Remember the Mobius strip, that clever paper loop with a twist in it? If you draw a line along it, you come back to where you started having drawn on both sides - and discover that there is in fact only one continuous side.
It's a satisfyingly intriguing concept, giving rise to myriad questions and ideas beyond the mere functional mathematics that dominates school life and has recently been exercising the mind of Carol Vorderman and her team, which published the findings of their enquiry into maths education last month. I've nothing against Vorderman; it's good to see a TV personality who makes being clever cool. But my heart sinks when ministers import yet another celebrity brain (albeit one whose university degree wouldn't meet Michael Gove's requirement for entry to the profession) to tell us what to teach.
Happily, her report is clear, tough and doesn't pull any punches. It's critical of the damage done by regulation and inspection: schools are pushed by targets, Ofsted and tick-box national curriculum approaches into drilling children in pedestrian mathematical routines. Vorderman deplores both the shortage of secondary maths specialists and the low level of primary teachers' maths skills. Far from the creative, mind-opening experience she desires, school maths thus becomes a mind-numbing, dreary process. A third of pupils makes no progress in their first year at secondary school and 90 per cent of children "who have failed to reach the target in the Sat at age 11 ... fail their GCSEs and leave school functionally innumerate". The problems are starkly outlined. Mercifully, Vorderman doesn't look overseas for the answer: "We cannot merely import a system ... and expect it to work."
As I read the report my spirits started to lift. Then came the fatal flaw: the recommendation of "a route map for introducing compulsory mathematics for everyone post-16". My heart sank again. That's the danger. All but one of Vorderman's panel are mathematicians, and specialists tend to focus on their subject to the exclusion of others. One thing teachers have to learn when they move into senior management is to broaden their subject-focused view to a whole-school vision.
Let's be clear. Young people should leave school functionally numerate. We must improve primary maths teaching so that children don't find themselves adrift aged seven and never catch up. But once the required level of competence has been reached - and there is a huge debate to be had about what that level of competence should be - we shouldn't keep banging children over the head with more maths if they don't want to specialise in it. We should give young people real choices instead of constantly telling them what is good for them.
Maths is vital and can be fascinating, but it doesn't have to rule everyone's school life until they are 18. Experts should define the minimum requirement and then back off. Prescription, assessment, targets and inspection should not be permitted to distort or wreck it. And, beyond that, minimum point maths should be an option like every other subject.
The Vorderman report charts an illuminating and important journey, but sadly gets lost at the end. Like every single-subject enquiry since Ken Baker first devised the national curriculum, Vorderman's solution involves increased compulsion. Same old same old. It's the Mobius strip again: we're back where we started.
Baker presided over the feeding frenzy when subject lobbies clambered on board and carved up the new curriculum. They created a sprawling, over-prescriptive monster. Two decades on, you would hope we had learned the lesson. But it seems we risk going round the loop once more.
Dr Bernard Trafford is head of the Newcastle upon Tyne Royal Grammar School and a former chairman of the Headmasters' and Headmistresses' Conference. The views expressed are personal.