In the test papers, Ravi surveys birds in the school garden, Dan and Ama count peas in a pod, Ingrid photocopies kites. David is at least studying blood cells with a microscope while Enid finds roots of a quadratic equation by trial and error.
Let Kirsty stand for a typical such pupil. Does she have any ambitions? If she lived in Singapore, Taiwan, or even Vietnam, she would probably already have a well-defined desire to be an engineer or computer programmer. For any scientific discipline she would have been taught the crucial importance of mathematics, and algebra in particular.
And so we scan the key stage 3 papers for testing of algebraic manipulation. In vain. You see it does not fit easily into a context. The limit is forming an algebraic expression, or substituting numbers into an expression. Under the new national curriculum orders it is only at level 8 that pupils need to be able to multiply out brackets, factorising a quadratic equation doesn't even appear under "exceptional performance". How vital therefore that Kirsty is tested on the little that she's expected to know.
But what will Kirsty do in the future? Perhaps she will find a future in the brave new world of IT with all the skills she has absorbed. After all, who needs maths to be an engineer if a computer package will do all the calculations at the press of a button?
Happily, or sadly, the European Society for Engineering Education has exposed this particular lie in its recently published "Core Curriculum for the European Engineer". The preface quotes the President of Exxon Research and Development: "Too few people recognise that the high technology so celebrated today is essentially a mathematical technology".
The report goes on to emphasise the importance of educating engineers to understand the concepts they are dealing with, and of having a thorough mathematical training as the best foundation for being able to respond flexibly to change throughout their career. "Trivial applications" are to be avoided in favour of mathematical rigour. "Without the means of understanding modern technological publications, almost always written using mathematical notation and with arguments mathematically expressed, the intended beneficiary could be reduced to the role of a passive observer in his developing field".
Poor Kirsty! A passive observer after all those relevant lessons on bird surveys and pea counting. We need perhaps a new style of key stage 3 question; and it could be in context, believe you me: "Kirsty has noticed that her mathematical education is being pathetically short-changed, and she has no intention of joining the unemployed in the dole queue. She has therefore decided to learn some real maths. The coloured beads and matchsticks have been jettisoned and instead Kirsty is going to factorise 20 quadratics. See if you can help her."
Go on Kirsty, you can do it! You'd better, because I'm relying on your generation to pay my pension.
Robert Barbour is head of maths at Hagley RC High School, Worcestershire.