Big ideas in the mathematics curriculum for older school students especially those that are hard to learn & hard to teach are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 & also has implications for a wider range of students. These are the ideas that really matter that students get stuck on & that can be obstacles to future learning. It shows how students learn why they sometimes get things wrong & the strengths & pitfalls of various teaching approaches. Contemporary high-profile topics like modelling are included. The authors are experienced teachers researchers & mathematics educators & many teachers & researchers have been involved in the thinking behind this book funded by the Nuffield Foundation. An associated website hosted by the Nuffield Foundation summarises the key messages in the book & connects them to examples of classroom tasks that address important learning issues about particular mathematical ideas.