Today, school mathematics syllabuses all over the world are being revised: the teaching world is in a state of ferment. From Illinois to Cracow, from Wellington (N.Z.) to Wellington, Shropshire, there are more than whispers of change. The suggestions for the actual changes vary tremendously: in Cracow, it is for the introduction of lattice structures and axiomatics; in the USA it is logic and truth tables (or was that last year’s model?). In Britain, some introduce groups, while others believe fervently in motion geometry; some ph their faith on vectors, while others tackle the problems of the negative integers. All are less than satisfied with the present syllabuses; but how many are concerned about how it is taught? In SME we are trying to see both sides of the coin and as the work develops it is becoming clear that we need to think carefully about both.