# All interest centres on perimeter

Extending Mathematical Ability through Interactive Whole Class Teaching By David Fielker, Hodder amp; Stoughton, #163;11.99

I'd been looking forward to this book, the latest in a consistently good series, Managing Primary Mathematics. David Fielker draws on a lifetime of experience, on transparent fascination with children's mathematical thinking and deep understanding of effective (if sometimes unconventional) teaching strategies. He offers a vision, some principles and some (almost) ready-made lessons.

At the same time, he insists that "this is my style, and I never expect everyone . . . to copy it". But the signposts are clear and sure; readers will be eager to see how it works in their classroom.

I, for example, could never get very enthusiastic about the topic of perimeter. Maybe I needed to approach it differently. Here are some ideas from Chapter 10: What triangles could we make with a perimeter of 12 units?Instantly, we're caught up in some "How many?" problems. How many different number-triples sum to 12? By a nice coincidence, the answer turns out to be 12 (but I had to decide what would count as "different"). So how many different triangles are there with a perimeter of 12? One of them has sides 3, 4, 5. Now that sounds familiar . . . but Pythagoras is another story, for next week perhaps?

How could we construct his most famous triangle accurately? Pupils might need to learn something about intersecting circles, and to acquire some skills with compasses. What else? Well 2, 3 and 7 also sum to 12, so can we draw that one? Apparently not! But why not? Which of the 12 number-triples do give triangles, then?

This gives something of the flavour of this delightful book. In the first chapter, the author argues that mathematically gifted children need enrichment (more depth, more responsibility) rather than acceleration.

He sets out some strategies to help teachers transform routine topics and exercises into richer and more challenging activities for these children - and others. The episodes with children recounted in this book (and in the hundreds of articles written by David Fielker in The TES and elsewhere) provide ample evidence that these strategies are not idle theory.

Most of these accounts (I've given the flavour of just one) indicate in some detail how a number of mathematical topics - chosen to embrace number, algebra, shape and probability - can be developed for enrichment activity, mainly at key stage 2.

A teaching approach that is good for able pupils turns out to be good for all. Conversely, it is worth remarking that (current orthodoxy notwithstanding) whole-class teaching as such is not a

major theme in this book; perhaps the publishers appended it to the title as an expedient afterthought.

No matter: this book is a feast, and one that I enjoyed enormously. I shall put it to very good use.

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

of London

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