Today I want to talk about why maths is so important, what has gone wrong with the way in which we share the joy of mathematics with the next generation, and what I think we should do about it.
The most influential language on earth is not English, or Mandarin but maths. Mathematics is the means by which we make sense not just of the natural world around us but also lay the ground for discoveries yet to come.
The Pythagorean revolution was prelude to the astonishing flowering of classical philosophy which laid the foundations of the Western world. Galileo recognised that it was through mastery of mathematics that the music of the spheres could be heard by man, and the shape of the earth made real. The thrilling breakthroughs he and his contemporaries made helped mankind move from an age of superstition to the rule of reason.
The Enlightenment, mankind's great period of intellectual flowering, the liberation from ignorance on which our current freedoms rest, was made possible by the work of mathematicians like Leibniz and Newton.
Gauss, the prince of mathematicians, called maths 'the queen of the sciences.' Why? Because of what Wigner famously called 'the unreasonable effectiveness of maths' - the miracle whereby pure maths can, sometimes centuries later, find practical applications never originally dreamed of, and the way in which a mathematical formulation of a physical principle leads to extraordinarily precise descriptions and predictions.
For example, the discovery of complex numbers found an application centuries later at the heart of Quantum Mechanics, and, extraordinarily, the most abstract realm of mathematical logic and set theory sparked, via Kurt Gödel's famous paper in 1931 on the incompleteness of logical systems, the work by one of Britain's great heroes, Alan Turing, on the fundamental structure of the modern computer.
It is maths combined with physical theories that has allowed mankind to progress from only the vaguest and most approximate understanding of our world to insights that inspire awe and wonder. Richard Feynman has described the precision of Quantum Mechanics as like being able to measure the distance from New York to L.A to the nearest hair's breadth. And for those of us navigating journeys even more fraught and perilous than an odyssey across America - such as driving from Notting Hill to Westminster without hitting roadworks - the precision of GPS satellite technology can guide us - and all thanks to the extraordinary precision of Relativity's equations.
The beauty, and wonder, of mathematical knowledge, the excitement inherent in following the paths trod by the great minds of the past, the infinite number of ways in which human curiosity can be stimulated, all underline the importance of teaching the next generation the sheer joy of maths.
Mathematics is the foundation on which our civilization rests and all those of us charged with a responsibility for educating the next generation should affirm the vital importance of teaching mathematics properly as a good in itself, as the opening of young eyes to boundless possibilities, an invitation to our children to stand on the shoulders of giants so they too can make discoveries which we can only imagine.
So my first priority in shaping a Conservative Government's policy towards the teaching of maths is to underline its crucial role as more than just an important subject area - mathematical understanding is critical to our children's future.
But if my commitment to maths springs first from my belief that every child should have access to a common inheritance of the best that has been thought and written I am also convinced that improving mathematics education is critical to the future prosperity of this country - and all its citizens. Investing properly in maths is necessary if we are to guarantee the growth on which the good society depends.
<h2>MATHS AND ECONOMICS</h2>
Our economic future depends on stimulating innovation, developing technological breakthroughs, making connections between scientific disciplines. And none of that is possible without ensuring more and more of our young people are mathematically literate and mathematically confident.
Mathematical understanding underpins science and engineering, and it is the foundation of technological and economic progress. As information technology, computer science, modelling and simulation become integral to an ever-increasing group of industries, the importance of maths grows and grows.
A few decades ago, the economics of the motor industry was based essentially on physical engineering, but the other day I read that the new Mercedes has nearly as many ECUs (Electronic Control Units) as the new Airbus A380 and that BMW now increasingly outsources its own car construction because it thinks that 90% of its future innovations will actually come from software and electronics.
Maths is intimately connected to the most fascinating and exciting developments in science and technology: the Large Hadron Collider at CERN testing the Standard Model of particle physics; the rapid development of genetic engineering; and the accelerating understanding of the brain and the amazing recent developments of brain-computer-interfaces.
Discoveries in all three of these realms are being driven by the applied mathematics of computer science. Computing power, in line with Moore's Law, is growing exponentially.
I saw on the web the other day that Bill Joy, one of the heroes of Silicon Valley, says that over the next decade the trajectory envisaged by Moore's Law will develop to yield an improvement by a factor of 100 in performance. If the best PC costs $1,000 now, by 2020 it will cost about 10 of today's dollars and Joy went on to say that a fundamental challenge for all of us is trying to envisage what the 'hundred dollar laptop' will enable us to do in educational terms by 2020.
But while we can rejoice in the breakthroughs being made on America's Western seaboard which maths is helping us all to enjoy the economic reality of our times is that power is shifting East. In China and India, and the other growing economies of the East, significant investment is taking place in the mathematical and scientific education of billions of young people who are poised to generate yet further breakthroughs.
There is, as the brilliant British mathematician Marcus du Sautoy would recognise, a certain symmetry at work here.
In his wonderful book 'The Story of Maths', Marcus teaches us about the original contributions of China and India to the the historical development of mathematics. The East was eclipsed for centuries, after the Renaissance, as the nation states of Europe and then the emerging democracies of North America drove progress forward. But now, once more, the world is shifting on its axis. As the East reasserts itself. With vigour
An analysis this month showed that in the period since Deng Xiaoping opened up China there has been a 64-fold increase in peer reviewed scientific papers from Chinese academics. The days are long gone when Asia was just the home of outsourcing and offshoring. China is increasingly developing a lead in the most innovative of industries, including nano-technology, genetic engineering and quantum computation. This shift of economic, and intellectual, power to the East raises profound questions for all of us. Questions to which maths can help us find the answer.
Because not only is maths fundamental to the operation of human reason and logic it is crucial to our economic, technological, and social future. We must value mathematics for its own sake, for the light it sheds on our deepest mysteries but we must also invest in it as the highest-yielding form of intellectual capital.
What's gone wrong in Maths and Science?
The challenge posed by the investment other nations are making in their mathematical and scientific future is all the sharper because of the problems we face in maths and science education in our own country.
There is a huge amount of expertise, enthusiasm and commitment among the country's maths teachers which I applaud. And they have never been worked harder, or been under greater pressure, than they are now. But they are trapped, like so many wonderful professionals who have dedicated themselves to teaching, in an educational system which has been in relative decline for years now because of bureaucratic failure.
In the most reliable international league tables we have, England has fallen from 4th in the world to 14th over the last ten years for the quality of science education and we have plummeted from 8th in the world to 24th in maths.
Over the past decade, over 3 million 11 year-old primary school children have not reached the Government's basic level in reading, writing and maths.
And while some Government apologists argue that poor performamnce doesn't matter we know that for every child who fails to reach the expected level, opportunity is narrowing. In 2007, of pupils who had not reached the expected standard by the end of primary school, only 10% went on to achieve at least grade C in GCSE mathematics at age 16.
Last year, about 60,000 children, about 1 in 10, did not even sit English and Maths GCSE, and 340,000, about 6 in 10 comprehensive pupils, did not get a 'C' in English Language, Literature, and Maths.
Perhaps even more troubling than the absolute numbers is the widening gap between rich and poor...
Only 1 percent of those pupils in the most challenging circumstances - those in Pupil Referral Units get five or more decent GCSEs including English and Maths.
Those pupils eligible for free school meals are the poorest in our society. Every year about 75,000 children qualify for free school meals (around 1 in 8 of all pupils). In 2008, 40% of those pupils eligible for free school meals did not get even one 'C' grade at GCSE.
Independent schools, which educate just 7% of pupils, produce more pupils who get three A's at A Level than every comprehensive school put together.
No child in Hackney, Newham, Sandwell, Knowsley or Lambeth got 3 or more good As at A level including Maths and Further Maths.
In 2008, only 53 children eligible for Free School Meals sat Further Maths A level.
In 2009 only 45 pupils eligible for Free School Meals got into Oxford or Cambridge.
This massive inequality in educational outcomes is not just an offence against social justice it is a massive waste of talent, a squandering of intellectual capital.
At the moment more than a million young people between the ages of 16 and 24 - nearly one in five - are not in education, employment or training.
And at the same time as opportunity has become so unequal, the qualifications we do award command less and less confidence.
Sir Mark Walport in his report on science and maths education for the Government, which was published last week, lamented the fact that there was "widespread concern within the science and teaching communities about the qualification system".
He reported in particular the profound concern about the lack of proper maths content in the 14-19 science curriculum.
His findings are only the latest academic warning about weakness in our curriculum and qualifications system. Work by the University of Coventry and the University of Durham has shown that it is easier to secure good pass marks at A level now than a generation ago, with papers which would have barely secured a pass now being awarded top marks.
Private schools are abandoning GCSEs for the IGCSE because of what one headmaster has called the "terrifying" absence of real science. The Royal Society of Chemistry has attacked changes to maths and science at GCSE as "a catastrophe" and Sir Mark Walport is clear that we need to enhance the place of rigorous subject knowledge and especially mathematical content in the whole science curriculum.
What is to be done?
If we win the election, we will launch an immediate program to overhaul the National Curriculum in the core subjects of English, Maths and Science so that changes can be introduced from September 2011. Our aim will be to define the knowledge that each child should master at each stage in their development before they can move confidently onto the next stage of learning. We will give teachers, parents and students an appreciation of the core knowledge that is required in ever year and make clear what knowledge children in other countries are mastering at the same sage.
The expectations we will set of what children should know will be more ambitious; it must be a floor, not a ceiling that limits schools' aspiration to introduce children to very challenging ideas at a young age; and it must allow schools to benefit from the extraordinary recent change whereby many of the top educational institutions are allowing students to view their content free online. Just think - now, every child in the world with internet access can watch lectures from institutions such as Oxford, Caltech or MIT for free. This revolution is transforming education and our approach to the curriculum must reflect this.
This review will require the full engagement of the maths and scientific community so I urge ACME, the Institute of Physics, the Royal Society of Chemistry and others to begin thinking now about the core knowledge that should be in the National Curriculum at what age, and what we need to do to make us world leading.
In this context, I am intrigued by the Mathematical Needs programme. One of the most frustrating things in this job has been how many people come to me with opinions about the curriculum and syllabus and almost never provide scientific evidence. It is great news that the maths community is pursuing this inquiry in a scientific spirit and the results of the Mathematical Needs programme will be very valuable to the Curriculum Review.
The Curriculum review, however, will focus on WHAT should be taught. We will not return to detailed prescriptions of HOW things are taught. Maths is alive and we are learning more all the time about how the mind works and how to teach more effectively. Marcus du Sautoy is pioneering new ways for children to learn maths through computer game technology and I think it is important that such innovation is allowed and encouraged - not squashed by Whitehall.
I also want to say something briefly about the science curriculum.
We know that it needs overhaul to improve the level of mathematical knowledge underpinning it. And we also know that separate GCSE sciences - physics, chemistry and biology, taught by specialist teachers - make the best starting point for A level. I don't mean that this is the only route but it is the best route for children who know they want to continue serious science post-16.
At the moment the science curriculum for those in Key Stage Three - preparing for GCSE - and for those pursuing Core and Additional Science at GCSE - doesn't even divide scientific knowledge into the discrete disciplines of physics, chemistry and biology. Instead there are hybrid headings - such as chemical and material behaviour or the environment, earth and universe - which take us further away from the essential disciplines of physics, chemistry and biology. So when we reconstruct the National Curriculum we will ensure that it is built around a basic entitlement to study each of these scientific disciplines in a proper, rigorous fashion. We will ensure that each of the three basic sciences takes its place within the curriculum in significantly greater depth and greater detail than now. Studying what has now become known as triple science should not be an elite activity but a basic curriculum entitlement.
Once we have reconstructed the curriculum to root it in core knowledge and benchmark it against other nations then it must be left alone to bed down without constant rewriting. We cannot continue with the pattern of the past decade with the curriculum in state of permanent revolution.
And just as the curriculum needs reform so does our approach towards examinations. The primary curriculum and Key Stage 2 tests need profound change. The Rose Review of the primary curriculum diminishes the place of Maths - we will not implement it. There should be more high quality maths in primary schools - not less.
I know people have serious concerns about the Key Stage 2 tests. In general, it is clear that they need serious reform. For example, the 2009 Key Stage 2 Maths test had very little geometry and zero algebra. We need your help to ensure it is a more rigorous exam.
And in the spirit of encouraging greater rigour, we will immediately allow all state schools to do the international GCSE starting this September. It is not fair that children in private schools can now dodge the problems with Maths GCSE that children in state schools are stuck with.
Some think that the iGCSE will become irrelevant if the new twin GCSE is a success. They may be right, maybe not. Either way, if the new twin GCSE pilot is successful, we will not, as the Government now plans to do, pause for a year and let the program stall - we will immediately roll it out across the country and we will, of course, ensure that all children have access to both of the GCSEs.
And we will also act to restore confidence in our A levels. I can announce today that we will make a radical change to the way in which A Levels are designed. My thinking has been influenced by the work of Sir Richard Sykes and his team who have been looking at the future of qualifications for us, and among his proposals, which will be published in due course, the case he makes for restoring rigour to A levels is compelling. We must ensure that A levels are protected from devaluation at the hands of politicians. The institutions with the greatest interest in maintaining standards at A-level are those which receive A-level students - our universities. The individuals with the keenest interest in ensuring A levels require the depth of knowledge necessary to flourish at university are our teaching academics. So we will take control of the A level syllabus and question-setting process out of the hands of bureaucrats and instead empower universities, exam boards, learned societies and bodies like ACME with the task of ensuring these qualifications are rigorous.
We will also ask Ofqual, the exams regulator, to report on how our exams compare with those in other countries so we can measure the questions our 11, 16 and 18 year olds sit against those sat by their contemporaries in India, China, Singapore, South Korea, Australia, New Zealand and Canada.
The aim of the next Conservative Government will be to have a school examination system which is the most rigorous in the world, safeguarded by the nation's guardians of academic excellence.
The quid pro quo of giving Universities much more power over A Levels is that in the future Universities must be more honest about which qualifications they prefer students to study. We know that some A levels confer a competitive advantage on school students when it comes to university entry but many universities are unfairly reticent about which qualifications they prefer. By maintaining the fiction that all are equally valued those students from schools without a tradition of playing the admissions system lose out. In the interests not just of transparency but real equality of opportunity, universities need to say very clearly which A Levels they think best serve students making choices critical to their future.
And while we are discussing the need for greater transparency I know that many of you have concerns about the lack of transparency which currently affects the operation of the QCDA and Ofqual. So I want to reassure you that their work will be opened up to public scrutiny, with all the hearings, work and documents which contribute to the shaping of the curriculum accessible to the public.
<h2>RAISING THE BAR ON TEACHER QUALITY</h2>
Of course, everyone in this room knows that important as the areas I've discussed may be, the single most important thing in education is not the curriculum, not qualifications, but teachers. The people who inspire the next generation to love learning.
I don't need to remind this audience about the overwhelming empirical evidence from around the world which demonstrates that the countries with the most successful education systems are those with the best-qualified teachers.
I have said repeatedly that nothing is more important than raising the prestige and esteem of teaching, helping to ensure that the quality of teaching our children enjoys improves even further, and guaranteeing that more and more talented people are drawn into teaching.
Which is why all our policies are designed towards one goal - making teaching more attractive and rewarding.
The first priority we have is making teachers feel secure, by implementing a series of policies to improve discipline which involve shifting power and authority back to professionals.
Second, we must attract and retain great people by having greater flexibility over pay and conditions. All schools, especially those which are struggling, must have the freedom to be able to attract specialists - particularly in reading, maths, and science.
It's also vital that schools have flexibility over pay so that they can reward teachers for longer hours. Evidence shows that the schools which have the greatest impact in poorer areas often do so by extending school hours into the evening and weekends so they can offer extra classes for struggling children. The Knowledge is Power Programme charter schools in America, which President Obama supports, insist on a longer school day to ensure children achieve more. Schools must be able to organise their timetables to be able to offer more children from disadvantaged backgrounds these opportunities and therefore they need the flexibility to reward teachers appropriately.
Further, as an extra incentive, we will make maths and science graduates a special offer - if you go into teaching, we will pay off your student loan while you remain a teacher. This could be worth many thousands and will, we hope, encourage more top maths and science graduates to go into teaching.
And we must learn from Finland and Singapore and make a particular effort to improve primary teaching.
We will require that all taxpayer funded primary teacher training courses offer specialist training in phonics and maths. Of course academic success doesn't automatically make you a good teacher but the international lesson is that we will raise the prestige of teachers if we raise the bar for training. It will no longer be acceptable to enter taxpayer funded primary teacher training with just a 'C' grade in English or Maths GCSE. Candidates will need to have at least a 'B' in English and Maths. This means that primary teachers will come from the top third of students rather than the top two-thirds as now.
Today, I also want to announce that we want to go further in supporting great teachers and great teaching.
One of the great success stories of recent years in our schools has been the Further Maths Network. They have done an outstanding job of raising the numbers doing both Maths and Further Maths A Level, and I am told to expect further increases. It is deplorable that Ed Balls has cut their funding.
A Conservative government would restore and enhance funding for the Further Maths Network. All parts of the DCSF will of course have to be scrutinised for savings given the calamitous deficit but within the more than half a billion pounds spent by the TDA we can be sure there will be the money required for the Further Maths Network.
We want many more children, especially those from poorer backgrounds, to have the opportunity to study A Level Maths and Further Maths - a passport for many poorer children to an infinitely richer life, culturally and financially - and it will, I believe, help create more excellent maths teachers throughout the school system right down to primary schools. One of my great priorities will be to help bring to all state school children the routine access to specialist teachers that is available to richer children in private schools.
<h2>HOW FAR CAN WE GO? </h2>
As you all know, I'm no mathematician but I and my team have talked to many over the past few years so I want to throw some questions out in the interest of scientific debate. As I said, the Government will be getting out of A Levels but there are some issues that I think the maths and science communities should and will address.
As I mentioned, there is often a lack of evidence concerning what children should learn when. I was interested that a very prominent academic in the assessment community let my team know about a book called Uncle Albert - a book by a physics teacher about Relativity for primary age children. It made me think - given great teachers, just how much more might an education system be capable of...? How advanced can maths and science teaching really be?
At the heart of the recent financial crisis lay an intellectual argument concerning the nature of randomness and possibilities for prediction. The financial models that blew up so spectacularly were often based on assuming that financial market movements would behave in accordance with certain statistical models - but they did not.
I asked various people about when people learn about key statistical concepts such as normal distribution and I was told that not unless they do S2, the second statistics paper at A Level, which few take. This means that very very few of our citizens could really get into the detail of the arguments concerning a profoundly important political issue - the collapse of the financial system. So, first, I want to ask - should the A Level have normal distribution and standard deviation as part of its core? Secondly, and more controversially, I want to ask - given how issues of randomness and prediction are so central to so many issues, should this subject not be brought into the GCSE curriculum, even if only, at least initially, for the top candidates?
I may be wrong but it strikes me that there is something extraordinarily hopeful about imagining a future British generation who are ALL educated to understand what probability and randomness really mean, a generation capable of having a much, much more sophisticated debate about crucial public policy issues than my generation is.
At other points in history, people have made decisions to spread information more widely. Could we be at such a point now?
With the enormous growth of computation and data processing I referred to earlier, is it not a task for our generation to aim for a genuinely revolutionary change and introduce far more fundamental statistical concepts to ALL our children?
Can we in that spirit ask profound questions about how much we can learn from other cultures about how maths is taught. How do our exams compare with the Chinese Gaokao exam? Some have said that the Gaokao is better at testing in-depth problem solving skills. Is this true? If it is, what can we learn?
Again in that spirit of testing boundaries, I have been told that calculus, which used to be in A Level Physics, dropped out of it over the past few years - yet it will be in the new pre-U. Should it be restored to A Level Physics?
Again, in that spirit of wanting the best for our children, I am told that in Singapore they let the top pupils skip O Levels altogether and push on to A Level at an earlier age. Should we make our system more flexible? For example, after the demise of the old AO Maths, still done in Singapore, about 10,000 now do a similar exam. Should we encourage this? Or might it be better to let clever children advance to do AS Levels at 16 instead of GCSEs? Or both? I don't know - but I do know that we must have a flexible system that does not bore very talented children by holding them back.
I stress, these are just questions, I know there are great debates about all of them, but I think it is important these questions are debated openly and honestly by the scientific community and they are questions that I want to make an effort to begin to answer in the first year of a Conservative Government. A Government I hope which will guarantee that every child becomes fluent and confident in what Galileo called 'the language of nature', every child becomes entranced by the wonder of mathematics and every child has the chance then to set the pattern of their own lives...