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Don’t jump, Felipe!

The weird world glimpsed at through maths exam questions

Peering over my son’s shoulder as he forced himself through a pile of practice IGCSE maths papers in readiness for this week’s exams, I was shocked both by the absence of pounds sterling and by the ardently international imaginary first names dreamed up by the question-setters. That ‘I’ stands for ‘international’ — and goodness, you’re not allowed to forget it.

‘Nyali paid $62 for a bicycle.’ ‘Alejandro goes to Europe for a holiday. He changes 500 pesos into euros at an exchange rate of…’ ‘Abdul invested $240…’ ‘At 05 06 Mr Ho bought 850 fish at a market for $2.62 each…’ ‘On 1 January 2000 Ashraf was x years old. Bukki was 5 years older than Ashraf and Claude was twice as old as Ashraf…’ At the sight of the final question, ‘Felipe stands 7 metres from a bridge’, I couldn’t help envisaging Felipe as a boy in suicidal mood, having had to navigate both this gruelling maths and the zealously multiracial landscape.

Bukki, Ashraf and Claude. Oh, I see: their names begin with ‘A’, ‘B’ and ‘C’, perhaps on purpose. For any imaginative teenager, though, it’s hard not to be distracted from the mathematical essence of the question by the temptation to flesh out this imaginary threesome: Ashraf the Arabian boy, Bukki the African boy, and Claude the P.G. Wodehouse character. As for Mr Ho, who gets up on the dot of ‘05 06’ to go to a market to buy far too many fish, paying dollars for them: what’s his story? A shopkeeper in Hong Kong?

I rang the headquarters of the Cambridge IGCSE exams to ask whether their exam-setters are given a list of acceptable names and acceptable currencies, as well as following the strictly international house style (long numbers are written in the international comma-less way, e.g. 580 000 000). Their press officer Adele Williams explained that IGCSEs are taken in 140 countries by 3,700 students, and numbers went up by 27 per cent last year. From Indonesia to Malaysia, from India to the USA, as well as in Britain, teenagers are sitting these papers, and it would be inappropriate for them to portray Amelia, Barnaby and Christopher going to buy sweets for £2.50, or James going on a 16-mile bike ride from Cambridge to Ely. ‘Where do the question-setters get their imaginary names and imaginary contexts from?’ I asked. A lot of them have taught overseas, she told me, travelling to the relevant countries to train maths teachers, and they pick up ideas for names and contexts as they travel.

If it’s snapshots of British life you’re looking for in your maths exams, you must go to home-grown, domestically targeted GCSE maths papers, rather than IGCSE ones. In GCSEs, the currency is still in pounds, not dollars, and the names, though multiracial, have a generous sprinkling of British ones thrown in — Ellie, Mike, Halima, Ashley, Paula, Jim, Jamal, Aysha — giving the kind of cross-section you might find in a typical academy or comprehensive.

Those IGCSE maths questions do have a whiff of wealth and glamour about them — a slight Patek Philippe air, what with all that changing of currencies, and journey lengths from Geneva to Gstaad. GCSE ones, by contrast, portray British life at its most tawdry. ‘Talil is going to make some concrete mix.’ ‘Sameena records the times some girls took to do a jigsaw puzzle.’ ‘Here is part of Gary’s electricity bill.’ ‘Ashley wants to buy some tins of paint.’ The choice of shops is Paint R Us or Deco Mart. In another question there are two brick shops: Barry’s Bricks and Bricks R Us. Unfunny imaginary names of shops. The imaginary food is (of course) healthy: ‘Here is a list of the dried fruit 24 people liked best: currants, raisins, sultanas and prunes…’

Do maths exam questions need to be adorned with imaginary characters, shop names, and foodstuffs at all? They used not to be. I remember our 1970s GCE O-level ones being bald and lacking in colour. ‘Three Christmas presents cost £23.80 altogether. The first cost twice as much as the second, which cost three times as much as the third…’ No mention of whether it was Peter or Alejandro who bought the presents, or what they consisted of. ‘A, B and C are three places at sea-level.’ ‘Two boys calculate the area of a circle…’ ‘An aircraft is flown from its base A…’

The lack of colourful detail made the questions more scary, but at least they weren’t dressed up as friendly, as they are now, when candidates have to wade through the top layer of story to get to the brutal essence of the question beneath. The commands in those days were terrifying. O-level maths papers in the 1960s and ’70s consisted of a succession of imperative verbs. ‘State’, ‘prove’, ‘evaluate’, ‘find’, ‘solve’, ‘construct’, ‘show’, ‘differentiate’, ‘verify’, ‘plot’. No one pretended this was any fun.

But if you search hard enough through those colourless 1970s questions, you occasionally come across bursts of real life which bring you up short. In a Joint Matriculation Board O-level paper from 1974, full of lifeless questions about going from A to B via C, I suddenly came across this: ‘A certain woman’s “vital statistics” are in the proportion 12:9:13. Given that the second measurement is 63cm, calculate the other two.’ I couldn’t help imagining bearded maths dons from Manchester, Leeds, Sheffield and Birmingham Universities (who devised that Joint Matriculation Board paper) salivating over this imaginary woman’s curves. (Or is she actually rather barrel-like?) I worried that a small bespectacled 15-year-old swot in 1974 might have had no idea what a ‘vital statistic’ was, and would guess that it was just a very important bit of maths.

Again, if you look hard enough, 1970s maths papers do give occasional insights into the social fabric of those days. ‘A football ground has standing room for 30,000 spectators and seats for 7,500 more. Admission costs 30p for standing and 80p for a seat.’ ‘The price of admission to a discothèque rises by 5p.’ Those were the days. And so were these: ‘A slag heap is in the form of a cone whose vortex…’ Far from using healthy dried fruit as the imaginary item, candidates in a 1974 paper were asked to ‘calculate the cost of 250 crates of whisky’.

To all IGCSE candidates this month, I say: just do the maths and don’t get distracted by the travel. That will come in the summer, if you’re lucky.

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