This forum is about wrong numbers in science, politics and the media. It respects good science and good English.
I find it strange that so many PhDs in one science or another don't even know the rules of basic arithmetic.
I can see one major problem with the BBC news article, it is written as though the words "numeracy" and "mathematics" (or "maths", with an "s" on the end, as it is known in the UK) are interchangeable.
There is an important difference between numeracy and mathematics. Numeracy is an everyday life version of applied mathematics. Mathematics is a much more academic subject which often has little everyday application. The "National Numeracy" website seems to have a fairly good page that explains the difference:
In the old version of the UK state education system, numeracy was concentrated on in the secondary modern schools, with grammar and technical schools concentrating on the academic subject of mathematics. How the more modern comprehensive system of state education, which replaced the three types of school with one, handles the numeracy versus mathematics issue I have no idea.
It is possible for people to be numerate without being formally good at mathematics. An example would be professional darts players who can perform pretty impressive feats of mental arithmetic but probably don't have too many 'O' levels in mathematics amongst them.
People can also be nominally good at mathematics on paper but hopelessly innumerate. An example of this might be the Greenies, who are often claimed to be better educated than average (you sometimes see news articles where Green party supporters turn out to have the highest IQ amongst supporters of political parties). I would imagine Jonathan Porritt and Caroline Lucas are likely to have maths 'O' levels. The innumeracy of the Greens was summed up a few years ago by the intervention of a Cambridge academic called David MacKay who wrote a book called "Sustainability without the hot air" after becoming exasperated by watching Greens lobbying for a low carbon world without having any real plan to achieve it where the numbers actually added up. MacKay was subsequently made the chief scientific adviser to DECC, presumably because he is the only Green-leaning person in the UK who has displayed any signs of numeracy.
I think I would dispute the idea that society is heading in a direction where greater numeracy is required of the hoi polloi. Industry is keen on selling products, and a major selling point for a product is that it makes life simpler, and such simplification often results in a reduction in the need for numeracy. Examples of these simplifications in my lifetime are: (a) decimalisation of the British money system from a more complicated older system forty years ago, (b) electronic pocket calculators appearing from the mid-70s making some lengthy arithmetic operations and the use of log tables redundant, (c) the general trend for people in the retail industry to need to be less skilled at mental arithmetic due to introduction of electronic tills and bar code readers, (d) replacement of navigation devices like sextants by GPS devices.
There seems to be an argument that greater numeracy is required to function in the new 'Information Age'. I'd agree that following politics seems to require more numeracy due to the substantial increase in the number of organisations that are trying to influence public policy and who often spin statistics in doing so. But you don't necessarily need the general population to be more numerate to deal with that - it might be cheaper to improve the numeracy of the political class or for the news media to adopt a policy where it is less enthusiastic about promoting numerically dubious activities like environmentalism.
I suppose on the numeracy versus maths issue it is worth adding the classic anecdote about this issue, the one about Einstein and the bus conductor. I managed to find what is hopefully an accurate version of the anecdote on the internet from a document called "From Misery to Enlightenment".
"To be a scientist you have to sacrifice a few things – for example,common sense. Common sense is a common quality of common people. A scientist is an uncommon person, he has an uncommon sense. With common sense you cannot discover the theory of relativity or the law of gravitation. With common sense you can do everything else.
For example, Albert Einstein was perhaps the only man in history who dealt with such big figures that only one figure would take up the whole page – hundreds of zeros following it. But he became so involved with big figures – which is uncommon, but he was thinking only of stars, light-years, millions, billions, trillions of stars, and counting them – that about small things he became oblivious.
One day he entered a bus and gave the conductor the money. The conductor returned some change; Einstein counted it and said, ”This is not right, you are cheating me. Give me the full change.”
The conductor took the change, counted it again and said, ”Mister, it seems you don't know figures.”
Einstein remembers: ”When he said to me, Mister, you don't know figures, then I simply took the change. I said to myself, It is better to keep silent. If somebody else hears that I don't know figures, and that too from a conductor of a bus.... What have I been doing my whole life? Figures and figures – I don't dream about anything else. No women appear, no men appear – only figures. I think in figures, I dream in figures, and this idiot says to me, You don't know figures.”
When he came back home, he told his wife, ”Just count this change. How much is it?” She counted it and said, ”It is the right change.”
He said, ”My God!. This means the conductor was right: perhaps I DON'T know figures. Perhaps I can only deal with immense figures; small figures have fallen out of my mind completely.” "
The above anecdote also reinforces my point in the previous post that, contrary to what the National Numeracy charity might think, the general trend in society is for low-level numerate jobs to disappear. People in the UK under 40 have probably never seen a bus conductor, except maybe on the old British TV comedy show "On the Buses" that is still shown fairly regularly on ITV3. It was a pretty skilled job, requiring somebody who was numerate and also had a sufficiently good visual memory to recognise any new faces that had appeared on the bus to collect fares from. But the suppliers of bus services decided to simplify things from their point of view, getting rid of the conductors in favour of an arrangement where travellers paid the driver as they got on the bus. Then presumably because the drivers weren't numerate enough to give change, most bus services eventually ended up operating an exact fare policy with no change given.