Table of Contents

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

Reviews

′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."
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