Reading the headlines of outrage after international school maths tests showed Britain lagging far behind Asian countries, you might conclude that our children are bad at maths. But is this the case?
Even if the Programme for International Student Assessment (Pisa) tests decently reflect today's maths standards, I believe that simply trying to climb up the table is wrong.
The problem is not the difference between Britain and Shanghai – which education minister Elizabeth Truss visited on a fact-finding mission last week – but the worldwide difference between maths in education and maths in the real world: everywhere, we are teaching largely the wrong maths.
Here's why. In the real world we use computers for calculating, almost universally; in education we use people for calculating, almost universally.
This growing chasm is a key reason why maths is so despised in education and yet so powerful and important in real life. We have confused rigour at hand-calculating with rigour for the wider problem-solving subject of maths – the necessary hand mechanics of past moments with the enduring essence of maths.
At its heart, maths is the world's most successful system of problem solving. The point is to take real things we want to work out and apply, or invent, maths to get the answer. One example involves four steps: define the question, translate it to mathematical formulation of that question, calculate or compute the answer in maths-speak and then translate it back to answer your original question, verifying that it really does.
The central change in real-world maths of the last 50 or so years is that we automated the hell out of calculating. Computers now do a fantastically better job than people – even well-trained ones – in almost all cases. An example I like to give is to pick up my iPhone, activate its Siri voice recognition and say: "Solve x cubed plus 2x plus one equals zero."
With any luck, back comes the answer – the three solutions, presented with graphs and formulas. This is a cubic which, except in special cases, even further maths A-level students don't get to.
In schools most of us learn the formula for solving a quadratic equation, but not a cubic. You must seriously question why we are spending years of our students' lives failing to be able to compute what my phone did in seconds. Instead, they should be grappling with real problems and applying maths to them. Defining questions and abstracting them to maths are crucial steps that Britain's (and other countries') schools spend woefully little time on, because students laboriously practise obsolete hand calculating skills.
Worse, the curriculum forces the use of toy problems. Real problems tend to be harder and messier, but it's possible to handle such problems only if computers do the calculating.
Indeed, it's the mechanisation of calculating that's powered maths to be applicable to so wide a swath of society. From medicine to mobile phones to finance, to the very computing technology that drives it, maths has become usable and useful because we've mechanised computing answers so successfully.
One of the scariest aspects of maths for many students is how disconnected from anything in their lives it seems to be. After my 2010 TED talk on the subject, a huge number commented to the effect: "This is the first person who's explained why any of the maths I learnt at school has any relevance to my life."
What a waste of human endeavour when the world's population is spending 20,000 student lifetimes a year learning hand-calculating.
Why would they use an equation, what problem would they be solving with it and how do they set it up? Even when our current system tries to give a context for maths, the problems are contrived so they're solvable with weak hand-calculating techniques, so that everyone can see that they are not useful in real life.
In real life the problem leads, and if the computation is messy and complex that's OK, the computer will probably cope. By removing the computer from maths education you remove most of the real context.
Just to be clear. I'm talking about using the computer for doing the computation and changing the subject-matter – which I call computer-based maths – not for replacing the teacher or changing the delivery of the existing content. Of course, we should modernise our delivery too, but however well we deliver the wrong subject it won't make it right.
The real world should be your guide: no one seriously claims computers have made real-world maths less conceptually demanding; quite the contrary.
Indeed, the reason governments around the world are panicked about maths is because of the chasm between students' understanding and real-life needs. It's not so much that maths education is worse than it was; instead, real life is much more demanding and we're running in the wrong direction to catch up.
Instead of rote learning long-division procedures, let's get students applying the power of calculus, picking holes in government statistics, designing a traffic system or cracking secret codes. All are possible, all train both creativity and conceptual understanding and have practical results. But they need computers to do most of the calculating – just like we do in the real world.
One recent direction that will help all of this is the government's new-found enthusiasm for computer coding in schools. Much of the reason given for why it's important is that everyone can understand the insides of the apps they're using.
But I think there's a much deeper point. Code is the modern way in which you express maths and the way to get computers calculating: it's that central. There's one country that pushed coding in schools before the UK: Estonia. It is also the first country to use the computer-based maths education system. There, my company has just finished building a completely rethought probability and statistics curriculum.
School students will be working on problems such as "Am I normal?", "Are girls better at maths?" "Will it rain tomorrow?" and "Should I insure my laptop?" They'll be using real, large datasets with all the difficulties that entails. They'll be doing coding and some of the maths they'll be handling is traditionally taught only at university.
What's really impressive is that Estonia has already come top in Europe in Pisa. And it recognises how being top on today's playing field isn't what's needed for tomorrow. Where Estonia leads, others will follow – not just in the process of learning but in the subject matter. It's happened with coding. Now it needs to happen with school maths or it will go the way of classics. Those who lead the charge will reap the greatest rewards, as Britain did with universal education in the 19th century.
Even better, I believe British culture makes us rather good creative problem-solvers, potentially world-beating if successfully tethered to the power of computer-based maths. Non-conformity, creativeness and looking around the rules is key to British (and Estonian) cultures and a great competitive, opposite to the cultural imperatives in many of the Asian countries doing well in maths tests, countries that may struggle to imbue such characteristics.
Playing the wrong game badly is hardly smart. Let's lead in rewriting the rulebook and succeed at the right game. Visiting Estonia would be a start.
Conrad Wolfram, physicist, mathematician and technologist, is founder of computerbasedmath.org
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