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.
Illustration: Mountain people
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.”
What a waste of human endeavor 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 current systems try to give a context for math, the problems are contrived so they are solvable with weak hand-calculating techniques, so that everyone can see they are not useful in real life.
In real life, the problem leads, and if the computation is messy and complex that is OK, the computer will probably cope. By removing the computer from math education, one removes most of the real context.
Just to be clear, I am talking about using the computer for doing the computation and changing the subject matter — which I call computer-based math — not for replacing the teacher or changing the delivery of the existing content. Of course, we should modernize our delivery too, but however well we deliver the wrong subject, it will not make it right.
The real world should serve as the guide: No one seriously claims that computers have made real-world math less conceptually demanding, quite the contrary.
The reason governments around the world are panicked about math is because of the chasm between students’ understanding and real-life needs. It is not so much that math education is worse than it used to be, it is that real life is much more demanding now and we are running in the wrong direction to catch up.
Instead of rote learning long-division procedures, students should be applying the power of calculus, picking holes in government statistics, designing a traffic system or cracking secret codes. All are possible, all train creativity and conceptual understanding, in addition to generating practical results. Yet 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 UK government’s newfound enthusiasm for computer coding in schools. Much of the reason given for its importance is that everyone can understand the insides of the apps that they are using. However, I think that there is a much deeper point to this. Code is the modern way in which one expresses math and the way to get computers calculating — it is that central.
There is one country that pushed coding in schools before the UK: Estonia. It is also the first country to use the computer-based math education system.
My company has just finished building a completely rethought probability and statistics curriculum in Estonia that will see students working on problems such as: “Am I normal?” “Are girls better at math?” “Will it rain tomorrow?” and “Should I insure my laptop?”
They will be using real, large datasets with all the difficulties that entails, as well as doing coding. Some of the math that they will be handling is traditionally taught only at university.
What is really impressive is that Estonia has already come top in Europe in PISA and it recognizes how being top on today’s playing field is not what is needed for tomorrow. Where Estonia leads, others will follow, and not just in the process of learning, but in the subject matter.
It has happened with coding and now it needs to happen with school math 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.
Playing the wrong game badly is hardly smart, so let us rewrite the rulebook and succeed at the right game. Learning from Estonia would be a start.
Conrad Wolfram, physicist, mathematician and technologist, is founder of computerbasedmath.org
COMMON MATH EXAM QUESTIONS
1. Find the values of x by factorizing the following: x2 - 10x + 21 = 0
2. What is the next number in the sequence: 1, 4, 10, 19, 31 ...
3. Solve the following simultaneous equations to find x and y:
4x + 2y = 44, and 3x - 6y = 18
PROBLEM-BASED QUESTIONS
1. Which is the best life insurance policy?
2. Should I insure my laptop?
3. Will it rain tomorrow?
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