Ben Goldacre

The Guardian,

Saturday June 7 2008

It is with deep regret that I must alert you to a frightening decline in the quality of maths in reports complaining about the frightening decline in the quality of maths in Britain. “The value of mathematics”, by thinktank Reform, has received a huge amount of flattering media coverage this week in the Times, the Telegraph, and even scored a second puff in the Guardian from Professor Marcus du Sautoy himself. There is less maths around. We suffer economically. People think it’s cool to be bad at sums. These are bad things.

An early factual claim in Reform’s document is simple: “about 40% of mathematics graduates enter financial services”. This – we are invited to agree – is a good thing. The report’s reference for 40% is a simple link to prospects.ac.uk, which isn’t very informative as it’s rather a large website. Chasing through the pages there, you will find “What Do Graduates Do?”, and then the maths page. There were 4070 maths graduates in their sampling frame of 2006. Only 2010 of those, however, are in UK employment (1.5% are working abroad, and the rest are studying for a higher degree, or a teaching qualification, or unemployed, or unavailable for employment, and so on).

Of those 2010 – not 4070 – 37.9% are indeed working as “Business and Financial Professionals and Associate Professionals”. So correct me if I’m wrong â€“ I’m always eager for that to happen â€“ but by my maths 2010 x 0.379 = 761.79, and that divided by 4070 = 0.1871, but let’s round up like the angry maths profs did and say that about 20% of maths graduates enter financial services. Not 40%. I call this “arithmetic”. For a bunch of people complaining about the substitution of woolly modern notions like “relevance” and “applied maths” in place of high end mathematical techniques, they don’t make a particularly good advert for their own skill set.

And even moreso when the dubious reasoning begins, like with their idea that if there were simply more people around with maths knowledge, there would therefore automatically be more (and more lucrative) jobs around requiring that knowledge, into which the new maths graduates would lucratively and instantly fall. I’m not entirely sure it works like that â€“ I am of course not an economist – but in extremis, I would mention that there are quite a few men in the north who are very good at mining, and I don’t see anyone in a hurry to open up new pits.

Unfortunately, in any case, even this aspect of their report may be marred by simple errors in applied arithmetic. The thinktank is worried that the loss of A-level mathematicians has resulted in lost earnings for the economy. If the number of maths candidates had remained constant, they say, there would have been an additional 430,700 over the period 1989 to 2007. In the adjacent table they say 430,031, but heck, that’s the least of our worries. They go on to reason thusly: “Each of these students would have earned an additional Â£3,080 per year due to the market premium on A-level mathematics, equating to Â£136,000 over their lifetime. The total gain to the economy over the period would have been over Â£9 billion.”

Now we’ll put aside the fact that the BBC said “a maths A-level puts on average an extra Â£10,000 a year on a salary [not Â£3,080], says Reform” because I can’t get Â£9 billion for that period with those numbers (I get Â£12 billion assuming a linear decline, although they may have access to more detailed data), and in any case Reform make assumptions which are not, at face value, tenable, including the notion that the extra earn would have survived a widening group of people with maths A level. We could go on.

I’m happy to agree that maths is economically useful, that maths exams are dumbing down, that people avoid difficult school subjects, and that humanities graduates who think maths is uncool are bores. What I would like is someone who can be bothered to sit down and reinforce my prejudices without perpetrating crass errors of overinterpretation and getting the basic arithmetic wrong. I’ve never fully seen the point of them, but I suspect that’s what thinktanks are there for. Again, I may be wrong.

[Sorry this was late up, my laptop broke and I’m away, will pop in links and any extra working later. I’ve had a couple of emails saying “the 40% figure was right because lots of the people who do postgrad will then go into finance. To them I say: (a) why have figures if they’re made up estimates and (b) says who? Will the people going off to do teaching courses work in finance? And will that make 40%? Etc /rant ]

## mottainai said,

June 8, 2008 at 3:55 am

Apologies in advance for long post.

It is interesting that Professor of Education John Marks is one of Reformâ€™s authors of the paper as he served on the Schools Examination and Assessment Council (SEAC), 1990-1993 and then the Schools Curriculum and Assessment Authority (SCAA) 1993-1997.

This body is criticized in a 1995 report by the London Mathematics Society â€œTackling the Mathematics Problemâ€ referenced by Steve Mayer in the article below: (both links follow)

sixthform.info/maths/files/AMaths2.pdf

www.lms.ac.uk/policy/tackling/report.html

I still need to read the complete paper by the London Mathematics Group but Steve Meyer does quote from it as follows:

â€œThe situation was exacerbated by the revised compulsory A-Level core produced by SEAC/SCAA which attempts more to accommodate diverse types of courses than to provide the predictable base needed by end-users. As will be seen from Appendix B, the amount of material that is now common to all the boards has been reduced to the point where those in higher education can infer relatively little from the fact that a student has a â€˜mathematicsâ€™ A-Level. . . . â€œ

Steve Meyer goes on to write himself â€œIt was a well written and sensible report, but it then triggered some unintended and unwelcome consequences. The report was in the forefront of the minds of those writing syllabuses for Curriculum 2000. As a result, the A level mathematics syllabus was strengthened with many topics, that had been dropped in the 90â€™s, put back in. The result was a national crisis in 2001, reported in detail in the press, with large numbers of AS mathematics students failing and not going on to A2.â€¦â€

â€œâ€¦The Universities were also dismayed to find that many students were no longer applying to study for mathematics degrees with the result that many mathematics departments have had to close.â€¦â€œ

â€œâ€¦The situation is as desperate as ever. This is, in my opinion, a result of the lack of co-ordination between the various levels of mathematics teaching. Mathematics is very much a linear subject and altering one part of it without reference to years above and below cannot work.â€¦â€

ã€€

The following should in no way be taken as a criticism of John Marks, especially as we donâ€™t know what contribution, if any, that he had on the Curriculum 2000 (John Marks left the SCAA in 1997) but Steve Meyer says near the beginning of his piece â€œâ€¦ Despite this, the teaching of mathematics is influenced by those that have little feel for the subject and who impose their own systems, then complain about the consequences.â€

We need to evolve a maths syllabus which allows teachers to deliver a complete core mathematics course and revise it inside the time allowed, while ensuring pre-requisites for changes are introduced first at lower levels so that students meeting the new topic have the grounding in it. And if it needs a steamroller approach to teaching students because it will only all fall into place at the end of the course, that needs to be understood by students so they see the point of (temporarily) doing something they don’t understand.

## Jonarific said,

June 8, 2008 at 10:28 am

I’m gonna use my own anecdotal experience (as if it could be anything else). Sorry for the length, but the thing about a-level maths adding value to your salary is crap in my experience.

Having got an A in A-level maths it has been bugger all use to me professionally. I have been in my chosen career for almost a year now, town planning now.

To go into planning you need to study a vocational post-grad qualification (or undergrad) that is accredited by the Royal Town Planning Institute. I needed to get at least a B in geography and another B and a C in other a-levels to get into my undergrad course of Geography and Planning (I got AAABC incidentally – they counted general studies the fools). And all I needed to get onto the accredited post-grad course was a decent undergrad course (so that was easy).

At least 50% of planners work in the public sector, like me. My salary is entirely dependent on the ammount of my experience (I can show you the pay sturcture if you like) and whether I am RTPI chartered (takes a kinda exam like essay and two years experience) and so whether I have an A-level in maths means nothing.

In the private sector it may help me get to interview if there were lots of candidates (which is why I took maths because it is known as a hard subject), but it would mean nothing to my salary which is based on your ammount and type of experience as far as I can see.

So A-level maths has been no use to me professionally (although it came in handy for our statistics module in my undergrad course and thats about it).

All my friends who did A-level maths have probably only found it useful, as I said abvove, in maybe helping them get to interview on the basis of their cv. Afterwhich it has meant nothing. The only thing maths is needed for is for those how have gone into something directly relevant, in which case the maths is apr for the course in the profession.

And if you want to study maths at uni, you would be expected to probably study further maths at a-level too, so maths by itself is kinda irrelevant.

/rant over

## ayupmeduck said,

June 8, 2008 at 10:36 am

The interesting thing for me is the story of what actually happens to the maths graduates that go into finance. Apparently, the demand for maths graduates in finance has been due to the development of complex derivatives:

findarticles.com/p/articles/mi_m0EIN/is_2007_Nov_5/ai_n21081650

Once these maths graduates got to work, they created complex models that were supposed to reduce risk. Some of the models were so complex that it took a long time to realize that they were completely wrong – but by the time the errors were found, billions had already been traded based on the models:

www.ft.com/cms/s/0/245bf02e-264d-11dd-9c95-000077b07658.html

But the biggest problem was that risk that they were supposed to cover was the risk created by a very simple equation that went something like this:

(99g + b)/100 = g

If g = “good debt” and b = “bad debt” then this equation could be applied repeatedly to “wipe out” masses of bad debt. All of a sudden the world was a bulging supply of triple-A rated “good debt”. Obviously this equation is wrong, and no matter how clever the maths was in the derivatives, the “bad debt” was still there.

On the other side of the coin is the demand for credit, and again simple maths was ignored.

The fundamentals of Economics are based on some simple proven assumptions and some basic maths – these parts of economics are just as scientific as the fundamentals of medicine or engineering. One of the fundamental principles is that where the supply curve meets the demand curve marks the price and the quantity:

en.wikipedia.org/wiki/Supply_and_demand

But it was exactly this solid and proven part of economics that finance and politics decided to ignore – it was, and to some extent still is, as if NASA decided to no longer factor gravity into their rocket program. Hence we repeatedly hear that the demand for credit in the form of mortgages is somehow bigger than supply. This ignorance of basic economics leads to even Gordon Brown saying things like “…we know that house building has failed to keep up with housing demand”. Which demand is this exactly, there is only a demand curve, not some magical demand which takes no account of supply? It’s like saying that “…we know that private jet production has failed to keep up with private jet demand”.

My conclusion: I bit more attention to basic maths within the Treasury, Northern Rock, et al. and there would have been no credit crunch.

## Nadia said,

June 8, 2008 at 7:41 pm

I’m not quite sure of the simple or proven assumptions that underlie neoclassical economics; including knowing absolutely everything and using that information in a perfect way.

In a dynamic system of what economists call ‘perfect competition’, demand can easily be greater than supply. The market will achieve equilibrium eventually and no one producer or purchaser will be able to change the equilibrium in the long run.

As it happens, I wouldn’t argue the market for mortgages is best described by perfect competition or indeed any form of neoclassical device. It appears to me to be a set of behavioural activities and institutions saturated by imperfect information.

I’m sorry if the language is overly technical. However, I am trying to stick up for unsimplified economics. I wish I could do it a bit more cogently. Sigh.

en.wikipedia.org/wiki/Perfect_competition

en.wikipedia.org/wiki/Neoclassical_economics

en.wikipedia.org/wiki/Institutional_economics

en.wikipedia.org/wiki/Behavioral_economics

en.wikipedia.org/wiki/Imperfect_information

## ossian said,

June 8, 2008 at 11:49 pm

To those who question the relevance of maths I’d like to share my experiences, from a hotel room in Paris. I studied Higher Maths rather than A Level, and enhanced this with 2 years of mathematics as part of a BSc in Biochemistry.

Not only did this learning assist when composing my dissertation on Formal Methods of Specifying Software for my MSc but it has proven even more valuable in the business career that has followed (a career that has no relationship to the subjects of my degrees).

I regularly build financial forecasts and market models based on mathematical skills gained in education. I curse my poor memory as I can seldom remember the correct models or methods to apply however I have learned one important skill: the ability to derive the correct answer by using first principles (and also perhaps a latent “feel” for numerical methods). The result has been a rewarding career without unemployment and a good pension to look forward to.

Of all the subjects that I have studied it is maths that has produced the greatest benefit. That said I wish I worked with more people who had studied English (and I realise my own abilities are found wanting in this area).

PS- I think the 40% refers to those who found employment in the UK which isn’t what they said and doesn’t justify leaving us to guess where the figures were derived from. The reasoning is at best woolly and at worst absent.

## Allo V Psycho said,

June 9, 2008 at 9:45 am

Can’t believe no one has mentioned Newsbiscuit in all this……

newsbiscuit.com/article/man-uses-calculus-at-work-224

“Man Uses Calculus At Work”

“Mathematics history was made this week when a man in the Manchester area used calculus in his everyday job. It remains unclear whether it involved differentiation or integration but there have been confirmed reports of lots of little â€˜dxâ€™ symbols having been spotted in the vicinity of a small business in Stockport.

Advising his Year 11 class of the news, ecstatic Maths teacher Reg Willard of Stockport Comprehensive was reported as saying this was a great day for teaching. â€˜I feel personally vindicatedâ€™, he said to a bemused audience of teenagers. â€˜For years I have been telling my pupils about the many and varied uses of calculus, and this has conclusively proved my point.â€™”

## nekomatic said,

June 9, 2008 at 9:56 am

ayup, I think most people understand what is meant by â€œwe know that house building has failed to keep up with housing demandâ€, namely that there are numbers of people who would rather like to buy a house but who can’t find one at a reasonable price. Of course ‘reasonable’ is a subjective quantity, but politics is subjective; and it does distinguish houses from private jets – very few people feel it would be ‘reasonable’ to expect private jets to be available so cheaply that everyone could afford one. Getting all outraged and spluttery at people using ‘demand’ to mean something other than its precise economics definition is a bit like elderly chemists ranting about misuse of ‘organic’ – it doesn’t really do them any favours.

I had a very annoying maths teacher who insisted that past pupils were forever contacting him to attest that Further Maths was the only A-level that they had found at all useful in later life. I feel I can reasonably dissent from this position myself, but I do have to admit that understanding the basis of principal component analysis has been pretty useful. And re using calculus, yes ha ha, but you can’t deny that understanding what’s meant by the rate of change of something with respect to something else has fairly widespread application.

## teej said,

June 9, 2008 at 10:15 am

â€œa maths A-level puts on average an extra Â£10,000 a year on a salary [not Â£3,080], says Reformâ€

Yet another example of correlation != causation. Just because people with a maths A-level earn Â£3k/Â£10k more on average does not imply that getting a maths A-level “puts on average an extra” however much.

## Squander Two said,

June 9, 2008 at 10:44 am

Jonarific,

> In the private sector it may help me get to interview … but it would mean nothing to my salary which is based on your ammount and type of experience as far as I can see.Your salary is also based on whether you actually get the job. Hence, helping you get to interview helps to increase your salary — from the salary you would have if you didn’t get the job you wanted to the salary you get in the job you want.

> My salary is entirely dependent on the ammount of my experience (I can show you the pay sturcture if you like)What possible relevance would that be? No-one comes up with figures about the effect of maths A-level on salary by looking through lots of employers’ pay structures to see which ones mention it. It’s done by comparing the actual salaries of people with and without maths A-levels. It appears not to have occurred to you that studying maths teaches you reasoning skills which are useful in a wide range of applications — including non-mathematical ones — and will therefore help you to do better in life. It’s nothing to do with whether you use Newton-Raphson methods at work every day. It’s to do how much more successful is the sort of person who can get their head around Newton-Raphson than the sort of person that can’t.

> I have been in my chosen career for almost a year nowWell, I can see why you would be absolutely 100% positive of the affect of your maths A-level on your entire fifty-year career, then. However, I’ll just chuck my own anecdotal experience into the ring, as a counterexample, if I may.

After university, I got a job sorting mail in a call centre, which led to work on the phones, which then shimmied sideways into call traffic forecasting and reporting, which led directly to a much better job with someone else, which led to opportunities to learn programming. I’ve gradually become a software engineer over the last few years, while also picking up all sorts of interesting IT things. At no point until this year have I ever needed a single qualification to get a job, yet in every single job the reasoning abilities I learnt in maths (and philosophy) have enabled me to move up the organisation and get more money.

Twelve years after graduation, I have, for the first time ever, got a job that requires a qualification: my employer doesn’t take anyone unless they have an A at A-level maths and pass a written test to demonstrate they haven’t forgotten it all. My salary increases from one year to the next are based directly on how many more relevant mathematical techniques I learn. I seem to remember, a few years ago, telling people that my qualifications had never been any use in getting a job. Had I only added “and never will be,” oh, how stupid I would look now.

And I use A-level maths stuff on a daily basis.

## fontwell said,

June 9, 2008 at 12:07 pm

I have been designing silicon chips for 15 years and was an electronics hardware engineer for a few years before that. To get started in this career I have done A Level maths, then in my electronics degree, further calculus, Laplace transforms, Fourier transforms and another two levels of transforms on top of that (I forget their names now but I think omega’s and Z’s were involved).

At work, over my entire 18 year career the most advanced maths I’ve used is a solving a simultaneous equation which resulted in a quadratic equation (non imaginary). This has happened twice. And for anyone who can’t remember, that is covered in O Levels.

## buffalo66 said,

June 9, 2008 at 4:47 pm

Squander Two,

It could be that brighter people tend to take A-level maths, and brighter people also do better at work and get paid more. In this case, it’s not that having A-level maths causes you to get a higher salary, but that both these things are caused by a third variable, the intelligence of the person.

I’m not denying the usefulness of A-level maths, but i do agree with teej that correlation != causation.

## thomasR said,

June 9, 2008 at 6:21 pm

>There is less maths around. We suffer economically. People think itâ€™s cool to be bad at sums. These are bad things.

All true. However, the conclusion that educationalists will draw from this is that children need more compulsory maths and more testing. This will continue, as it does now, to put people off maths for life.

This is sad because even arithmetic is interesting if you are allowed to approach it freely, when you are ready.

See John Holt’s classic: “Why Children Fail.”

## heavens said,

June 9, 2008 at 8:49 pm

A few years ago, I ran across a United States labor agency that does some job testing. As I recall, they figure out how good your mathematical (or other) skills are with an online test, and line it up with their data on actual jobs. I took the test and scored in the top category for maths (hardly surprising in my case) and below median for mechanical skills (like where to put a heavy object on a multi-axle trailer: also not a surprise).

However, what did surprise me was the overall information they had collected about mathematical skills:

About 20% of the population had the math skills needed for the “top” 10% of jobs (ranked according to their use of math). This represents an oversupply of people who have slogged through advanced maths and who will not use it on the job.

About 10% of the population had such poor skills that it affected their job prospects: These are people who couldn’t make change or figure out how much money should be in their bank accounts.

So I think there’s some truth to the complaint that we’ll never need this stuff on the job. (Not that your career is the only reason to study maths.) Certainly the bottom 10% of people have some problems.

However, while we might not be turning out enough few super-maths people, I doubt that we have too few people with the skills to be an accountant, a nurse, or an engineer.

## Becky said,

June 10, 2008 at 11:19 am

If we’re talking about the relevance of Maths A-level to those wishing to work as “Business and Financial Professionals and Associate Professionals” its perhaps worth noting that to become a financial professional you don’t, uh, actually need a Maths A-level. Deloitte, KPMG, Ernst and Young etc etc require only a maths *GCSE* for their graduate programs. A-level maths is entirely superfluous if you wish to be an accountant, tax advisor, investment manager, stockbroker etc. That said I’m sure more specialised roles within the industry require it and it would probably be helpful in the oh so fun exams…

## jamesdoeser said,

June 10, 2008 at 12:07 pm

Which person (Paul Brown – that’s who) seems to make much the same argument again in Today’s Grauniad.

www.guardian.co.uk/commentisfree/2008/jun/10/2

## superburger said,

June 10, 2008 at 2:38 pm

why *should* studying maths/science be considered only in the context of future job prospects?

I mean, nobody says “what’s the point in getting A-level english, it’s not needed for any job you are ever going to do….

ditto RE, Art.

Maths is worth studying because it is interesting. When most people say ‘maths’ they mean the arithmetic and basic algebra/trig. Probably agree that arithmetic and some algebra is dull, but thats nothing but one of the basic tools of maths that you need for the interesting stuff.

It’s like saying “pH testing is dull, so chemistry is dull”

As for KPMG etc, it’s no surprise they don’t need any real qualification in maths. Accountancy, etc is a utilitarian job with plenty of ‘people’ focus.

The people making the real money (for themselves, at any rate) in finance have very often have PhDs in maths/physics/theoretical chemistry – people who can model stochastic process like derivative price fluctuations and write decent code to implement the models.

## ferguskane said,

June 11, 2008 at 11:39 am

All for Maths, but who are these PhDs who make money by modeling stochastic processes? Ok, many make money by ‘modeling’ such processes, but not (as far as I can see) by producing robust models, with true predictive value.

I’ve certainly yet to see any proof of the utility of these mythical models. Of course, you’ll tell me that nobody gives their money making secrets away for free, but that’s hardly an argument. At the least we should be seeing billionaires appear from nowhere, with no explanation of how they did it.

While I dispute the value of PhD level maths in the stock market, lets be clear: science is impossible without maths and science is the basis of all modern living. We need maths.

## AmberFoxTwo said,

June 12, 2008 at 2:15 am

I dunno guys, it all seems to fit and make sense to me.

JT

www.Ultimate-Anonymity.com

## Diversity said,

June 12, 2008 at 8:20 pm

Usually when a think tank makes an arithmetical nonsense (they do that from time to time) it is because they have employed a good statistician. I never yet met a really good statistician who could be trusted to add up.

However that excuse won’t wash for Reform. No good statistician would have let that wrong base for a percentage through.