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Contemporary math teaching does not add up

Problem-setting is the key to math, but curricula all over the world are teaching rote-learning when computer-based education is more appropriate

By Conrad Wolfram  /  The Observer

Illustration: Mountain people

Reading the headlines of outrage after international school math tests showed that Britain is lagging far behind Asian countries, one might conclude that British children are bad at math, but is this the case?

Even if the Programme for International Student Assessment (PISA) tests decently reflect today’s math standards, I believe that simply trying to climb up the table is wrong.

The problem is not the difference between Britain and Shanghai — which British Minister of Education Elizabeth Truss visited on a fact-finding mission earlier this month — but the worldwide difference between math in education and math in the real world: everywhere, people are teaching largely the wrong math.

Here is why: In the real world, people use computers for calculating — almost universally — while in education, they use people for calculating, again almost universally.

This growing chasm is a key reason math is so despised in education and yet so powerful and important in real life. We have confused rigor at hand-calculating with rigor for the wider problem-solving subject of math — the necessary hand mechanics of past moments, with the enduring essence of math.

At its heart, math is the world’s most successful system of problem-solving. The point is to take real things one wants to work out and apply or even invent math to get the answer. One example involves four or so steps: define the question, translate it to mathematical formulation of that question, calculate or compute the answer in math-speak and then translate it back to answer your original question, verifying that it really does.

The central change in real world math over the past 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 x3 + 2x + 1= 0.”

With any luck, back come the three solutions, presented with graphs and formulas. This is a cubic, which — except in special cases — even advanced students do not get to.

In schools, most people learn the formula for solving a quadratic equation, but not a cubic. One must seriously question why we are spending years of students’ lives failing to be able to compute what my phone did in seconds.

Instead, the experience they should be gaining is how to take real problems that they face and apply math to them. Defining questions and abstracting them to math are crucial steps that worldwide curricula spend woefully little time on, because it is all being spent laboriously practicing obsolete hand-calculating skills.

Worse, it forces the use of toy problems. Real problems tend to be harder and messier, but it is only possible to handle such problems if computers do the calculating. It is the mechanization of calculating that has powered math to be applicable to so wide a swath of society.

From medicine to mobile phones, from finance to the very computing technology that drives it, math has become usable and useful because the world has mechanized computing answers so successfully.

One of the scariest aspects of math for many students is how disconnected from anything in their lives it seems to be. After my 2010 Technology, Entertainment, Design talk on the subject, a huge number of people commented to the effect: “This is the first person who’s explained why any of the math I learned at school has any relevance to my life.”

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