Developing Thinking in Algebra

′Mason, Graham, and Johnston-Wilder have admirably succeeded in casting most of school algebra in terms of generalisation activity? not just the typical numerical and geometric pattern-based work, but also solving quadratics and simultaneous equations, graphing equations, and factoring. The authors raise our awareness of the scope of generalization and of the power of using this as a lens not just for algebra but for all of mathematics!′ - Professor Carolyn Kieran, Departement de Mathematiques, Universite du Quebec a Montreal

Algebra has always been a watershed for pupils learning mathematics. This book will enable you to think about yourself as a learner of algebra in a new way, and thus to teach algebra more successfully, overcoming difficulties and building upon skills that all learners have.

This book is based on teaching principles developed by the team at The Open University′s Centre for Mathematics Education which has a 20-year track record of innovative approaches to teaching and learning algebra. Written for teachers working with pupils aged 7-16, it includes numerous tasks ready for adaption for your teaching and discusses principles that teachers have found useful in preparing and conducting lessons.

This is a ′must have′ resource for all teachers of mathematics, primary or secondary, and their support staff. Anyone who wishes to create an understanding and enthusiasm for algebra, based upon firm research and effective practice, will enjoy this book.

This book is the course reader for The Open University Course ME625 Developing Algebraic Thinking

John Mason has led the Centre for Mathematics Education in various capacities for fifteen years. His principal focus is thinking about mathematical problems, and supporting others who wish to foster and sustain their own thinking and the thinking of others. Other interests include the study of how authors have expressed to students their awareness of generality, especially in textbooks on the boundary between arithmetic and algebra, and ways of working on and with mental imagery in teaching mathematics.

Alan Graham has worked in Mathematics Education at the Open University since 1977. Before that he taught mathematics in a secondary school. He has also worked on a Schools¹ Council Project Project on Statistical Education (POSE) based at Sheffield University. He has taken a leading role in producing several innovative OU packs aimed at teachers. He has written over 20 short plays for BBC Schools Radio under the series title Calculated Tales. Over the last 10 years, his work has concentrated on two main areas, Statistics and Graphics calculators. He has published numerous books in these and other areas, including Teach Yourself Statistics, Teach Yourself Basic Maths and the Calculator Maths series.

Sue Johnston-Wilder is a Senior Lecturer at the Centre for Mathematics Education at the Open University. Her main interests are the role of technology, history and modelling in promoting understanding of mathematics and of statistical processes, the professional development of teachers, particularly developing deeper understanding of mathematics through new technology, and the recruitment and retention of Maths teachers. She has authored three books and has contributed articles to many more books and journals.