International research is used to inform teachers and others about how students learn key ideas in higher school mathematics, what the common problems are, and the strengths and pitfalls of different teaching approaches. An associated website, hosted by the Nuffield Foundation, gives summaries of main ideas and access to sample classroom tasks.

1. Introduction to key ideas in teaching mathematics ; 2. Relations between quantities and algebraic expressions ; 3. Ratio and proportional reasoning ; 4. Connecting measurement and decimals ; 5. Spatial and geometrical reasoning ; 6. Reasoning about data ; 7. Reasoning about uncertainty ; 8. Functional relations between variables ; 9. Moving to mathematics beyond age 16

`Based on key ideas in curriculum content, associated research on learning, and mathematical reasoning in a range of topics, this book provides an exciting resource for professionals in mathematics education. Its links to the supporting web resource are invaluable for teachers of mathematics in a wide age range. I recommend it to all who grapple with engaging students with mathematics and enabling their development of mathematical understandings.' Barbara Jaworski, Professor of Mathematics Education, Loughborough University

A resource for understanding the key ideas in school mathematics for students aged 9 to 19 Quick links to classroom tasks throughout the book via a website for practitioners, developed with the Nuffield Foundation Written by ex-school teachers who are active researchers and stay in close contact with teachers and schools Summarises research so that readers can base their work on up-to-date knowledge about learning Extensive bibliography

Professor Anne Watson taught mathematics in secondary schools for 13 years and since then has been a mathematics educator at the University of Oxford. She has always worked closely with teachers as well as researching mathematical learning, and has run numerous seminars and workshops throughout UK and abroad. Associate Professor Keith Jones taught mathematics in secondary schools for 12 years, during which time he was involved in curriculum development. Since then he has been a mathematics educator, first at the Institute of Education, London and now at the University of Southampton. He has led initial teacher courses in mathematics and his research involves working with teachers and students in schools and colleges. Professor Dave Pratt taught mathematics in secondary schools for 15 years and was involved in curriculum development, especially in relation to the use of technology in mathematics classrooms. Since then he has been a mathematics educator, first at the University of Warwick and then for the last three years at the Institute of Education, London. He has led PGCE courses for the initial teachers training in mathematics and his research involves working with young students.

A resource for understanding the key ideas in school mathematics for students aged 9 to 19 Quick links to classroom tasks throughout the book via a website for practitioners, developed with the Nuffield Foundation Written by ex-school teachers who are active researchers and stay in close contact with teachers and schools Summarises research so that readers can base their work on up-to-date knowledge about learning Extensive bibliography