Maths: What Is It Good For?

Not since Einstein wrote E=mc² on a blackboard has anything containing an equals sign created such a hullabaloo as the now infamous Hannah's sweets question in last week's Edexcel  GCSE maths paper. The question, which got distilled down until it fitted into a 140 character Tweet, appeared to make little sense at first. It began  by stating that Hannah had a bag of sweets, some of which were orange and some yellow, that she then took and ate two. The students sitting the exam were then asked to show that n2-n-90=0, which at first appeared to be the mathematical equivalent of a non-sequitor, until  online articles began appeared that explained that the question was not asking for a solution to the equation, but was asking that the students did some basic probability.[1]

"Albert said that e=mc2"

Like no other subject, maths has always had a reputation for posing questions that try to smuggle the real world into the equation, although more often than not the links  are somewhat tenuous, or else the "participants" in the question are performing some apparently illogical or pointless exercise, like 'John and Matthew are filling a swimming pool 50 metres by 25 metres by 2 metres with Coca Cola, how many cans will they need to buy to complete their task?' But no amount of camouflage can hid the fact that like most questions in most exams, students are being asked to regurgitate facts they have learned by rote, with perhaps a little analysis thrown in. Yet whether it is showing that n2-n-90=0 or calculating how many 330ml cans of Coke are required to fill a swimming pool of certain dimensions, most people taking maths exams (or most other subjects, come to that) will know one thing for certain; after they have finished their exams they are extremely unlikely to need to call upon that knowledge again. Naturally those students going on to study a subject at university will use the knowledge they gathered in their chosen subject, but what thereafter?

Early tweets on the subject expressed students' frustration with the question

In many respects education is about learning to learn, learning to analyse, learning to apply rather than learning facts. For most people, education is about becoming capable rather than the specifics of subjects that will never be applicable to their work or indeed their home life. I once worked in an IT department where there were as many people with degrees in agriculture as there were in computing (there were one of each). There being no relevance in an agricultural degree in writing COBOL, the significance of that degree was obviously only in the particular programmer's ability to learn, assimilate and process information. How one gets from agriculture to computer programming is proof that that individual, like many people, did not know what it was they wanted to do when they started their course, or at least had their mind changed about what they wanted to do at some point during their time at university. Knowing what you want to do when choosing A levels or a university degree is helpful if not essential, and although embarking a medical degree without an ambition to be some sort of practitioner would be wasteful, I imagine there are many people whose career choice only becomes settled after they have started studying or even after they have finished. When I was at school I envied those people who knew exactly what they wanted to do when they left; I was one of a fairly large group of people who sort of drifted into a career. Forty years later I sometimes wonder what became of the people who knew what they wanted to do; did they achieve their goals I wonder? And those like me who ended up in jobs through inertia rather than ambition, how happy were they with their decisions? Going back forty years or more, to the days when I was taking my O and A Levels, I do not remember anything like the pressure that was exerted on my generation of students compared with that faced by 16 and 18 year olds today. I took eight O levels; passing four would have been considered a success, so long as one was maths and another  English and as it happened I passed seven. Nowadays, when 16 year olds are taking ten or more GCSE's, just passing is not enough; A's and A*'s are all that people want.

Hannah's sweets, the full question.

Funnily enough, the one O level that I failed was one which would have been quite useful in later life, at work. I failed French, and in some ways it was a conscious decision. I had no aptitude for the subject and disliked it immensely. I concluded that if I concentrated all my efforts on it to the detriment of my other subjects, I might just scrape a pass, so I abandoned any pretence of revising for the exam and failed miserably. When I ended up in the international payments department at HSBC I found that even a passing knowledge of French was useful as many banks in France and almost all of those in Algeria and Morocco would only correspond in that language. To my amazement I found that although I could not speak the language I could translate many of the telexes we got from the banks in those countries. The little French I remembered from school actually proved useful;  it certainly proved more useful than physics or history, both of which I passed, which made me wonder if I ought to have tried harder with French at school.

I somehow passed maths at O level, since when my use of the subject has been minimal and confined to arithmetic; algebra, quadratic equations and the like baffled me then and continue to do so now, but I cannot ever recall a time when I have thought to myself "I really wish I could remember my polynomial multiplication" so, as with the knowledge I gained in other subjects but which I subsequently forgot, that has never been a problem for me.

And that is something which students finishing their GCSE, AS and A2 exams would do well to remember. As important as those subjects are now, as important as the grades they will get in August will be, come ten years time, or five years time and for some people, even in just one year's time, those grades will be irrelevant except as a matter of nostalgia. The knowledge that they acquired will be useful principally to try and answer some questions on University Challenge. I am not saying that exams aren't important or that we should not care about grades but just as important, if not more so is learning how to learn and how to interpret and apply knowledge. The skills I learned at school that proved most useful once I started work were a retentive memory, curiosity and having an enquiring mind. At no time has being unable to show that n2-n-90=0 proved to be a disadvantage; better French would have been useful though.

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[1] The Guardian explained it as well as anyone, here: http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jun/05/how-to-solve-the-maths-gcse-question-about-hannahs-sweets-that-went-viral