Why do students study maths? More to the point, why is its study mandatory right up to the point when they are old enough to jump on a moped and rev away from it as fast as they can?

These are the kind of rich existential questions that a teacher of mathematics like myself spends his Christmas holidays pondering, in the quiet fortnight when students are not heckling me, demanding answers to the very same.

It’s a conundrum that vexes others too. Celebrated journalist and columnist Simon Jenkins - once of this parish - has made a second career out of it, railing against mathematics in columns in the national press in 2008 (“I breakfasted on quadratic equations, but it was a waste of time”), 2014 (“For Britain’s pupils, maths is even more pointless than Latin”), 2016 (“Our fixation with maths doesn’t add up”) and 2018 (“Once children were birched at school. Now they are taught maths”). Read Jenkins and you’ll come away thinking mathematics a kind of absurd purgatory that has no place in a modern education system.

Thankfully, it being an odd-number year, we are likely to be spared further instalments until at least next January. So in the intervening silence I’d like to take the opportunity to posit another view, one that might also arm teachers with something to sling back at pupils once the groans begin again.

Sadly, the regularity of these anti-maths missives hint at the traction this view has. Rare is the parents evening when I don’t get someone across the table bragging about how bad at maths they were. Jeremy Clarkson bragged about his “U” at O-Level Maths while hosting a quiz show last night. I have taught in schools where senior leaders have quipped to same the effect and - following embarrassment at ministers getting simple times tables wrong in live interviews - politicians are now advised not to try to answer maths questions when on TV.

English and Science rarely have to defend themselves against regular attack in the popular press. Why? Is it because literature is considered somehow inherently virtuous, and elevated as art? Though the poetry of Eliot is almost divine, it is still something formed from words familiar enough, arranged in ways penetrable enough, that we can be fed by them. Not so much integration of trigonometric functions or tangents to speed-time graphs, tripping the casual observer with complex couplets formed of illegible symbols.

Science is spared by being rooted in the practical. Medicines, new technologies, new fuel sources - these are all scientific problems that we understand we need experts to work on. By contrast mathematics can feel so oblique, so disconnected from our experiences that it is easy to shoot down.

I wonder though whether the persistence of the trope is partly because the answer offered by cheer leaders for maths has so often failed to convince. Look at the books wheeled out in maths’ defence and the majority seem to be based on two counter-claims: maths is not absurd and useless. Maths is FUN! Maths is AMAZING!

For the avoidance of doubt, despite appearances last thing on a Friday afternoon, I do believe both of these things. It’s just that I’m not sure that our best approach with students who’ve had genuine struggles with the subject from a very young age that the reason that they should persevere with it is because they simply haven’t yet seen how FUN it is, or how AMAZING. For me, that’s rather like trying to tell a kid who loathes the foul-tasting antibiotic they’ve been prescribed to take it - though they’ve consumed a number of doses already - as it’s actually DELICIOUS, and pretty much the most exciting thing someone can do is take medicines every day.

I’ve very much enjoyed many of these maths-focused books. There’s a lovely “wow” factor in some of the number-trickery, and my own children have been impressed (people, this is no mean feat) by chapters on various mathematical problems. But they can present mathematics as something of a performing monkey: something to be astounded by rather than something you need in your life every day. So, perhaps inevitably, the disconnect comes when young readers return to their textbooks and have to meet the demands of the GCSE curriculum.

Is the problem then with the syllabus content we are asked to deliver? It is tempting to consider - as Jenkins would suggest - ditching quadratic equations.

“In the age of computers,” he writes, “maths beyond simple and applied arithmetic is needed only by specialists.” But - and I hate to apply a slightly advanced technique of logic here - but if we kept on with this thinking, what would we be left with? How many of us need to know how oxbow lakes are formed? Spelling and grammar? Well, autocorrect can sort that. A few specialists might need to be able to discuss how themes of guilt and shame function in An Inspector Calls, but - to draw on some pretty sophisticated probability theory - really, what are the chances anyone in your class will?

Jenkins continues: “Ramming [maths] down pupils’ throats in case they may one day need it is like making us all know how to recalibrate a carburettor on the off-chance that we might become racing drivers.”

Apparatus criticus

I’m not sure how good Jenkins’ Latin still is, but this argument about teaching only what is functional quickly hits reductio ad absurdum, diminishing the curriculum of anything beyond the basics until we might as well all quit at the age of 7 once we are toilet-trained and can chat to Alexa to order takeaway food.

His error is to argue that what schools do is primarily vocational: teaching carburettor calibration because the nation needs racing drivers. It is the same mistake made by my pupils asking: “When are we ever going to need this?”

Not only are he (and they) wrong, but to think that education is aimed mostly at vocations is to fundamentally misunderstand both what it is that we do in schools and how advanced economies like ours work.

Although practical skills are an essential part of the curriculum, because there are just so many different careers out there it would be foolish to try to aim students towards them, especially with technology changing the labour market so quickly. Instead, what we focus on is teaching a set of more elemental competencies. For want of a better word, let’s call them all languages.

Learning a language is different to learning to calibrate a carburettor because it offers a set of tools that can then be applied in a multiplicity of ways, rather than just one. In the most general sense, what we do in school is teach a bunch of languages, a suite of different ways in which the world can be interrogated and explored. Students learn about their home language; they likely study a modern foreign language and perhaps an ancient one. They learn the language of history: a means of using sources, dates and facts to understand the past. They hopefully learn a language like HTML, to read and write music and ways of speaking poetically.

In this rubric, mathematics is one more in this language tool-box, another way of speaking about the world. (It can be a cruel language because its rules of grammar are so stark. One mistake in German and you’ll probably be mostly understood; an algebraic mistake might quickly descend into complete incomprehension.)

This is how I answer my students when they ask why they are grinding through quadratic equations. I expect that they will prove as useful to them in their future career as their studies of the Battle of the Somme will. But this is not the point of what they are doing. Through focused work on specifics, they are learning much more elemental skills. It is these wide competencies across multiple languages that deliver them into the world of work equipped not to cope with one job - bricklayer, hairdresser, accountant - but to be able to adapt to many situations. And this is precisely what a smart economy needs: not young people trained in narrow specifics, but ones fantastically polyglot, and thus able to create, innovate and invent.

This is what mathematics is for, and this is why we insist that students study it. Not because it is fun and amazing - though it can be both - and not because it will help them avoid being fleeced when they start earning and spending - though it might. We teach them mathematics because it is the most brilliant language for solving complex problems and developing minds that are logical and rigorous in their thinking. We do this not to the exclusion of poetry or theatre - two other wonderful forms that exist to help us explore the human condition - but in complement to them.

Yes, this work of language formation should be made as engaging as possible, just as gym sessions might be for a football team, but the most vital aspect of our work is to keep students’ eyes on the greater goal ahead: becoming men and women skilled with all kinds of different languages, able to march out into the world and engage with it poetically, historically, technologically, musically …and mathematically too.

Kester Brewin is a maths teacher and author