The arena in which the preparation of student-teachers for the teaching of mathematics takes place is shifting its foundations and moving its boundaries. The whole basis of teacher education at secondary level is in flux with a move towards teacher-education programmes which are largely school based. Increasingly, there is seen to be an important role for the school teacher who acts as mentor to the student teacher in some relationship with a tutor from the initial training i nstitution.; Teachers who are being encouraged to take on the mentoring role need preparation for its demands and teacher education courses need increasingly to make provision for the education and support of mentors. The purpose of this book is to discuss the mentoring process, to provide ideas and to highlight issues. It provides both practical help and guidance, and a philosophical consideration of the development of mathematics teachers and teaching.