Developing Thinking in Algebra: (Published in Association with The Open University)

′This is an incredibly interesting and thought provoking book. Intended for anyone interested in developing their own mathematical thinking, or of the students they teach, whether at a primary level or right through to FE. The book is a delightful blend of theory and practice - encouraging the reader to participate, to solve problems and to develop their own thinking′ - Peter Hall, Imberhorne School, East Grinstead′ 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

Table of Contents:
PART ONE First Encounters with Expressing Generality Using Mathematical Powers; Meeting Mathematical Themes Using Symbols Depicting Relationships PART TWO More Experience of Expressing Generality More on Powers, More on Themes Symbol Manipulation Changing Representations PART THREE Yet More Expressing Generality Solving Problems Reasoning Graphs and Diagrams PART FOUR Themes and Structure Powers, Constructs and Strategies Final Reflections

Review :
‘Mason, Graham, and Johnston-Wilder have admirably succeeded in casting most of school algebra in terms of generalization 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 generalisation and of the power of using this as a lens not just for algebra but for all of mathematics!’ - Professor Carolyn Kieran, Département de Mathématiques, Université du Québec à Montréal ′This is an incredibly interesting and thought provoking book. Intended for anyone interested in developing their own mathematical thinking, or of the students they teach, whether at a primary level or right through to FE. The book is a delightful blend of theory and practice - encouraging the reader to participate, to solve problems and to develop their own thinking′ - Peter Hall, Imberhorne School, East Grinstead