Mathematics as a Constructive Activity

Learners Generating Examples

By: Anne Watson, John Mason

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Paperback | 17 May 2005 | Edition Number 1

At a Glance

Paperback
244 Pages

Dimensions(cm)
22.86 x 15.24 x 1.3

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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. Classroom stories show the practicalities of introducing such shifts in mathematics education. The authors examine how their approach relates to improving the learning of mathematics and raise future research questions.

*Based on the authors' and others' theoretical and practical experience, the book includes a combination of exercises for the reader, practical applications for teaching, and solid scholarly grounding.
*The ideas presented are generic in nature and thus applicable across every phase of mathematics teaching and learning.
*Although the teaching methods offered are ones that engage learners imaginatively, these are also applied to traditional approaches to mathematics education; all tasks offered in the book are within conventional mathematics curriculum content.

Mathematics as a Constructive Activity: Learners Generating Examples is intended for mathematics teacher educators, mathematics teachers, curriculum developers, task and test designers, and classroom researchers, and for use as a text in graduate-level mathematics education courses.

Industry Reviews

"...found this book enlightening and delightful, useful for the teacher and thought provoking for the researcher....one of the most enjoyable and enlightening aspects of the book, namely, the more than sixty mathematical tasks sprinkled between it covers."
-International Reviews on Mathematical Thinking

"The authors...describe this text as being 'about the teaching strategy of asking learners to construct their own examples of mathematical objects.' They 'show not only can all learners construct mathematical objects, but the act of construction can engage learners who might otherwise be passive and uninterested.' Recommended."
-CHOICE

"The book is a worthy addition to any library. It will appeal to a diverse audience: Anyone who enjoys the thrill of communicating and sharing the satisfaction of unanticipated discoveries through the act of constructing examples will welcome the book."
-Mathematical Thinking and Learning

"I have read the book both as a mathematics educator, and, more recently, as a teacher educator. Both I and my students have been constantly surprised, as we read each chapter, at how applicable, fresh, and generative the idea of using learner-constructed examples in the classroom has been....Everyone, from the kindergarten to the high school teacher, and from the special education consultant to the doctoral student, has found ideas to work with, to try, and to challenge and improve their own practices."
-Nathalie Sinclair
Michigan State University

"....I found this book enlightening and delightful, useful for the teacher and thought-provoking for the researcher." --Michael N. Fried, ZDM 2006 Vol. 38

"The book is a worthy addition to any library. It will appeal to a diverse audience: Anyone who enjoys the thrill of communicating and sharing the satisfaction of unanticipalted discoveries through the act of constructing examples will welcome the book."--Mathematical Thinking and Learning, Vol. 8, No. 4

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