Shapes from three different angles

CREATIVE MATHEMATICS: Exploring Children's Understanding. By Rena Upitis, Eileen Phillips and William Higginson. Routledge Pounds 12.99

Tim Rowland on how a primary teacher, a researcher and an education specialist collaborated in a series of classroom projects at a school in Vancouver, Canada

Creative Mathematics: Exploring Children's Understanding is the outcome of a collaboration between Rena Upitis, the researcher; Eileen Phillips, the primary school teacher; and William - Bill - Higginson, the mathematicseducation specialist. Rena travels across Canada from Kingston to Vancouver, to spend a year working on maths projects in Eileen's Year 45 class. Each chapter focuses on one of their shape-oriented projects (on topics such as tessellations, animation, kaleidoscopes), beginning with separate accounts from Rena and Eileen of what actually happened in the classroom, concluding with some reflections, fresh angles and connections by Bill, Rena's university colleague back in Kingston. Part of the novelty of the narrative is that Bill witnesses nothing of the work in action, although he sees some of the products and is in regular communication with Rena.

So, what is the sum of these parts? At the most basic level, here is a book full of bright ideas for the mathematics classroom, exciting and colourful projects, fun maths that will do wonders for the maths display corner. But that is only the tip of the iceberg, for the authors are at great pains to convey not only the what of these projects, but also the why. The purpose of the book is to be a manifesto rather than a menu. It is about the energy and creativity of motivated children. The commitment inherent in the fluent writing is revealing of the different qualities of the dramatis personae as their plot unfolds.

Rena is cast as the artist and musician, the ideas-person who lights up the classroom with her enthusiasm. It might require a self-confident teacher to cope with having Rena share her professional space. A teacher rather like Eileen in fact, possessed with a love of children and of mathematics (in that order), coupled with a fierce honesty and realism about the workings of a primary classroom.

While Eileen's commitment to the projects is evident, she occasionally reminds us of the practicalities of one teacher working with 30 children. For example, she reflects that "At this time, I do not think I will attempt an animation project...on my requires too much guidance, overseeing and careful mediation". (She proceeds to consider circumstances that would make it manageable).

Finally, there is Bill, wise and eclectic, a different kind of ideas-person with an encyclopaedic knowledge of his library and a fascination for the potential of new technologies.

Two major, related themes running through the book are reality ("real" maths as opposed to textbook maths) and authenticity.

For Rena, the intrinsic, aesthetic appeal of the materials she uses with children is an essential pedagogical and mathematical ingredient. Maths takes on meaning for her through the mediation of the senses, in music, art and design, and these projects set out to develop mathematical thinking in media associated with such contexts. Yet there is a tension here, because a valid and stimulating classroom activity with "authentic" materials does not of necessity stimulate thinking of a mathematical kind. Significant mathematical connections are very evident in some of the projects, but not in all ; even Bill is occasionally hard pressed for comment, and goes off at a tangent about games or the Internet.

Many readers will enjoy a delicious sense of deja vu, recalling pre-SATS primary maths projects which valued and aimed to promote creativity as well as compliance. Eileen reports similar pressures in Canada, and her determination not to be compromised. Given the current angst about numeracy, shape and space could well be marginalised in the next revision of the maths national curriculum. This book reminds us of what we could be about to lose.

Tim Rowland lectures in primary mathematics education at the Institute of Education, University of London

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