It is, however, disappointing that a government which is happy to set standards in every other aspect of school life has not seized the opportunity to dictate what pupils should be wearing on their heads. What is needed is a hat for the new millennium - the design based on Mr Mandelson's Dome. If fitted with a sufficiently long strap expander - of the kind used in baseball caps - the same hat could accommodate a head, however big it grew.
So tomorrow's young scholar could wear her dome from first day in nursery to her degree ceremony when she would proudly doff it to Prince Harry, Ginger Spice, Michael Owen, Chris Evans, La-La or whoever happened to be chancellor of her university.
A government that is committed to giving every pupil an e-mail address would obviously want the hat to incorporate the latest advances in new technology. Knitted into the fabric would be personal stereo, mobile phone, pager, spare mouse and - most importantly - an electronic tagging device. As part of the Government's drive to keep a closer check on pupils' academic progress, every pupil who enters the British educational system is being allocated a unique identity number.
So, in the same way as cars have to be fitted with registration plates, a child should be required to display her identity number at the front and the rear of her hat. It will be of great assistance to the police, who will have to take on the responsibility of rounding up truants. The number should also be displayed on the top of the hat, which would make life that little bit easier for very tall teachers of very short pupils.
Teachers, of course, need to know more than a child's identification number: for example, date of birth, known allergies, attendance record, attainment levels in the various national curriculum subjects, whether she has free dinners, contributed enough Tesco computer vouchers and suchlike. This information could be recorded in a bar code which could be stamped on to the brim of the hat.
To facilitate registration and assessment, pupils would simply step on to a slow-moving conveyor belt - like those used in supermarket checkouts - and the teacher, equipped with a barcode reader, would swipe them as they glided past.
There is no reason why a policy of compulsory millinery should apply only to pupils. Teachers, who already complain about having to wear many different hats in the course of a working day, would welcome the opportunity to appear in a range of headgear: an SAS balaclava for the surprise raid on the bike shed; a hard hat for any lesson in the room with the crumbling ceiling; a Sherlock Holmes deer-stalker for conducting one of those interminable investigations of who did what to whom with whose protractor; a reversed baseball cap for the teacher who is trying to be with-it; and a thinking cap for anyone in the profession who still has time to engage in so arcane a pursuit.
Any hat chosen by a teacher would, of course, be fitted with a tagging device and other sophisticated surveillance equipment to ensure that the wearer maintained the high standards being set by the Government. Incidentally, a superteacher will not be required to wear a hat. The halo will suffice.