Shock news: one in five children are below average!

On the train to London last week I found myself sitting opposite a good friend of mine, Steve. He's an intelligent man, who works as a financial advisor in Norwich. I had to spend some of the train journey checking page proofs for the fourth edition of Mathematics Explained, so inevitably the conversation turned to children, schools and mathematics teaching.

'But it is a disgrace that one in five children leave primary schools unable to read, write and add up, isn't it?' said Steve at one point, reproducing a statistical 'fact' quoted often in newspapers and by ignorant politicians.

This is really very annoying! The fact is that one in five children at the end of Year 6 in primary schools do not achieve level 4 in mathematics and English. But when the national curriculum assessment structure was established it was – and always has been and still is – based on the notion that level 4 should be the achievement of an average pupil at age 11. So all that the results tell us is that one in five pupils are below average. Well, of course they are! That's how averages work. Do people really think that it is a disgrace that some children are below average?

Another fact is that 35% of 11-year-olds are achieving level 5 in mathematics. Where are the headlines about this shocking result? This looks like a pretty good spread to me: in 2009, 21% below average, 44% average, 35% above average.

Of course, I'm not complacent and I'd be the last person to say that we cannot improve the mathematics achievement of pupils in primary schools. But please let's stop this ridiculous misinterpretation of the statistics, whereby 'average level' changed into 'expected level' – and from that into statements about the proportions of primary pupils who 'fail to make the grade'.