The new White Paper shows the Third International Mathematical and Science Study data most graphically on page 83, with England being in 20th place out of 25 countries. Leaving aside the successful mathematical areas of geometry and investigations, there is clearly a problem with basic arithmetic.
As an employer of less able youngsters and a one-time secondary maths teacher, might I suggest some diagnostic possibilities?
* The mathematics syllabus is far too extensive and daunting for the less able pupil. The need to reach the less useful, higher-level skills means that basics are skipped over too fast.
* The phenomenon of "unlearning" comes into play by age 13 whereby constant difficulty with the basics that were badly learned at the start only reinforces the sense of failure.
* There is an optimum age for most pupils, between 13 and 15, when they should be out using their arithmetic in real work situations before they pass the age when they will cease to learn properly. Many English people have an irrational fear of precision, which manifests itself as contempt for long words, foreign languages or hard sums. Even good teachers find this hard to counter, yet in most work situations, "near enough" is just not good enough.
* Most other subjects have by now managed to avoid the worst effects of precision phobia by removing exactness from the syllabus and dealing more with concepts; failure to practise the skills of rigorous accuracy elsewhere has a bad impact on maths.
Perhaps other readers would like to comment on this list and make their own suggestions.
41 Meon Road Mickleton Chipping Campden Gloucestershire