How many schoolboys does it take to change a light bulb?

Many years ago I was waiting at a bus stop to go to Brownies when an older lady came and studied the timetable and, after tracing the 0645 to 0715 times with her finger, decided that she had about a fifteen minute wait for her bus. Being a good Brownie, I pointed out that those were the morning times and, if she looked from 1845 onwards, she'd find a bus was due in a couple of minutes. Her reply was along the lines of "Oh, I can't make sense of all that 24 hour nonsense, so I use the bit I understand". As a nine-year-old or thereabouts, I was shocked that she didn't realise that you can't make the morning times apply to the evening just because that's all you can read.

Yesterday morning, on the train to work, I was listening to the conversations of three secondary school boys (well, I had little choice but to listen - their shouting came well over the sound from my MP3 player). They were passing round a Key Stage 3 Mathematics book, and one was repeatedly asking the others to "test me on the brown box". Eventually, one of them agreed.

"How many feet are there in 12 yards?"

A long pause, then "Four? ... No, eight"

The first boy gave him the correct answer, then the one who had asked to be tested grabbed the book back and complained "That's not fair, that's not in the box. We're only supposed to know single units, like three feet in one yard. You should only be asking me single units".

I was appalled. Any amount of knowledge is no use without the willingness at least to try to apply it (a friend of mine, with a First from Oxford, didn't know how to remove spilled cherryade from a cream, long-piled carpet, so left it until the library opened two days later when he could research it). I've heard it said that children are only taught how to pass exams these days, but surely that includes some element of applying what you've learnt? And anyway, knowing that there are three feet in a yard is not mathermatics but memory skills; multiplying those three feet by the 12 yards and coming to the right answer is mathematics. But if that's Key Stage 3, then I'm really worried. Apart from which, why were they learning Imperial measures?

But should I have been surprised? In a quiz a few months ago, we were asked the name of Scrooge's dead partner in "A Christmas Carol", and one of my colleagues said, without even thinking, "I've never read it, so I don't know". Somewhere along the line to her PhD she's got the idea that, if she hasn't studied something in a worthy text, she doesn't know the answer. Even if she does.

Looking back to when I was a Brownie waiting for a bus I think, perhaps, I was hard on that woman. She has some knowledge, and was trying to use it, albeit incorrectly. I would be happy to have more people like her around these days.