Tuesday, 18 April 2023

Proof of the theorem?


In relaunching his mathematics strategy yesterday, having done little or nothing about implementing it since the last time he launched it (anyone else see a pattern emerging there?), the Prime Minister claimed that the UK economy is losing “tens of billions” of pounds a year due to functional innumeracy. The first question which sprung into my mind was that often voiced by my old maths teacher, “show me your workings”. That thought was closely followed by memories of the same teacher's strictures about applying the ‘reasonableness test’ – if an answer looks or feels wrong, it probably is.

If we take “tens of billions” to mean £20 billion – the lowest possible mathematical interpretation of the number – and compare it to the UK’s total GDP of £3.1 trillion, it implies that the UK is losing just over 0.6% of GDP every year, purely (according to Sunak) as a result of the fact that children are only taught mathematics until they are 16 rather than 18. According to the government’s own figures, that’s equivalent to between 7 and 8 trade deals with Australia. In ten years’ time. ‘Show me your workings’ is an apt response.

I don’t doubt that there is an economic cost to innumeracy (although a substantial part of that cost may well be the result of having a surfeit of innumerate politicians who pluck arbitrary figures out of the air), but attributing that to the fact that most pupils are not taught any maths after the age of 16 looks like a non-sequitur to me. As someone with three maths A levels to my name (I’ve always liked numbers and what they can tell me), I can honestly say that I don’t think that much of what I learned in the field after reaching 16 has been of much practical use to me in life, no matter how interesting I found it at the time. It seems far more likely to me that the problem of functional innumeracy lies not in the age to which maths is taught in schools, but in the extent to which what is learnt matches what is being taught. That is to say, at its simplest, that maths teaching up to the age of 16 is far from universally effective, and that putting that right would be a better use of any additional resources which can be made available. That isn’t a criticism of teachers as such – we know that there is a huge shortage of specialist teachers of the subject, and has been for a long time. It’s just that assuming that lessons delivered = lessons learned, especially when they are delivered by non-specialist teachers, is an invalid premise. And if they can’t deliver the resources and the processes to get the basics right, the chances of a successful outcome to Sunak’s latest half-baked proposal are close to zero, a statement which can be confidently made even without having enough data to calculate a precise probability.

There is an old adage which claims that 97.8% of all politicians’ statistics are made up on the spot (although estimates of the precise percentage vary), and in this case Sunak’s numbers appear to provide proof of that theorem. It's not exactly a first for him.

1 comment:

dafis said...

...."surfeit of innumerate politicians who pluck arbitrary figures out of the air" sums up the problem. Indeed far too many politicians seem to have graduated with joint honours in Waffle and Fudge.
I'm very much in favour of diverting students wherever possible towards the so called STEM subject areas but for the vast majority a better grasp of Arithmetic would suffice to enable that basic numeracy that impinges on most lives. The "twpdra" that I encounter among otherwise well educated people who come out with drivel like "oh,I'm no good with numbers" still amazes me after years of such declarations. It seems that most Cabinets have an infestation of such people.