GCSE mathematics and Sixth Form Mathematics are now out of step. Sixth Form Mathematics and University Mathematics may also soon be out of step. These are two far reaching statements—but what has this got to do with rugby balls and a minibus?

By now many of us currently or recently involved in GCSE mathematics, whether as students or teachers, have become used to mathematical investigations, applied problems and project write ups all lasting about two weeks. How times have changed. It is now quite common for 15 and 16 year olds in their GCSE mathematics lesson to work in groups on open ended problems. Gone are the days (familiar to some of us!) of solving endless lists of quadratic equations and stopping without hesitation the first time b2 is less than 4ac. Generations of pupils will now, if the National Curriculum does not completely move “the goal posts”, be growing up on a new range of discoveries made possible by the introduction of fresh ideas and new starting points. “222 and all that” and “Watch out” for example are two standard pieces of coursework encountered by many pupils in their GCSE training.