shannon), carried out at the University of Lancaster, to build resilience against extreme flood events.

Extreme value theory was not invented for those reasons, but as invariably happens with mathematical theories developed initially because they are beautiful and fascinating, that theory has turned out to have immensely important practical applications. Algebraic geometry is an important set of ideas in pure maths, some of which were in my course, and pure mathematician turned economist Elizabeth Baldwin has applied the theory of algebraic geometry to microeconomics to design an effective auction system for carbon permits. Her work has been used by the Bank of England, and more and more maths is being used in the social sciences and humanities.

Protect Pure Maths is calling for the Government to demonstrate their understanding of the transformative power of maths by launching a strategy for maths to strengthen UK leadership and to equip us to compete in a global economy that is increasingly dominated by big data, complex systems and artificial intelligence. The Institute and Faculty of Actuaries also provided a briefing for the debate, and it points out that mathematics is fundamental to the work of actuaries in insurance and pensions, and in health and care.

In January 2020, there was a warm welcome for the commitment by the then Prime Minister to invest £300 million of additional funding into research in the mathematical sciences. Of that, £124 million has been spent on projects of national importance, including on institutes, small and large research grants, fellowships, doctoral studentships and post-doctoral awards.

Some of that work is concerned with solving current challenges of the kind that I have referred to, but some rightly is to pursue intellectual inquiry of the kind that characterises pure maths, the output of which will almost certainly yield real-world applications in future, although they are not apparent at the moment. More than half the additional investment—£176 million—has not yet been allocated.

The chief executive of UK Research and Innovation has stated:

“We did not receive £300 million specifically labelled ‘mathematical sciences’ despite the announcement.”

The announcement that she referred to was made by the then Prime Minister. We are surely not in the position where a crystal-clear announcement, attracting lots of attention, made by a Conservative Prime Minister, turned out to be untrue. A recent written answer on this from the noble Lord Callanan in the other place suggested that there was doubt about whether the funding would be forthcoming. I hope the Minister will clarify that, and confirm that the funding already announced for hugely valuable mathematical science research will be delivered.

Without that additional £176 million, doctoral studentships, fellowships and research programmes will remain unfunded. University maths departments need clarity about the sustainability of maths funding, in order to give the go-ahead for research and innovation programmes that will last years into the future—programmes that will underpin future technological breakthroughs of great economic importance.

Marcus du Sautoy, Simonyi Professor for the Public Understanding of Science at the University of Oxford, has made the point that

“maths underpins all science and technology”.

So it makes sense, he says,

“to allocate funds to mathematical research, even at a time of tight finances…It would be incredibly unwise to now abandon that pledge.”

We have seen welcome progress with advanced maths education since I was doing the Minister’s job more than 20 years ago. The trend then of falling numbers of A-level applicants and undergraduates was halted and, I think, reversed. Changes introduced by another maths graduate, Charles Clarke, when he was Secretary of State, started the improving trend.

The Protect Pure Maths campaign was initially established in response to some UK universities cutting back their maths provision. Governments might be reluctant to intervene in the decisions of individual universities, but the Government should make clear the strategic importance of maths, and incentivise and support universities to give it priority, particularly beyond Russell Group universities, because maths is becoming an almost exclusively high-tariff degree. There is big growth at many high-tariff university maths courses, with one leading maths department in England increasing its intake from 300 to 600 undergraduates a year, but the courses at low-tariff universities, many of them highly regarded, are shrinking. One of them has gone from 150 to 35 undergraduates a year.

Students from lower-income backgrounds are much less likely to go to university outside their local area. If maths courses become too small to be viable, we will see the emergence of maths deserts, which would reduce access to one of the best degrees in terms of future earnings. We need strong and sustainable maths departments at universities in all parts of the country, and in universities of all kinds.

The other key issue for this Maths Week debate is the low take-up of maths in the UK post GCSE. More 16 to 18-year-olds should be encouraged to take up core maths, which is an invention of this Government that I imagine the Minister had a good deal to do with at the time. The background is that, in 2010, the Nuffield Foundation published a report titled “Is the UK an outlier? An international comparison of upper secondary mathematics education”. It turned out that the answer to that question was yes. Twenty-four countries were surveyed, and the UK had the lowest level of participation in upper secondary maths. Of the 24, England, Wales and Northern Ireland were the only countries with participation of less than 20%.

In June 2011, the then Secretary of State, the right hon. Member for Surrey Heath (Michael Gove), looked forward to a situation in which

“within a decade the vast majority of pupils are studying mathematics right through to the age of 18”.

In 2014, he said that by 2020—two years ago—the vast majority of students would be studying maths in some form after the age of 16. He meant not just A-level maths but the new qualification of level 3 core maths, which teaches the statistical and analytical skills essential to every profession, from law to medicine, and from journalism to manufacturing.

That increase has not happened. Progress in the last eight years has been lamentable—one might even say negligible. The UK remains an outlier. In Germany, Japan and the USA, well over 50% of 17-year-olds are studying maths in some form. In Finland and Ireland, the figure is over 80%. In the UK, it is still below 20%.

The right hon. Gentleman is giving an exceptional speech. I am delighted to speak out in Maths Week for the subject that I studied and love. Does he agree that one of the challenges for rural schools particularly is that, because of the restrictions of their rural settings, they are unable to have specialist science, technology, engineering and maths sixth forms? I hope the new ministerial team will apply more maths in general to their funding decisions. In rural schools, the funding simply does not add up, and in large education authorities, such as Devon, we do look not at the variance in achievement but only at the average.

I am grateful to the hon. Lady for her well-informed and valid comment. The big problem is the shortage of teachers. In rural schools and elsewhere, getting hold of teachers with specialist maths abilities who are able to teach the subject post 17 is a big challenge. I very much agree with her. The Government should invest more in recruiting, developing and retaining maths teachers, because the lack of teachers is the key problem with the take-up of core maths. We need subject-specific continuing professional development for all maths teachers, and we need to upskill maths teachers who do not have a maths degree.

Maths is hugely valuable in enabling us to solve the big challenges that our society faces, and in building the economy. The Government must deliver the full commitment of funding into research in the mathematical sciences pledged by the then Prime Minister in January 2020. Degree-level mathematics must not become the preserve of the well-off. As the Government repeatedly said some years ago, we also need much higher take-up of maths post 16, as we see in the most successful economies around the world. The Government must fulfil their earlier promises. I very much look forward to the Minister’s response.

It is a pleasure to serve under your chairmanship, Mr Paisley—for the first time, I think. I congratulate the right hon. Member for East Ham (Sir Stephen Timms) on securing this debate, which concerns a subject that I, he and my hon. Friends regard as very important. I thank him for his generous comments about my reappointment. He, too, was a Schools Minister, and I know how deeply he cares about the education of the next generation, particularly children from disadvantaged backgrounds.

Mathematical sciences are fundamental to our success as a nation. A deep mathematical and scientific knowledge and understanding is a necessary element of everyday life, but is increasingly required in more and more occupations and higher education courses—not just in the sciences but the social sciences and humanities. The Government are committed to ensuring that all pupils have a solid grounding in maths and science, and to encouraging greater participation as they progress through their school careers so we can grow the numbers of engineers, research scientists and technology experts of the future.

Improving mathematical knowledge at all levels is likely to deliver significant returns in terms of labour market skills, individual success—as the right hon. Member for East Ham said in his speech—increased productivity and longer-term economic benefit. It will allow us to lead the way in scientific innovation. Keeping the UK’s place at the leading edge of science and technology will be essential to our prosperity and competitiveness in the digital age.

The Government recognise that demand for STEM alumni at all levels is growing. That is why we must ensure that everyone, regardless of their background, has the opportunity to pursue STEM careers. Improving the quality of maths and science teaching, and increasing the number of young people who study those subjects beyond GCSE, is key to addressing the STEM shortage, and to supporting the UK economy and its growth. The Department is therefore encouraging more students into STEM subjects across all key stages, from primary and secondary school to higher and further education.

The Government have committed to substantial spending on maths, digital and technical education to increase the take-up and better teaching of STEM subjects in schools and colleges. Instilling a deep understanding and love of mathematics—shared by my hon. Friend the Member for North Devon (Selaine Saxby) and the hon. Member for Strangford (Jim Shannon)—from an early age is vital. That is why the Department introduced teaching for mastery, which is a pedagogy based on high performing jurisdictions, including Shanghai and Singapore, that emphasises whole-class teaching and builds knowledge systematically—step by step and in small increments. That helps students to gain fluency and a deep understanding of mathematical concepts. I saw that at first hand when I visited Shanghai schools a few years ago.

The Department has spent over £100 million on the teaching for mastery programme, delivered by maths hubs—40 school-led centres of excellence in maths teaching that are responsible for a range of activities to improve the teaching of maths in all schools, from primary school to the age of 18. The hubs are supported by the National Centre for Excellence in the Teaching of Mathematics, which is funded by the Department for Education. I pay tribute to Debbie Morgan and Charlie Stripp of the NCETM for their brilliant work over many years in improving the teaching of arithmetic and maths in our primary schools, and more recently in our secondary schools.

Results from the trends in international mathematics and science study 2019 showed that our year 5 and year 9 pupils continued to perform above the international averages in maths and science. That included a significant improvement in maths for our year 5 pupils, taking us to our highest ever score. This year also saw the roll-out of the first regular multiplication tables check on year 4 pupils. Knowing one’s tables by heart, up to 12 times 12, is essential for more complex maths involving the application of fractions and algebra, where instant retrieval of numbers is so important. I will resist asking any of my hon. Friends and hon. Members their times table questions now—I have had that done to me too many times.

Post 16, ensuring more students are studying maths beyond GCSE is a fundamental aim. Maths continues to be the most popular A-level subject, with 87,000 students taking it in 2022, up from 69,800 in 2010. Further maths entries at A-level have also risen, from 10,800 in 2010 to over 14,000 in 2022. But there is more to do, particularly to ensure that students from under-represented groups, as referred to by the right hon. Member for East Ham, are participating in the subject. That is why the Department continues to fund the advanced maths support programme, which provides high-quality professional development and online resources for teachers to support schools and colleges to expand their post-16 maths curriculum. Over 3,000 state-funded schools have participated in the programme since its launch in 2018.

As the right hon. Gentleman mentioned, the Government would like to see more students studying core maths qualifications designed for sixth-formers who are not studying maths at A-level, but who wish to continue to study maths. That will prepare those students for the mathematical demands of university study and employment. More than 12,000 students took such qualifications last year, but there is more to do to raise awareness and encourage their take-up.

It was the Government’s ambition that the great majority of students in the 16 to 18 range would study maths in some form—mostly core maths. Does that remain the Government’s ambition, and how long does the Minister think it is likely to take to achieve that ambition?

The right hon. Gentleman is absolutely right to say that is the Government’s aim. I think we will have more to say on this issue in the coming months, because it is essential in an advanced economy such as Britain that more young people are studying maths—even those like me, who did well at maths O-level but did not go on to study it at sixth form because I was studying history, economics and English. I now wish that I had taken at least some post-16 qualification in maths. More young people would benefit from that, so it continues to be the Government’s objective.

To help tackle the challenges, the advanced maths support programme is rolling out a national team of specialist core maths advisors to support participation in core maths and to develop expertise and best practice. Their role will be to support schools and colleges to establish core maths provision, and to provide continuing professional development and dedicated support. The advanced maths support programme also provides free maths resources for teachers and students. The Department is supporting schools and colleges with additional funding through the advanced maths premium, which is a £600 incentive payment per student and per qualification to boost growth in level 3 qualifications in schools.

In science, the Department funds a range of programmes, including the Stimulating Physics Network, which offers tailored support to schools to increase the rates of progression to physics A-level and the uptake of physics among girls. As of October 2022, 299 continuing professional development days have been delivered. The Isaac Physics programme is designed to increase the number of students, particularly from typically under-represented backgrounds, studying physics in higher education, and it serves about 80% of schools. In 2022, there were a total of 35,800 A-level physics entries—an increase from 27,800 in 2010.

The right hon. Gentleman and I can agree that we need all students to be competent and digitally literate to succeed in the digital age. The computing curriculum introduced in September 2014 provides pupils with the broad knowledge they need to specialise later—for example, in computer programming and AI—from key stage 1 to key stage 4. It also facilitates further study at A-level, and on to degree level and other post-16 options. England was one of the first G20 countries to place coding in the primary curriculum, introducing pupils to writing computer programmes and how computer networks operate. Computer science was one of the fastest growing GCSE subjects between 2013 and 2019, and we are confident that our spending on improving computing education will inspire more pupils to take the subject at GCSE.

The right hon. Gentleman mentioned the funding of mathematical sciences research. Research in mathematical sciences is key for the advancement of all areas of science and technology, and it is a vital area of science in itself. An additional £124 million has been committed to mathematical sciences, on top of between £25 million and £30 million a year for grants, fellowships and studentships, which UKRI’s Engineering and Physical Sciences Research Council has always invested in this area. Absorbing any additional uplift to mathematical sciences into core budgets would require significant reductions in other engineering and physical sciences disciplines. That would reduce critical capabilities in disciplines such as engineering and information communications technology, which, alongside mathematical sciences, are key foundations of the UK’s ambitions in areas such as net zero and AI.

This commitment of £300 million—£60 million a year over five years—was given in a blaze of publicity by the then Prime Minister in January 2020. Surely the Minister is not telling us that the right hon. Member for Uxbridge and South Ruislip said something that was not true.

What I am saying is that this funding is not ringfenced. Rather than ringfenced budgets addressing single priorities, UKRI aims to create a portfolio of investments where each pound contributes to delivering multiple priorities, providing much better value for money and leveraging the benefits of UKRI as an integrated research and innovation funder. In this context, UKRI is looking for opportunities to support foundational mathematical research across its entire portfolio.

The right hon. Gentleman also referred to the issue of teachers in response to an intervention by my hon. Friend the Member for North Devon. The Government are ensuring that all schools have access to highly skilled teachers. Teaching remains an attractive and fulfilling profession and the number of teachers remains high, with more than 465,000 working in state-funded schools across the country—24,000 more than in 2010. The Department has made substantial incentives available to attract the brightest individuals to teach high-demand subjects, including a £27,000 tax-free bursary in chemistry, computing, maths and physics, and prestigious scholarships in those subjects worth £29,000. There is also substantial continuous professional development for new and existing teaching staff through the early career framework and a new suite of national professional qualifications.

In conclusion, I hope that this Chamber will understand how committed the Government are to science and to ensuring that all pupils have the chance to succeed.

I thank the Minister for giving way one final time. I just want to go back to the question of the £300 million. Does he accept that the then Prime Minister, the right hon. Member for Uxbridge and South Ruislip, absolutely clearly said that the £300 million was for research in mathematical sciences? It was ringfenced in his announcement. Surely that commitment should be honoured?

The right hon. Gentleman has made his point, and I have made the point that UKRI has an un-ringfenced approach in how it allocates its investments. It is important to allow that institution discretion to determine how it allocates its funding. Of course, fundamental foundational research in mathematical sciences goes right across all the disciplines that UKRI oversees.

The Department continues to deliver substantial spending on maths, digital and technical education, and to increase the take-up and better teaching of STEM subjects in schools. We are clear that the acquisition of knowledge is the basic building block of education to which all pupils should have fair access. A knowledge-based curriculum can stimulate critical thinking—a skill that can be acquired only through the teaching of solid subject content. The Government are steadfast in maintaining our position as a world leader in scientific research, and are committed to ensuring a pipeline of knowledge and technical understanding to provide the UK with a highly expert workforce for the future.

Thank you, Minister. My son is a mathematics student, so I found that particularly interesting. For the record, 12 times 12 is 144.

Question put and agreed to.


That this House has considered the contribution of the mathematical sciences to society.

Sitting suspended.