Which is the more interesting number: 64 or 65? Brought up on a traditional diet of tens and units, then there is not much between the two. But having a strong "number sense" may lead you to seeing 64 as far more mathematically intriguing than boring old 65. Not only is 64 a perfect square, it is also a perfect cube and it is two to the power of six.
Julia Anghileri's book is all about ways in which we can help children develop such "number sense" and not only have effective strategies for calculating but also a sound "feel" for the structure of numbers. When the mathematics curriculum is being broken down into increasingly atomised objectives, this book is a welcome read with its emphasis on the bigger picture and how ideas connect. However, issues of progression are still addressed and many of the chapters provide a helpful overview of stages in children's understanding.
Understanding, as opposed to merely performing, is a theme that runs throughout the book. I particularly like Anghileri's distinction between calculating for problem-solving and calculating for exploring structure. While the National Numeracy Strategy may embrace these ideals, many mathematical activities still seem to focus only on calculation or calculation's sake. As someone once said, calculation should lead to insight. Asking whether a calculation leads to insight into a problem or insight into number structure has the potential for focusing children on learning rather than simply being able to complete "sums".
While there are plenty of ideas here for different ways of representing numbers to encourage the learning of number sense, this is not a teaching handbook of the sort that is full of classroom-ready lessons - it is more like a book on nutrition than a collection of recipes. Readers will have to develop their own activities based on the principles outlined: in a similar way children need to develop their own, personal, number sense.
Teaching Number Sense is a slim volume that can easily be read from cover to cover (and how many maths teaching books can you say that about?). Not all of the number curriculum is dealt with in the same detail: while strong on the four rules of arithmetic, it does not give the same depth of coverage to decimals, fractions and percentages. But any teacher in training or more experienced teacher wanting a sense of the bigger picture in teaching number should find this a good starting point.
Mike Askew is a lecturer in mathematics education at King's College, London