Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and 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 and also has implications for a wider range of students. These are the ideas that really matter, that students get stuck on, and that can be obstacles to future learning. It shows how students learn, why they sometimes get things wrong, and the strengths and pitfalls of various teaching approaches. Contemporary high-profile topics like modelling are included. The authors are experienced teachers, researchers and mathematics educators, and many teachers and 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 and connects them to examples of classroom tasks that address important learning issues about particular mathematical ideas.
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.
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