This volume seeks to provide evidence for the effectiveness of "traditional" and "progressive" teaching methods in school mathematics. It reports upon case studies of two schools which taught mathematics in totally different ways. Three hundred students were followed over three years and the interviews that are reproduced in the text provide an insight into what it meant to be a student in the classrooms of the two schools. The different school approaches are compared and analyzed using student interviews, lesson observations, questionnaires given to students and staff and a range of different assessments, including GCSE examiniations.