2012 marked the centenary of the birth of one of this country’s great heroes - Alan Turing. Through his groundbreaking work in computing and computer science, cryptography, artificial intelligence and, perhaps most importantly of all, the mathematical theory of computability - Alan Turing shaped the world we live in today and continues to shape our unfurling future.
Less than a century on, we are all, more than we even realise, Turing’s heirs.
Language and logic
We live in a world governed and ruled by maths. Algorithms are woven into the architecture of our lives, directing the cars through our streets and the planes through our skies; bringing shopping to the door and the world to our desks.
Whatever subject and job you do, it is there.
Just over 50 years ago, the scientist and novelist CP Snow claimed that science and the humanities had become ‘two cultures’ - divided, alienated and mutually suspicious. A famous squabble with literary critic FR Leavis, who contemptuously described Snow as ‘intellectually as undistinguished as it is possible to be’, only seemed to confirm his theory.
What I think is so interesting, half a century on, the Cold War between science and art is over. Last summer’s Olympics opening ceremony seamlessly combined Isambard Kingdom Brunel and William Shakespeare, Tim Berners-Lee and Mary Poppins.
Our greatest living artists like David Hockney and Alison Lapper have found new inspiration and impetus by creating work on the iPhone and iPad and through digital imaging. Historians like Niall Ferguson analyse sweeping historical trends and the march of human progress through statistics, technological innovation and the growth of so-called ‘killer apps’.
In other words, understanding the language and logic and structure of mathematics is no longer a narrow discipline practiced by removed specialists. It is universal.
That is why we are so determined to make sure that the next generation is fluent in the language of maths, the universal language of the modern world. The increasing earnings premium for maths at A Level, degree level and beyond shows its draw.
We are changing our curriculum to reflect the demands of the 21st century.
Students will be starting languages at age 7 - because language proficiency is increasingly important in a more open world.
Children will also be learning programming at primary school so they can ‘speak computer’ as well as using it.
But the growing importance of maths shows we need to do more to make sure children speak that language too. That is why we are redesigning the primary maths curriculum to focus on mastery and fluency of the vital building block of mathematics, which is arithmetic.
Last year, the Secretary of State set out his ambition that within a decade the vast majority of young people will be studying maths right through to 18.
No longer can these skills be considered a minority pursuit - maths has gone mass market.
We are not there yet
We know that is the aspiration, unfortunately we are not there yet.
According to the Nuffield Foundation, we have the smallest proportion of 16- to 18-year-olds studying maths of any of the 24 countries examined: far less than nations like France, the US, Ireland, New Zealand, Russia, Australia, Estonia, Spain, Germany or China. 85 per cent of Japanese students are studying the equivalent of A Level maths - in England it’s just 12 per cent of young people.
New data from TIMSS 2011 shows that England’s maths performance has not improved since 2007 either at age 10 or at age 14. Put together with PISA 2009 data, it does show a worrying lack of progress - while the East Asian nations are extending their lead.
When we delve into the detail of these studies it’s even more worrying. The gap at age 10 between our strongest and weakest maths performers is one of the widest in TIMSS - with fewer of our pupils overall reaching the very highest levels. A growing number of our students don’t even reach the lowest benchmark on that scale - 12 per cent at age 14, three times as many pupils falling behind in this country as in the US.
OECD maths results in PISA 2009 also showed that the gap in achievement between English boys and girls was one of the widest in the world - with boys 20 points ahead, equivalent to around half a year of formal schooling.
Girls are less likely than boys to study maths beyond 16 and less confident about their ability overall. Independent research has found that ‘girls rate their own ability (in maths) as lower than that of boys as early as the first year of primary school, even when their actual performance does not differ from that of boys’.
Lower income pupils are also falling behind, particularly in maths. At 16, the attainment gap between children on free school meals and the rest of the population is wider in maths than in English, history, or the sciences. Only 46 per cent of pupils on free school meals achieve GCSE maths at A* to C, compared with 70 per cent of the rest of the population.
At A Level, comprehensive students are half as likely to study maths as their colleagues at independent or grammar school - whereas they are equally likely to study history or English.
Why is this?
When considering this problem it’s quite hard to pin down exactly why there are greater issues in maths than other subjects. There are deep seated cultural issues with maths in this country which need to be challenged - in our culture where, inexplicably, it is completely acceptable for adults and children to shrug their shoulders and say, laughing, ‘I’m rubbish at maths’. It would be unthinkable for anyone to say, almost proudly, ‘I can’t read’, or ‘I’ve never quite got to grips with writing’.
But as well as a cultural block - there are also problems with the level of attainment and the architecture of our system which have not helped maths to flourish.
On Monday, Nuffield followed up their blockbuster Outliers study with another major report with King’s College London, examining universal participation in post-16 maths.
It found that one of the most important factors in determining whether or not young people continue with maths after 16 is prior attainment. In other words, if we get maths teaching right from the start of primary right through to GCSE, more young people will finish GCSE feeling confident and comfortable in maths - and participation after 16 will naturally increase.
Strengthening the primary curriculum
A new primary curriculum will focus on mastering essential arithmetic at an early stage. This doesn’t mean a pick and mix approach, but a deeper, richer, stronger curriculum with a new emphasis on problem-solving, practice and fluency, ensuring that children are properly prepared for secondary school and beyond.
To ensure that children build up their mathematical fluency and become comfortable with basic calculations, we’re removing calculators from primary tests from 2014. Rather than requiring children to know the 10 times table by the end of year 6, pupils will learn all of their multiplication (including the 12 times tables) earlier, by the end of year 4.
And, crucially, we are putting arithmetic, numbers, fractions, decimals and percentages at the heart of our new curriculum.
These essential skills are the bedrock of the subject, vital for almost every higher-level specialism and essential if children are to feel confident and capable as they move on to secondary school. The countries which regularly out-perform us in international tests like TIMSS or PISA - East Asian nations, in particular - make sure that every pupil masters arithmetic and number, gaining a rock-solid grasp of these fundamental mathematical skills before moving on to more advanced topics.
But as last year’s TIMSS results showed only too clearly, where East Asian nations perform extremely well in arithmetic, our children do relatively poorly. By contrast, English children achieve comparatively high marks in data at an earlier age, than in high performing nations.
The issue is that data does not provide such a solid foundation for further study as arithmetic. No wonder, therefore, that English pupils perform relatively poorly at age 14 in PISA tests on the topics at the core of the curriculum, algebra and geometry - both heavily dependent on arithmetic.
Our reforms to the curriculum will enable our country to be on a par with the highest-performing nations. That means shifting the balance away from data and towards arithmetic, so that children become secure and confident in the basics of the subject when they leave primary school. There is a role for statistics when these fundamentals have been mastered.
Practice makes perfect
A vital part of that mastery is practice.
The truth is that high-quality, productive practice is essential in learning any skill whether penalty shootouts or piano playing, manipulating Spanish verbs or sine and cosine. As the legendary golfer Gary Player said, ‘the more I practice, the luckier I get’.
No one can predict what will make the ‘light bulb’ ping above a child’s head - converting fragile insight into secure, confident understanding. So pupils need plenty of opportunities to practise a technique in a wide variety of contexts, working through increasingly demanding problems on their own and with a teacher.
Research by King’s College has shown that the number of young people in this country with a poor grasp of basic calculation has more than doubled over the last 30 years. 15 per cent of children today cannot successfully solve even the most basic problems - questions involving simple arithmetic like doubling, trebling and halving - compared with just seven per cent in the mid-1970s.
I think this question of practice is one of the most important differences between top-performing countries and here. As well as focusing on arithmetic and number, pupils in South East Asia spend more time than English children on high-quality, productive practice - and end up with deeper, stronger mathematical understanding.
Teaching the most efficient calculation methods
Another essential reform to the primary curriculum is to ensure that all pupils are taught efficient calculation methods - rather than spending too much time on confusing, time-consuming methods like chunking and gridding.
These tortured techniques have been the trend in recent years. Instead of simple, efficient columnar long multiplication and division, children have been taught to rely on intermediate methods, splitting numbers into smaller chunks and parts, working them out separately and repeatedly adding numbers together, or taking them away.
Supporters of these methods say that they are useful in helping children to understand the concept behind the calculation. But all these methods are slow and simplistic, only effective on the most basic sums. Children cannot progress to more advanced maths without learning the efficient, written methods; and the shift between the two leaves children more confused than ever.
Parents are often utterly baffled, and complain that they have no idea how to help children with their homework - even one of my colleagues with a maths degree; while education experts from other countries are even more befuddled, unable to fathom why the British education system has adopted an untried method for teaching maths, which holds back the most able and confuses everyone else.
High-performing jurisdictions like Singapore, Japan and Hong Kong leave out gridding or chunking from their textbooks entirely - and the best schools in this country don’t use them either. Ofsted research looking at 20 high-achieving primary schools found that the maths teachers avoided chunking because, as they put it, it confused pupils, particularly the low attainers. The National Centre for Excellence in the Teaching of Mathematics agrees - developing new guidance which makes it clear that children should learn efficient calculation methods as quickly as possible, with no encouragement for chunking or gridding whatsoever.
So the new National Curriculum will specify that children should learn efficient calculation methods like columnar addition and subtraction and short and long multiplication; and KS2 tests will be designed to reward pupils whose working shows they have used the efficient methods.
In other words, if children get the right answer, they get the marks. If they get the wrong answer, but their working shows that they were using the most efficient methods, they will still be rewarded.
Qualifications at 16
Fixing weaknesses in the curriculum will be vital in driving up standards in the classroom. But we also need to make sure that assessment and qualifications are right.
In maths, one of the most serious problems in recent years has been the steep rise in the number of schools choosing to enter pupils for maths GCSE early. In 2005, 1 per cent of pupils took maths GCSE early. In 2010, the figure had leaped to 27 per cent.
Of course, there will always be a small number of high-fliers who take exams early as part of a planned programme of accelerated progression.
But disturbingly, many schools seem to be choosing to enter pupils of all abilities early as a way of performing well in league tables - choosing to ‘bank’ a C grade at age 13 or 14, even if the child could have achieved an A or A* at age 16. Department for Education research has shown that these candidates achieve worse grades overall than those who sit the exam at the normal time, even after re-sits are taken into account.
We are talking to Ofsted about how to tackle this problem and will also consider it in the imminent accountability review. In every case, and every school, the best interests of pupils should and must come first.
This is particularly worrying because attainment at 16 is very closely linked to whether young people go on to study maths at A Level or beyond. By entering pupils early, schools are effectively limiting pupils’ achievements and ending their maths careers five years early.
The new maths core at 16-19
All the evidence from international tests and league tables suggests that high performing countries put core academic subjects at the centre of their curriculum for longer than we do in this country. Nowhere is this more striking than in 16-18 maths.
The introduction of Curriculum 2000 sent the numbers studying maths plummeting - from 56,000 before the introduction of it to 44,000 afterwards. More than a decade on, I’m delighted that the number of young people taking maths A Level is increasing - indeed, maths and further maths exam entries have risen 50 per cent since 2000 - and degree entries are also rising fast.
But there’s still much further to go - and we’ll be saying more about our plans in the next few months.
Last year we announced that maths will be compulsory for students up to the age of 19 who have not achieved a C at GCSE - a decision supported by this week’s Nuffield report.
That doesn’t mean that young people who have achieved a C or above at GCSE should wave maths goodbye. On the contrary, we want many more students to study maths after 16 - whether they are doing arts or sciences in the rest of their options.
Countries with higher maths uptake between 16 and 18 tend to offer mid-level qualifications at this age - what I describe as core maths - effectively as an alternative to A Level. The Nuffield report found that the availability of appropriate qualifications in advanced mathematics is absolutely ‘crucial to increasing participation’.
We are keen to see a range of approved qualifications that can provide rigorous, respected mathematical options for 16- to 19-year-olds who have achieved at least C at GCSE. For example, these could be a subset of a more traditional maths course or a statistics and probability qualification - like one which has increased take-up in New Zealand.
We are also funding maths in education and industry to work with Professor Tim Gowers, professor at the Department of Pure Mathematics and Mathematical Statistics at Cambridge University and Fields Medallist, devising a whole new problem-solving course. The course will be based on considering intriguing, real-life questions using mathematical rules and techniques - learning to think about the world in a mathematical way.
It will give young people studying literature an insight into logic, aspiring politicians an understanding of probability - and show thousands of young people how mathematical rules shape and govern our world.
Tim Gowers wrote a brilliant explanation of his approach on his blog, and later in ‘Should Alice Marry Bob?’ in the Spectator, and I urge you to read them if you haven’t already. They really illustrate a new way of looking at maths. If those early outlines are anything to go by, this course will appeal to students of all disciplines.
What I’m doing at the moment is talking to higher education and working with organisations like the Advisory Committee for Mathematics Education to look at other possibilities for new post-16 courses. The critical point is that these qualifications must be respected by higher education and employers.
We are also working to improve existing 16-19 maths courses and stretch top students. At the moment, even the brightest 18-year-olds at this country’s top universities are struggling. Academics warn that too many students are arriving to study maths or mathematics-related degrees without the basic mastery they need - which inevitably means that they struggle with the demands of a university course.
Cambridge University’s maths department is developing a rigorous, top-quality curriculum and teaching materials for advanced maths, focusing on key mathematical ideas such as complex numbers and trigonometry. Cambridge is a world-leader, with some of the best mathematicians in the world - and this work will give many more students the deep knowledge and skills needed for further study or employment.
Led by Cambridge professors and the University’s Millennium Mathematics Project, the programme will provide free online materials for students and teachers, helping them to explore connections between different areas of mathematics and to develop key mathematical skills and clarity of thought.
We have also expanded the work of the Further Mathematics Support Programme delivered by MEI. The programme is a huge success story, largely responsible for further maths becoming the fastest-growing A level subject last year. So we have increased its funding, helping to support every schools and college that wants to offer its pupils further maths.
In 2011, the Chancellor announced funding for specialist maths Free Schools for 16- to 18-year-olds, supported by strong university mathematics departments and academics, and giving our most talented young mathematicians the best possible preparation for university.
And I’m delighted that King’s College London is planning to open the first in September 2014 - giving promising 16- to 18-year-olds the benefit of their inspirational teaching and global reputation.
Supporting current teachers
The quality and skills of the workforce will be vital in driving up standards - and all of these schemes have excellent professional development and comprehensive training and teaching resources at their heart.
We are continuing to fund high-quality CPD for primary, secondary and post-16 teachers through the National Centre for the Excellence in the teaching of mathematics. And we are encouraging CPD providers to learn from what we already know does and doesn’t work - for example, ensuring that great textbooks and enrichment material (from Tony Gardiner’s books on maths to the world-renowned Russian textbooks) become more widely known and used.
I can also announce today that we are funding Imperial College to develop and pilot a one year course for teachers of A level mathematics to improve their factual mathematical knowledge, confidence and fluency. Like Cambridge, Imperial College is a world leader, with a global reputation. Its experience will improve the quality of advanced maths teaching in schools and colleges, and the skills of students entering university.
And recruiting higher calibre candidates
For new teaching recruits in every subject, we have increased the level of numeracy required - ensuring that every new teacher is able to pass a test equivalent to a B grade at GCSE maths.
We’ve introduced prestigious £20,000 scholarships for aspiring maths teachers, led by the Institute of Mathematics and its Applications, the London Mathematical Society and the Royal Statistical Society for Maths.
And although most primary ITT courses prepare generalist teachers who teach across the curriculum, we want primary schools to have the opportunity to employ maths specialists.
So the first trainees will be starting our new primary maths specialist programme in September this year - and an extra £2000 bursary for those with at least a B in A level maths will help to attract the brightest and best into our primary schools.
This country can be proud of our mathematical heritage. From Sir Isaac Newton to Charles Babbage to Ada Lovelace to Alan Turing - English mathematicians have shaped the world we live in and will shape the future still to come.
But what was once the domain of the exceptionally gifted has become the currency of how we live. Maths is the universal language of the modern world - and across every career and every discipline, its importance will only grow.
That is why I want to see more girls taking maths, more comprehensive schools offering advanced maths and more students across the whole country studying and enjoying this great subject.
Because unless we make maths universal, our young people will never be able to reach their full potential. And, critically, we will fail to compete against those countries where maths is considered a birthright - the Asian nations beating us in the international league tables and pulling further ahead every year.
By redesigning the curriculum and assessment, improving the standard of teaching and expanding the range of qualifications, we can make sure that every young person in the country - male or female, rich or poor, dreaming artist or single-minded scientist - masters maths early, and studies it for longer.
Because the only way to create the next generation of Turings and Lovelaces is to make fluency in the universal language of maths our top priority.