Writing in the Guardian, mathematician Conrad Wolfram says learning by rote is not the answer but unlocking the creative power of problem-solving is what will enthuse British schoolchildren and make them world-class…
…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…
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…
Conrad Wolfram, physicist, mathematician and technologist, is founder of computerbasedmath.org
Here’s Conrad Wolfram’s Ted Talk “Teaching kids real math with computers”
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Conrad Wolfram goes on to recommend analysing the system in Estonia (in which his company is involved) which, he claims, is the first country to use the computer-based maths education system. What do you think of his arguments? Are we missing the point in the way we teach maths currently? Please let us know in the comments or via Twitter…