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Developing Thinking in Algebra
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Developing Thinking in Algebra



April 2005 | 336 pages | SAGE Publications Ltd
'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


 
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

‘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


The first chapter 'First encounters with expressing generality' gave helpful examples and clear explanations which show the link between generalisation and algebra. Hopefully this will demystify algebra for our students. The mathematical tasks also help students engage in the topic, making the content more accessible and also providing potential lesson activities.

Mr Richard Harvey-Swanston
School of Education, Brighton University
September 28, 2016

The book is practical in its delivery of how to change your own view and thinking about the teaching of algebra as a classroom practitioner through hands-on activities and teaching methods. This research-based text is a recommended read for student teachers, those with an interest in algebra and for the primary mathematics specialist.

Mr Manish Kothari
School of Edu. Theology and Leadership, St Mary's University, Twickenham
March 3, 2016

This book will be an invaluable resource for students when they are getting to know the diverse range and experiences of learners and issues surrounding the teaching of algebra. Many student teachers automatically assume that the teaching of algebra is very easy as they have often understood and enjoyed from an early stage but the reality is often much more complicated when they undertake classroom practice.

Mr Andrew Gallacher
Faculty of Education, Glasgow University
March 4, 2013

I just received the book today, so I can't write a feedback yet.
In a few weeks ...
thank you,
Jeanne

Dr Jeanne Albert
Al-Quds Bard Master of Arts in Teaching Program, University of Al-Quds
February 20, 2013

I would recommend the book for readers who want to develop their knowledge in algebra. This book allows me to explore different ways to solve problem and how to explain it.

Mr Frederic Turban
Mathematics, Bury College
March 8, 2012

I very much liked the structure of the book and the fact that it had many examples and points of reflection. That said I would have liked to see a chapter about 'rich' mathematical algebraic tasks and a chapter where some students' solutions were shown in detail and aspects of developing students' thinking in algebra discussed in some detail. Overall definitely a recommended text for my students.

Dr David Cooper
Education (Walsall), Wolverhampton University
February 22, 2012

Sample Materials & Chapters

Extra exercises from the book

Chapter 1


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