Developing Thinking in Geometry
- Sue Johnston-Wilder - The Open University
- John Mason - The Open University
`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' - Professor Sylvia Johnson, Sheffield Hallam University
'This book exudes activity and interactivity. Moreover, it provides challenge in the context of a significant pedagogy, one that is not just present but actually made explicit. It is undoubtedly a book to learn geometry with, but also one to learn to think more deeply about geometry, about its nature and essence, and also about its teaching and learning' - David Pimm
Developing Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. As well as discussing key teaching principles, the book and accompanying interactive CD include many activities that encourage readers to extend their own learning, and consequently their teaching practices.
The book is constructed around the following key themes:
- invariance;
- language and points of view;
- reasoning using invariance;
- visualising and representing.
These themes draw 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 geometry.
This is a 'must have' text for all primary mathematics specialists, secondary and Further Education mathematics teachers and their support staff. Anyone who wishes to create an understanding and enthusiasm for geometry based upon firm research and effective practice, will enjoy this book.
This is the course reader for the Open University Course ME627 Developing
Geometric Thinking
'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."
An excellent book; highlighted some of the key issues with geometrical reasoning.
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.
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.
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.
