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16-to-18 Mathematics Education

Volume 542: debated on Tuesday 27 March 2012

Last week, the Secretary of State for Education told the Association of School and College Leaders:

“Lest anyone think we have reached a point where we should slacken the pace of reform—let me reassure them—we have to accelerate.”

I completely agree, and one critical area for reform must be sixth-form provision, especially in maths where we have our largest issues.

Britain’s poor performance in maths is well documented. According to the OECD programme for international student assessment—the PISA study—the UK is ranked in 28th place for maths, although it is in 25th place for reading and 16th place for science. Too often, maths in Britain is seen as something that is nice to have, rather than as the vital tool that it ought to be in our modern society.

Perhaps our weakest area concerns our take-up of mathematics between the ages of 16 and 18. A study by the Nuffield Foundation found that Britain had the smallest proportion—below 20%—of students studying maths between the ages of 16 and 18, when compared with places such as Russia, Japan and Korea where virtually all students in that age group study maths, Canada where the figure is 80%, or France where it is almost 90%. Britain is a massive outlier in terms of maths education for that age group, and that runs contrary to our economic interests and to the interests of individual students who are taking A-levels or a vocational equivalent. A study by Professor Alison Wolf showed that maths A-level has the highest earnings premium of any subject, adding up to 10% extra to the earnings of a maths graduate.

I am following closely my hon. Friend’s important argument. As well as the earnings premiums for A-levels, Professor Wolf also identified the huge premiums obtained by maths and English GCSE. Will my hon. Friend go on to talk about the importance of GCSE maths retakes, as well as the A-level?

I will come to that point. It is important to give those who do not achieve maths at GCSE the option to retake that course in a different way between the ages of 16 and 18, so that they obtain a good qualification that will be useful for the rest of their lives. The 16-to-18 age group is particularly important, yet it is where this country has a gap. Those are the people who will go on to study maths, physics, information technology and engineering at university, yet we all know from speaking to businesses in our constituencies about the great skills gap in that area.

I completely agree with my hon. Friend; she makes an important point. Not only does this issue affect those young people who are effectively devoid of an appropriate education, but it is a serious problem for our competitiveness and business. Does my hon. Friend agree that it is imperative that schools and colleges engage more with businesses to understand that gap?

My hon. Friend makes a good point. It is a huge shame when businesses have to look overseas to recruit quantitative staff, engineers or people to carry out numerical analysis, when this country has so many students who could fulfil those roles if they received appropriate training and qualifications.

Even for those who do not go on to study maths and science at university, a good background in maths is vital. The next generation of primary school teachers, journalists and politicians must ensure that they know the basics of that subject, because if their maths is not up to scratch, we will have a damaged ecosystem. The next generation of children will not get a proper maths education at school, and that will lead to poor quality numerical analysis in our press and media and poor quality statistics in public life.

I am a former A-level maths student and my hon. Friend has my full support. I am determined to see more young people start up their own businesses, and strong mental arithmetic and mathematical skills are an essential component of that. I hope that my hon. Friend will add new businesses to her list.

I thank my hon. Friend for that contribution. Our massive problem with maths causes a lack of social mobility and problems with university access. Students who attend comprehensive schools are half as likely to study maths as their private school counterparts and one third as likely to study further maths, but they are equally likely to study history or English. The problems of social mobility in mathematics and science do not exist in arts subjects, and the Government should consider that when looking at how to improve social mobility and access to university. Many students do not have the choice to study further maths, because only 50% of comprehensive schools offer that option. Given that further maths is needed to study maths or physics at top universities, many people are therefore put out of contention for the opportunities that we would wish them to have.

I am pleased that the Government are taking action. In the autumn statement, the Chancellor recognised the existing problems with maths education for 16 to 18-year-olds and announced that new free maths schools would be set up across the country. I am pleased to be backing one of those schools, the proposed Sir Isaac Newton school in Norfolk, which will take those students who are most talented in maths and science and educate them not only in A-level maths and further maths, but beyond that to pre-U level. Academics will support that school and ensure that students learn the cutting-edge mathematic and scientific techniques that will help them get to the top universities.

My county of Norfolk has a particular problem with maths. Nationwide, 33% of students who obtain a grade of A* to B at GCSE maths go on to study the subject at A-level. In Norfolk, that figure is 25%—a massive gap. We want to improve that situation and get more people studying A-level maths.

The development of the new maths schools is positive, and I applaud the Government for that innovation, which has already been seen in many other countries. However, we need further reform in two key areas. First, we must overhaul the sixth-form funding regime, and secondly—one of my hon. Friends alluded to this—we need more varied maths qualifications post-16.

Unbelievably, for post-16-year-olds, the Young People’s Learning Agency currently awards more money per capita for students studying psychology and media studies than to those studying mathematics. It also awards more money to science subjects—there is a 12% funding premium for all those subjects on top of the amount that is given to the school for maths. The justification for that 12% funding premium is that those other subjects need additional equipment. However, as anyone who has been involved with schools will know, the greatest cost is in teaching resources, rather than equipment.

At the moment, our funding formula is based purely on the amount of equipment needed, rather than the cost of recruiting teachers. Maths is the most difficult subject for which to recruit teachers; there are more vacancies for high-school maths teachers than for any other subject, and schools often end up paying a premium. One school in my constituency advertised for a newly qualified maths teacher. It offered £44,000, but received just one application.

Another school has flown in maths teachers from Canada to fill the shortfall in available teachers. Fewer than half of secondary maths teachers in this country hold a maths degree. We have a massive problem with the recruitment of maths teachers, yet the funding formula means that maths is disadvantaged when compared with science subjects and courses such as media studies, psychology and film studies. Furthermore, because the funding system is weighted towards deprived students, there is an even greater funding differential for deprived students doing media studies, as opposed to deprived students doing maths.

We have a completely topsy-turvy system in which the underlying financial incentives are asking schools to get lower-income students to do subjects such as psychology and media studies, rather than subjects such as maths, which has the highest earnings premiums and is known to result in greater lifetime earnings. We need to turn that system upside down. We need a subject premium based on the value of mathematics. I have illustrated why mathematics is a particular case and why reform is needed urgently. We are seriously suffering in terms of international competitiveness because we are not delivering enough mathematics capability.

I suggest that through the YPLA mechanism that I mentioned, mathematics should be given a 30% uplift. That would deal with some of the teacher recruitment issues. I would like further mathematics to receive a 50% premium, so that we can increase the number of state schools that offer further maths from the currently very low 50% and so that all sixth forms eventually offer that important option. That will ensure that every child in this country has the chance to go on to study maths or physics at a top university or, indeed, subjects such as computer science—we also need more people in those areas. What I have suggested would give schools a strong incentive to offer those subjects, and I do not think that it would cost anything additional from the education budget.

At the moment, under the YPLA funding regime, we have a huge range of weightings. Some subjects are rated up to 1.7. Those are not A-level subjects but some of the vocational subjects. We are talking about rebalancing the incentives in the system, so that those subjects that will deliver most for our economy and for the students and in which teacher recruitment is hardest get a premium. At the moment, we have the opposite situation.

I would also like to see a greater number of maths options post-16. Current participation in A-level maths and further maths is heavily weighted towards those gaining an A* at GCSE: 73% of students who get an A* in maths take an A-level in it, but only 6% of those who get a B do so. The number is much lower than for other subjects. One quarter of those who get a B in English and one fifth of those who get a B in history go on to do those subjects at A-level. The reason is that we have a one-size-fits-all maths and further maths course, rather than having different options for young people who will go on to study different subjects.

My hon. Friend is making excellent points, but I want to probe the question of further education colleges. They, too, need to have appropriate provision in maths, because a large proportion—almost 50%—of all post-16s go to FE colleges, and we do not want them to miss out, either.

I thank my hon. Friend for his intervention. To clarify, the funding to which I am referring applies to both FE colleges and sixth forms. It is a single funding pot that applies to the whole lot. Indeed, recently the Government levelled the playing field between FE and sixth forms. The plans that I am talking about would apply to both FE colleges and sixth forms.

For 16-to-18 maths, we need a range of tiers in which some options are harder than others. The Sunday Times reported at the weekend that Sir John Holman is drawing up plans for what those options would look like. When we are drawing up the options, we need to consider the failings of previous attempts to create different maths options for those aged 16 to 18. I am referring specifically to the use of maths A-level. It purported to provide real-world experience, but leading Fields medallist and Cambridge maths professor Tim Gowers said:

“it is blindingly obvious from the sample papers that it is not testing different skills…and is deeply boring, and not even all that relevant to the people who are actually taking the exam”.

The problem with use of maths was that, first, it was laid out as equivalent to A-level maths, which it simply was not. Secondly, it attempted to be relevant, but not in a way that could be applied to the real world.

What is needed is a decent set of qualifications, all of which are rigorous. They need to be on a scale, so that people know exactly where they fit in the qualifications framework. I suggest that that would involve, first, an option whereby students learn the basics of maths. Secondly, they learn the intermediate techniques that support arts and social science subjects. Finally, they get the advanced maths that can lead right through to a technical career.

One of the important elements is that further maths needs to be more advanced than A-level maths. Under the previous Government, there was an effort to make those two subjects equivalent on the ground that all A-levels had to be equal. That is clearly nonsense. We clearly need an option for more advanced students to study, so that those going on to do sciences and social sciences have a mainstream A-level option. Let me suggest an outline for the framework. A-level maths should be a strong preparation for university. We should have a slimline version for those who are majoring in social sciences. Maths should be a core part of the apprenticeship programme. I have recently met apprentices in my constituency who have told me how useful they find studying top-up maths to be in completing their courses and gaining skills on the job. There should also be a new course that provides a fresh approach to the basics for those who have failed to get a GCSE grade C in maths.

All that needs to happen fast; there is a case for dealing with it urgently. We need a sixth-form funding formula that puts a subject premium on maths, rather than the subject discount that we have at present, which has caused a very low take-up of A-level maths. We also need to ensure that there is a full offer for 16 to 18-year-olds. That would have a dramatic effect on take-up, and I urge the Government to act on it as soon as possible.

First, I congratulate my hon. Friend the Member for South West Norfolk (Elizabeth Truss) on raising this subject, which is of great importance to us. She is right to hold the Government’s feet to the fire. Indeed, she has form on that in this and other areas of education. I congratulate her on a very well argued and cogent case.

Secondly, I apologise because I am not the Minister of State, my hon. Friend the Member for Bognor Regis and Littlehampton (Mr Gibb), who is the Minister responsible for schools. That is not something that I find myself doing often, but my hon. Friend had to visit a school elsewhere in the country today; otherwise he would be responding to the debate.

Thirdly, I should declare an interest, as my son has just passed his A-level in mathematics rather well, outpacing my own meagre grade B O-level from all those years ago when we had O-levels.

All of us would agree that mastery of mathematics empowers people. In a world that requires higher-level mathematical skills than ever before, we all want young people to have the chance to develop the mathematical fluency and confidence that they need for study, for work and for their personal lives. That fluency can be achieved only by using mathematics regularly over a sustained period—getting used to it. The reality is that far too many pupils do not achieve the required standard in maths by the time that they leave school, as my hon. Friend pointed out.

I agree with my hon. Friend the Member for South West Norfolk that there is a pressing need to improve social mobility and that an education system that demands high quality and rigour will help us to achieve that. We know that, too often, pupils from low-income backgrounds are steered away from rigorous academic subjects, such as mathematics, in a way that hinders their later success in higher education and employment. England, along with Wales and Northern Ireland, has an exceptionally low rate of participation in mathematics beyond the age of 16, as she said. Fewer than 20% of pupils go on to study mathematics in any form. As my hon. Friend mentioned, the Nuffield Foundation has shown that to be the lowest level of participation of any of the 24 developed countries included in its survey. Worse still, only 15% of pupils go on to study mathematics at an advanced level. In addition, about half of young people start post 16-education having failed to achieve a good grade in mathematics.

As my hon. Friend made clear, there is a great deal of evidence that school leavers do not have the mathematical skills that they need to function properly in the workplace and for further study. Lack of good numeracy competence is a frequent complaint from employers; I have heard it in my constituency time and again. There is emerging evidence from universities that students studying non-mathematical subjects, including the sciences and social sciences, often lack the basic numeracy and statistical skills needed to succeed in their undergraduate courses. Skills that could have been developed during sixth-form studies have not been. In some cases, universities have found it necessary to provide additional maths courses to address that knowledge gap and to bring students up to speed. That cannot be right. We must have a system in which all our school leavers have the necessary skills before they start university courses or move into employment.

The low rate of participation in maths is all the more worrying given what we know about the impact of maths achievement on a young person’s life chances. The Centre for Economic Performance found that those who took mathematics to A-level ended up earning 10% more on average than those with similar ability and similar backgrounds who did not.

In its “Mathematical Needs” report, the Advisory Committee on Mathematics Education noted:

“Not only are university courses in many disciplines increasingly quantitative in content, but there is also a steady shift in the employment market away from manual and low skills jobs and toward those requiring higher levels of management expertise and problem solving-skills, many of which are mathematical in nature.”

That is why the Secretary of State last year set out his ambition that, within 10 years, the vast majority of young people should be studying maths from 16 to 19, and I am grateful to my hon. Friend for acknowledging some of the progress the Department is making.

Of course, we must focus on ensuring all young people have a basic level of knowledge and understanding in mathematics. However, even when students gain a good grade—A* to C—at GCSE, there is no guarantee that they have the numeracy skills needed in the workplace and particularly ones that are portable from one workplace to the next. The CBI report “Working on the Three R’s: Employers’ Priorities for Functional Skills in Maths and English” showed that 32% of employers would like to see school leavers’ ability to do mental arithmetic improve.

For many entering further education, apprenticeships or employment in craft and technical areas, the break in their maths education from 16 to 18 is very damaging. The same is true for nurses and primary school teachers, who must go on to use and develop mathematics. It is essential that the mathematical skills developed to age 16 continue to be practised throughout sixth-form study to maintain fluency.

In addition, 25% to 30% of students reach university without the maths skills our universities need—I apologise if my speech seems overly littered with statistics, but it is about maths, so I suppose I can get away with it. Many students go to university to study a subject in which studying maths at a level above GCSE would be advantageous. That includes those who study economics and other social sciences, as well as sciences such as biology and health sciences. However, even students taking fine art may benefit from further mathematical knowledge in their future employment. It is important that such students not only maintain fluency in pure mathematical skills such as algebra, but complement those skills by studying statistics, modelling and the application of mathematics to complex systems.

It is encouraging that the number of pupils choosing to study A-level mathematics and further mathematics is increasing. In 2011, A-level maths had more than 75,000 entries, compared with just under 50,000 in 2006. The numbers entering further mathematics increased from about 6,500 to nearly 11,500 over the same period. However, many more pupils do not continue with their study of mathematics between 16 and 19. Getting more young people to study maths must be our first priority. That means ensuring that young people who have not achieved a grade C in GCSE maths are supported to achieve a good maths qualification post-16. We have been consulting on new study programmes for 16-to-19 year olds, which will include mathematics courses for all such students.

Our second priority is to ensure that all young people can take challenging, rigorous maths qualifications that give them the skills to progress. We are working with mathematics subject experts and universities to make that a reality, because it is clear that their support and engagement are essential if the take-up of advanced mathematics is to increase.

The ACME is calling for evidence from those with an interest in mathematics so that it can advise on appropriate post-16 pathways for pupils who have achieved grade A* to C at GCSE, but who do not currently continue to study mathematics. The ACME is expected to report its findings and propose new pathways at its conference in July. We await its report with interest, and I am sure my hon. Friend will want to see its findings, too.

If all young people are to study mathematics to 18, it is essential that they benefit from excellent mathematics teaching. My hon. Friend is right about the difficulties in recruiting mathematics teachers in some areas. I am glad to say, however, that we are seeing increased recruitment of mathematics trainees. Recruitment targets were met for the first time in 2010-11 and 2011-12, while the quality of trainees, as measured by degree class, increased in both those years.

We know we need to do a lot more. That is why we have launched bursaries of up to £20,000 to attract the best graduates to train as mathematics teachers. By the end of this Parliament, we will at least double the size of Teach First, which has an excellent record in attracting outstanding mathematics graduates. We are also improving the quality of teaching through support for professional development.

We have expanded the further mathematics support programme delivered by Mathematics in Education and Industry. The programme will continue to provide universal support to schools and colleges that want to provide further mathematics. It will focus on those centres that are not currently offering that A-level option, ensuring that more students from disadvantaged backgrounds have the opportunity to study it. I think my hon. Friend will very much appreciate that.

Expanding the programme will allow it to do more to inspire key stage 4 pupils to study further mathematics at A-level, and it will help to ensure that they are better prepared to do so. The programme will focus on equipping teachers with the skills needed to stretch and enrich their pupils’ mathematical education during key stage 4. It will provide more than 2,000 teacher days of development opportunities, enabling it to reach more teachers than previously.

That aspect of the programme will put in place a coherent route for mathematics teachers to progress from teaching GCSE maths, to teaching A-level maths and then to teaching further maths. It will also enable teachers to prepare students for the sixth term examination paper or advanced extension award examinations, which will improve their prospects of getting on to the most competitive maths and science courses at top universities.

We are investing £6 million over three years to fund the activities of the National Centre for Excellence in the Teaching of Mathematics. The centre will co-ordinate and quality-assure the training of mathematics teachers across all phases of education, including those delivering new courses developed to achieve the aim of mathematics for all to age 18.

My hon. Friend mentioned free schools. As she said, the Chancellor announced funding in the autumn statement for specialist maths free schools for 16 to 18 year olds, which is a particularly exciting development. She has been generous in her support of the free schools programme, and I am encouraged to hear about her proposals for a free school in Norfolk with a strong focus on science and mathematics education.

I agree with my hon. Friend that there is a need to ensure that pupils, parents and schools are aware of the demand for people with high-level mathematical skills and that our funding systems do not encourage schools and pupils to go for the easier options. Currently, schools and colleges receive the same basic level of funding for all students who pass an A-level, regardless of the grade they achieve or the subject taken. As my hon. Friend noted, however, funding for post-16 courses is subject to programme weighting, which is intended to reflect the relative cost of teaching particular subjects. Subjects that are wholly classroom-based, such as mathematics, receive a lower weighting than others, such as science subjects, which have a greater lab-based element, and she gave other examples.

I note with interest my hon. Friend’s proposal that we should establish a subject premium for mathematics and further mathematics. We consulted recently on changes to 16-to-19 funding, and we are currently considering the responses to the consultation. My hon. Friend may hear more about that later.

My hon. Friend will recognise that the funding system is not always the best means of incentivising take-up of one subject above another. We are working with mathematics subject experts to consider the measures that will be necessary to realise our ambition that all young people should continue to study mathematics up to 18.

The A-level system must meet the needs of universities and employers. For far too long, the design of A-levels has been in the hands of officials and bureaucrats, with their range of committees and advisory panels. That has led to a focus on exam structure, at the expense of content and need, and at the expense of young people enjoying and being inspired by maths and wanting to carry it forward. Addressing that issue is part or the challenge.

It is clear that existing A-level maths courses may not develop the full range of mathematical skills required to meet the needs of all students and the wide range of further study and career options they will pursue. As we set out in the White Paper “The Importance of Teaching”, we are working with Ofqual, the awarding organisations and higher education institutions to ensure that universities and learning bodies can be fully involved in the development of A-levels.

The evidence from around the world clearly shows that high-performing nations ensure that children receive a first-class maths education. Head teachers, parents and pupils need to hear a clear demand for mathematics and mathematical qualifications from universities and employers, and we need to support expert mathematicians in their endeavour to ensure that the right range of demanding and rigorous qualifications is available to meet the needs of pupils and the demands of universities and employers.

My hon. Friend has long been one of the most vocal champions of excellence in mathematics education, and my ministerial colleagues are looking forward to working with her in the months ahead. Let me once again express my gratitude to her for raising this important subject with her customary energy and enthusiasm.

Sitting suspended.