Paul Chambers was educated at Cambridge and Nottingham Universities. Subsequently, he worked in three different schools before spending many years recruiting and training teachers of mathematics at one of the largest providers of teacher education in the country. He has worked as external examiner for two universities. He has direct experience of several different programmes of initial teacher education, including full-time and flexible PGCEs and a three-year BSc with Qualified Teacher Status. He is fully conversant with the demands of other routes into teaching, such as School Direct and Teach First programmes. Previous publications include several articles in mathematics magazines for teachers and joint authorship of teachers’ packs for AS and A level mathematics. He was one of Her Majesty’s Inspectors for nine years. Robert Timlin studied mathematics and theoretical physics then undertook further studies leading to the award of a PhD. Rob qualified as a teacher after a PGCE where he studied with co-author Paul Chambers. Rob has taught in several schools in the North West of England and in London. He has been both a successful Head of Department and Assistant Headteacher. He has also worked as an educational consultant, advising local authorities and other public and private bodies on the teaching of mathematics. He has taught on a number of higher education courses, including the establishment of a successful PGCE Mathematics course at Liverpool John Moores University, and the role of Principal Lecturer in Mathematics Education at Manchester Metropolitan University. He has taught on undergraduate teaching courses and on mathematics degree courses as well as on Master’s degrees in educational practice.