Explain this
Mathematics as a Constructive Activity
How the publisher describes it:
“This book explains and demonstrates the teaching strategy of asking learners to construct their own examples of mathematical objects. The authors show that the creation of examples can involve transforming and reorganizing knowledge and that, although this is usually done by authors and teachers, if the responsibility for making examples is transferred to learners, their knowledge structures can be developed and extended. A multitude of examples to illustrate this is provided, spanning primary, secondary, and college levels. Readers are invited to learn from their own past experience augmented by tasks provided in the book, and are given direct experience of constructing examples through a collection of many tasks at many levels.”
Review by Steve Bishop
In brief:
The book provides a stimulating read - and provides some ideas to help stimulate mathematical thinking among students. It will be useful to teachers at all levels.
“The starting point is that mathematics is a constructive activity”
This book examines the strategy of ‘asking learners to construct their own examples of mathematical objects’. The starting point is that mathematics is a constructive activity and that students get most out of mathematics when they are actively engaged in constructing mathematics.
The book is replete with examples of such student activity - but not only that. Sixty-four tasks are provided within the book to make the reader stop, think and construct their own examples, such as: ‘Think of some integers that have only two factors’; ‘Construct a two-dimensional object that has a constant diameter but is not a circle’; and ‘Find at least six ways to cut a square into quarters’.
Reading this book is rather like being taken on a journey. The first chapter looks at what is meant by an example. In general the word example is used very broadly - it can ‘stand for anything from which a learner might generalize’ (p. 3). Chapter 2 describes ways in which teachers can ask students to generate their own examples by looking at classroom incidents. The next chapter looks at developing from individual examples to ‘example spaces’, which can be understood as a larder from which something appropriate can be chosen. This is then developed in chapter 4 by also considering counterexamples and ‘nonexamples’. The great thing is that the reader is encouraged not merely to be an observer of the journey, but to participate by thinking about the tasks.
Chapter 5 and 6 look at tools and strategies for making use of ‘learner-generated examples’. One great thing about the book is that it includes many classroom examples which give glimpses of how the approach can be used; this is particularly true of Chapter 6.
The final chapter examines maths as a constructive activity. Here many of the threads are drawn together.
One appendix provides some historical context, the other some suggestions and hints for the tasks. Unfortunately, only eleven of the sixty-four tasks were covered. There are nine pages of references, an author index and a subject index.
The book provides a stimulating read - and provides some ideas to help stimulate mathematical thinking among students. It will be useful to teachers at all levels.
Steve Bishop • Mathematics lecturer, City of Bristol College
Paperback: 248 pages
Publisher: Routledge; 1 edition (28 Jun 2005)
Language English
ISBN-10: 0805843442
ISBN-13: 978-0805843446
Product Dimensions: 22.6 x 15.2 x 1.3 cm
