Where have all the parrots gone?
Asking children to give examples of mathematical terms can be both amusing and depressing. It's common knowledge that a polygon could be a dead parrot, and children have had fun with "common factors" and "vulgar fractions" too. Until recently, we could expect numerous, albeit more prosaic, examples illustrating the correct use of such terms in the national curriculum. Most of these have now gone like the parrot.
So why were examples included in the first place? Scanning those in the document's 1989 version I wondered if they were there for reassurance. After all, although programmes of study and attainment targets were new to us, much of what was exemplified was familiar. I'm sure I was not alone at the time in going through the examples and picking things I commonly did with my classes.
Many of them had worked well in the past, though there were exceptions. The mention of conkers as non-standard units of weight made me feel very inadequate. I know many teachers use them and I was left feeling this had only been disastrous for me, with the "non-standard units" promptly being skewered, vinegared and used for quite a different purpose.
Some examples were less familiar, and perhaps these were the important ones. A notable new item was probability at level 1 and the statement given, "recognise possible outcomes of simple random events", sounded very technical and needed explanation. The example offered was "realise that a new baby will be either a boy or a girl". This is the first time that I have heard the birth of a baby described as the outcome of a simple random event and although I was left wondering if I'd misunderstood something it was one of my favourites.
Perhaps the examples were not there just to tell us the statements' meaning but carried a more subtle message. Certainly, taken as a whole they depict maths as a useful, active subject closely related to real life. We are taken through the problems of shopping, parking and predicting the weather, and the encouragement to use and apply is clear. I was also interested to see the examples include many mentions of the use of calculators, more so than the statements themselves.
Perhaps the examples were there to clarify the differences between levels. So at level 2 the suggestion was "find a 14 of a piece of string" whereas at level 4 we had "estimate 13 of a pint of milk". Was that because 14 was a level 2 fraction, and 13 was a level 4 fraction? (There was no such thing as a level 3 fraction.) Or was it because the task of estimating with liquids was deemed to be harder?
Some years after these examples first appeared I talked to some students about the possible difficulties of the latter task. The next week, they said they had no milk in their flat but had tried dividing a pint of brandy between them. They were less accurate than they had hoped, but inspired by my talk of trial and improvement, they promised faithfully to try again and I understand they strove patiently for perfection at regular intervals.
The 13 of a pint survived into the 1991 national curriculum, but others were lost or replaced. Sadly, we were no longer told where babies came from, nor were we exhorted to "drop drawing pins from a certain height", an idea which filled me with dread.
An interesting development, though, was the inclusion of games and patterns from different cultures in the examples, and the suggestion that issues like world hunger and infant mortality can be explored using maths.
So what has happened to these examples now? A few survive, as short italicised phrases squeezed into the programmes of study though the examples writers seem to have run out of steam as they reached the higher levels. The key stage 1 programmes of study break into italics 15 times, key stage 2 breaks into italics six times, reducing to five at key stages 3 and 4 combined, and just one example is given in the key stage 4 further material.
Given that so few examples remain, you would not expect any new ones, but at least one has crept in at key stage 2. It invites pupils to investigate the general statement that "wrist size is half neck size". I have encountered that idea before, and it has great potential as long as no one uses string and then pulls it tightly round someone's neck to confirm their hypothesis.
I shall miss the examples. Not that I think they are needed. It is teachers' right to invent, use and share examples as they suit their classes, and there is no need for them to be outlined in a formal document. But I enjoyed reading them, comparing them, hunting the hidden messages. And I found out where babies come from.
Jenny Houssart is a lecturer in mathematics education at Nene College, Northampton.