Computers do it better
In a dim, steeply raked lecture hall at the Royal Institution, many men and a few women are shuffling politely along the narrow rows to find a seat. Around their necks, everyone wears outsize plastic ID wallets containing a neatly folded itinerary to this, the first Computer-Based Math Education Summit.
Even without the IDs, you could perhaps guess that this event was something to do with computers or maths - the front rows are filling up first.
While delegates fiddle with laptops and phones (the Twitter hashtag is #computermath, we are told), the man who set up the conference sits by the stage, all alone, his knees raised because the seat is too low for him.
Conrad Wolfram, whose 2010 TED (technology, entertainment, design) talk on maths education has been viewed online more than 500,000 times, has a big idea. He wants computers to be used in maths lessons - or rather, he wants maths lessons to be entirely transformed by computers.
The problem, he says, is that maths in the real world has never been so popular or so crucial, but it has changed so much that it is now a different subject from the maths we teach in schools, which he says is now more akin to ancient Greek: something that may have an esoteric interest for many, but is not worth the world's governments spending billions of pounds on educating every single citizen to do.
His talk at the Royal Institution restates his case. Maths, he says, has four steps: 1) Posing the right question; 2) Turning the real-world question into a mathematical formulation; 3) Computation; and 4) Turning the mathematical formulation back into a real-world answer and verifying it.
"The crazy thing is forcing the entire population to do step three by hand," he tells his audience. "It is the one step that computers do better than humans."
To emphasise why, he points out that calculating is the machinery of maths, not the goal. Throughout most of history, that machinery has limited what we can achieve with maths; now there are far fewer limits on what we can do. But in the classroom, the curriculum still focuses on the machinery.
"What has happened with technology and maths is that teachers have taken the content of the curriculum and added computers to improve learning. That's not a bad thing. I think a lot of great things are happening that I am not knocking in any way. But we need to look at the basic content of maths. The content has fundamentally changed because computers have fundamentally changed the subject." The crowd is rapt.
Wolfram is managing director of the European arm of Wolfram Research. The US-based company was founded by his older brother, Stephen, a legend in the computing world for developing Mathematica - one of the most popular programs used for higher-level maths. The company widened its public appeal with the launch of WolframAlpha in 2009. This is a "computational knowledge engine", meaning that, when you type something in, it comes back with the answer rather than links to various websites.
'Radical but not radicalised'
If you go to WolframAlpha and type in "Who is Conrad Wolfram?", it will tell you that he is a 41-year-old businessman born in Oxford. But he is also, according to the National Endowment for Science, Technology and the Arts (Nesta) and The Observer newspaper, one of Britain's 50 new radicals. When his status was announced, Wolfram tweeted: "Glad to be viewed as radical but not radicalised(!) (Reminds me of that school nickname Conradical)."
Wolfram's parents were Jewish refugees from 1930s Germany. His mother, Sybil Wolfram, became an Oxford professor of philosophy and his father, Hugo Wolfram, was a textile manufacturer and novelist. Conrad was sent to the independent Dragon School in Oxford and then Eton College. He went on to study maths and natural sciences at the University of Cambridge. He is married to Stella Hornby, an ophthalmologist, and they have a young daughter. In his TED talk, he recounted an anecdote about his daughter creating a pretend laptop by folding a piece of paper in half. "You know," he told her, "when I was your age, I didn't make these. Why do you think that was?" She thought then replied: "No paper?"
He looks like a textbook academic, with bushy hair and wire glasses. He speaks confidently, without a preacher's zeal or a salesman's patter. And when, during his lecture on computer-based education, his computer does not "plot sin x" on command, he carries on regardless, simply remarking that it is not the best demonstration. His speech is mid-Atlantic - a mostly British accent peppered with American turns of phrase. It is noticeable when you are speaking about a school subject that is spelled differently in the two countries.
"In my TED talk," he says, "I decided to use (the word) 'math' because it was for an international audience. That was the thing I was most castigated for: 'How can you be a Brit? Talk about "maths".'
So does his crusade mean that his daughter can get out of learning her multiplication tables? Unlikely, he thinks, as those parts of maths that are practically useful, or conceptually empowering, should still be done. "I estimate things in my head every day, using times tables. They are useful to know," he explains.
But inverting matrices or solving quadratic equations? We should think hard about whether these are really useful. Wolfram's idea to liberate students (and teachers) from hand calculating is gaining momentum. He has no background in maths education, but this may be working in his favour. One eminent professor remarked that those within maths education have been saying similar things for years without garnering the attention that this successful businessman has.
And of course, catching the wave is all about timing. High-profile names in computing, such as Ian Livingstone, have now successfully persuaded the government that computer science should be taught instead of ICT, which is concerned more with using software than creating it. Michael Gove has agreed. The Raspberry Pi, a #163;22 stripped-down programmable computer, was launched in February. When Wolfram is asked what the calculation part of maths should be replaced with, he answers "programming". He has challenged politicians to go further with curriculum reform - just as the UK is in the process of reforming its maths curriculum.
It is no good, he argues, simply to teach maths better. It is the wrong subject. The question is, which country will be first to let go of the traditional hand methods and leap into computer-based maths?
The Royal Institution in London's Mayfair was founded in 1799 with the aim of introducing new technologies and teaching science to the general public. It was where Michael Faraday, inventor of the electric motor, spent much of his career, and 14 Nobel prizewinners have worked there.
Wolfram tells the delegates there that he encounters three main objections to his idea: that children need to learn the basics first, that computers dumb maths down and that hand-calculating procedures teach understanding. The most infuriating of these is that computers dumb maths down. "Any tool can dumb things down if used badly," he says. "But used carefully, computers can improve the experience, give people larger problems. The problems in schools are dumbed down because they have to be able to be neatly worked through - 5x2 + 2x + 1 = 7 is dumbed down.
"Procedures are important and knowing how to procedurise is important. This is called programming. More programming means maths could be more practical and more conceptual. I'm not suggesting we go down to the lowest common denominator. For example, we could teach calculus earlier. It's taught late because it is procedurally hard - it's not a hard concept."
After the lecture, one member of the audience asks Wolfram what the general reaction to his idea has been. His response is telling. "I thought the most likely reaction would be a huge barrage of stuff saying, 'You're a bastard for suggesting maths should change.' That hasn't been the reaction. The reaction has been much more, 'We kind of agree with you, but we can't see it happening - there are so many cogs in the way.' That's sad."
And he suggests a familiar method for resolving this problem. Zoom out from all the detailed implementation calculations and concentrate on the big picture. It is the concept - getting the maths right - that is important. Not how it is going to happen. Not step three.