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Developing Thinking in Geometry
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Developing Thinking in Geometry

First Edition
Edited by:


September 2005 | 288 pages | SAGE Publications Ltd

"All readers can use this book to reignite their fascination with mathematics. Fosters not only a curiosity about geometry itself but crucially focuses on how learners can actively engage in thinking about geometry and its central key ideas."
—Sylvia Johnson, Professor, Sheffield Hallam University

"Exudes activity and interactivity. A book for learning geometry, learning to think more deeply about geometry, and also about its teaching and learning."
—David Pimm, Professor, University of Alberta

Developing Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. Discussing key teaching principles, the book and its accompanying interactive CD-ROM include many activities encouraging readers to extend their own learning, and teaching practices.

Drawing on innovative approaches for teaching and learning geometry developed by the Open University's Centre for Mathematics Education, this resource is constructed around the following key themes:

  • Invariance
  • Language and points of view
  • Reasoning using invariance
  • Visualizing and representing

 
Introduction
 
BLOCK ONE
 
Invariance
 
Language and Points of View
 
Reasoning Based on Invariant Properties
 
Visualising and Representing
 
BLOCK TWO
 
Invariance in Measurement
 
Measuring Areas and Volumes
 
Geometrical Reasoning
 
Visualising
 
BLOCK THREE
 
Transformations and Invariants
 
Language and Points of View
 
Reasoning with Transformation Geometry
 
Visualising Transformations
 
BLOCK FOUR
 
Themes and Structure
 
Powers, Constructs and Strategies

'Geometry is often given less time in the teaching timetable than other aspects of mathematics. This book encourages practitioners to think about and raise its profile, indeed achieving what its title suggest' - Primary Practice

`This creative, innovative and fascinating book/CD package is one you "MUST BUY". All prospective, new and experienced teachers of mathematics can use it to transform their teaching. All readers can use it to reignite their fascination with mathematics. This book fosters not only a curiosity about geometry itself but crucially focuses on how learners can actively engage in thinking about geometry and its central key ideas. Symbolically, the book/CD invites readers to engage actively with it, so that its very style embodies the approach to thinking about geometry that it advocates.

The structure of the book is helpful in supporting readers who want to dip into the book for a particular topic or theme and the authors have interspersed geometric, reflective and pedagogic activities woven into a rich interplay between the ideas themselves and ways in which teachers might facilitate learners' engagement with the ideas.

By making the focus of this book, thinking about geometry, the authors have highlighted the dimensions of geometric activity that enable us to engage. Throughout, the emphasis is on meaning making and the ways in which we visualize, represent, communicate and reason about geometric ideas. Images abound and the reader is encouraged to conceive geometry both dynamically and statically. Communication and meaning making are the essence of any learning and the authors have been very successful in conveying that message' - Professor Sylvia Johnson, Sheffield Hallam University


"This book contains an amazing collection of geometric problems that will interest and challenge most readers, though its pedagogical context is designed primarily for mathematics teachers. Part of a three-book series written by the Open University's Centre for Mathematics Education, it focuses on geometric thinking--what it means, how to develop it, and how to recognize it. Using curricular and research documents as a foundation, the book's structure thoroughly develops four key ideas of geometric thinking: invariance, geometric language and points of view, reasoning, and visualizing and representing. Using a great number of interesting and clever activities (many provided on the accompanying CD-ROM), each key idea is developed and discussed thoroughly, and readers are strongly encouraged to participate actively as both problem solvers and geometric thinkers. An additional section discusses the related pedagogical issues surrounding each key idea, followed by two concluding sections that provide a unified structure for the four geometric themes and many teaching strategies that were developed. Again, the book is exemplary in its provision of rich problems and pedagogical commentary, offering a welcome perspective on geometrical thinking that spans the primary through the high school grades. Summing Up: Highly recommended."

J. Johnson
Western Washington University
CHOICE

An excellent book; highlighted some of the key issues with geometrical reasoning.

Miss Syreeta Charles-Cole
Teacher Education Department, Carshalton College
October 13, 2016

This text is a recommended read for student teachers, those with an interest in geometry and for the primary mathematics specialist. The book introduces the ‘big ideas’ of geometry to the reader with a varied amount of activities that help build geometrical understanding through reflection and visualisations. The book also contains a CD-ROM with an array of additional material to support geometrical understanding, including interactive activities and audio files.

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

I would recommend the book for readers who want to develop their knowledge in geometry. 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 geometrical tasks and a chapter where some students' geometrical solutions were shown in detail and aspects of developing students' thinking in geometry discussed in some detail. Overall definitely a recommended text for my students.

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

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