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Thursday 10 March 2016

Our fixation with maths doesn’t add up

Simon Jenkins in The Guardian


Who will win the Varkey Foundation’s million-dollar “best teacher” prize this week in Dubai? Hot favourite is Britain’s star maths teacher,Colin Hegarty, whose videos are followed by a million viewers worldwide. Hegarty has been hailed as the great hope for British maths.

Like much of the public realm, British maths is “in crisis”. The country is languishing alongside America way down every league table. Evidence of this was cited in a new poll from YouGov, measuring the public’s knowledge of maths, science and English. In maths, roughly a third of those surveyed had no idea how to calculate a mode, a median, a “line of best fit” or the area of a circle.

I seriously doubt this poll, since it implies that two-thirds did know the answers. All on whom I tested it failed, including myself. Nor could they see the point. With one voice they replied: “That’s the sort of thing you learned at school.” So what is the point? It merely ensures that many pupils, like the bright child of a friend of mine with maths blindness, have their schooling undermined by the government’s fixation with maths.




Colin Hegarty has been shortlisted for the $1m Varkey Foundation teacher prize. Photograph: Linda Nylind for the Guardian

There is nothing, except religion, as conservative as a school curriculum. It is drenched in archaic prejudice and vested interest. When the medieval church banned geography as an offence against the Bible, what had been the queen of the sciences never recovered. Instead Latin dominated the “grammar” curriculum into the 20th century, to the expense of all science. Today maths is the new Latin.

Science at least improved. In 1988 Thatcher hailed a “dash for science” to halt the decline in young people opting for science subjects. It failed completely. Then in 2006 a radical new GCSE syllabus dragged school science away from test tubes and Bunsen burners towards everyday life, to pollution, global warming, additives, health and diet. Since then the reactionaries have turned to maths as the talisman of educational success. It is in maths that we must beat the Chinese, the Singaporeans and the Finns. Pisa league tables of “top nations” are pored over. Maths teachers are paid more, have their loans written off, are entered for global prizes. No one dares mention the calculator.

Any league table that has China at the top, Britain at 26th and America at 36th tells me something more important than merely who is good at maths. If the US and Britain – among the most vigorous economies and most successful at science – are so bad at maths, it suggests their young people are applying themselves to something more useful. Chinese students are rushing to British and US universities to join them.

No one would argue that pupils should not be able to add, subtract and multiply. But I studied higher maths, from calculus to number theory, and have forgotten the lot. All the maths I have needed comes from John Allen Paulos’s timeless manual, Innumeracy. It is mostly how to understand proportion and risk, and tell when a statistician is trying to con you.

I agree with the great mathematician GH Hardy, who accepted that higher maths was without practical application. It was rather a matter of intellectual stimulus and beauty. A new book by Michael Harris, Mathematics Without Apologies, goes to the extremes of this stimulus, to the categorical ladder, incompleteness theory and the Black-Scholes equation, used to assess financial derivatives. It ends in the “inconsistency nightmare”, that nought might possibly equal one.

We accept the need for maths in advanced physics and in computing algorithms, much as we accept Greek for archaeology and Anglo-Saxon for early literature. The “mathematics of finance” school at Columbia University is lavishly sponsored by Wall Street firms, for good reason. But that does not mean every primary pupil must spend hours, indeed years, trying to learn equations and πr2, which they soon forget through disuse. Maths is for specialists, so why instil arithmophobia in the rest?
Charge the maths lobby with the uselessness of its subject and the answer is a mix of chauvinism and vacuity. Maths must be taught if we are to beat the Chinese (at maths). Or it falls back on primitivism, that maths “trains the mind”. So does learning the Qur’an and reciting Latin verbs.

Meanwhile, the curriculum systematically denies pupils what might be of real use to them and society. There is no “need” for more mathematicians. The nation needs, and therefore pays most for, more executives, accountants, salesmen, designers and creative thinkers.

At the very least, today’s pupils should go into the world with a knowledge of their history and geography, their environment, the working of their bodies, the upbringing of children, law, money, the economy and civil rights.

This is in addition to self-confidence, emotional intelligence and the culture of the English imagination. All are crowded out by a political obsession with maths.

The reason is depressingly clear. Maths is merely an easy subject to measure, nationally and internationally. It thus facilitates the bureaucratic craving for targetry and control. The prominence of maths in the curriculum is education’s version of Orwell’s imaginary boot, “stamping on your face … forever”.


------ Reply from a Maths teacher


Maths isn’t the problem - the way it’s taught is



Tim Gowers in The Guardian


A county council gathers data about where road accidents take place, identifies an accident blackspot, places a speed camera there, and notices that the frequency of accidents decreases. Moreover, this is not a one-off: many other councils have observed similar reductions. Does this show that speed cameras improve road safety?

The answer isn’t as straightforward as one might imagine – and the way to understand this is through mathematics. Unfortunately, the way the subject is taught often leaves people with a narrow and misleading view of what maths is. No wonder Simon Jenkins attacked the subject in Thursday’s Guardian.

Mathematics should be a tool for increasing one’s thinking power but for many children it is just a set of rather pointless rules for manipulating symbols. The problem becomes clear if one asks children a question such as the following: a number 35 bus pulls up at a bus stop and eight passengers get on; what is the age of the bus driver? A large percentage of children, their minds numbed by years of symbol manipulation, will give the answer 43. This is a tragedy: rather than being trained to think, these children have been trained to do the opposite.

To return to the speed cameras, the evidence initially seems conclusive. However, the correct answer is neither a clear yes nor a clear no, but rather that more research is needed. Consider what would happen if the locations of accidents were completely random. Then, just by chance, some places would have noticeably more accidents than others while the data was being collected and these places would be identified as blackspots. But since they would not in fact be more dangerous than anywhere else, the later accident rates at these “blackspots” would tend to decrease to more like the average, whether one installed speed cameras or planted apple trees. This phenomenon is known as regression to the mean. Further investigation is needed to determine whether speed cameras make a difference over and above the difference one would have expected anyway. (It turns out that they do.)

Regression to the mean is one of several statistical phenomena that are counterintuitive until you understand them. But once you do, you become better at making decisions. This is important for individuals – whether we like it or not, we all have to take major decisions based on statistical evidence – and it is even more important for people in positions of authority, whose decisions affect other people.

It is therefore good for the health of a country if its population has high standards of mathematical literacy: without it, people are swayed by incorrect arguments, make bad decisions and are happy to vote for politicians who make bad decisions on their behalf.

So how might mathematics education be different? The way it is often taught, children are asked to take a huge leap of faith: that the symbol manipulation that seems pointless now will one day be useful to them. But this is true for only a small minority of children, who enjoy the symbol manipulation for its own sake and later find themselves drawn towards Stem subjects, where it is indeed very useful. The rest know perfectly well that they will never reach this promised land. What can be done for them?

An indication is given by the speed-camera example. It shows that regression to the mean is an important mathematical phenomenon that can be explained without the need for any calculation or symbol manipulation. Why not use examples like this to bring statistics alive? That way we could explain the point of means and standard deviations rather than just asking people to calculate them.

Of course, some proficiency in calculation and symbol manipulation is important – and it improves one’s conceptual understanding – but it should not be all that is taught. We could also ask children open-ended questions, such as whether it is more dangerous to travel by car or by aeroplane. A question like is not explicitly mathematical, so it is less likely to trigger the brain’s off switch. And if it doesn’t, the ensuing discussion will convey why we should care about multiplication, division, averages and probabilities, what we can say about them when we do not have exact numbers handed to us on a plate, and how to frame mathematical questions to help make decisions that are of practical interest.

I am not suggesting that all maths should be introduced this way. But until our mathematics classes encourage people to think, rather than merely play games with marks on paper, the Simon Jenkinses of this world will continue to confuse mathematics with mindless symbol manipulation, attacking the subject itself when their real target should be today’s curriculum.

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