High aims of the low lands
England got used to Dutch invasions during the 17th-century when Admiral Tromp sailed boldly up the Thames, causing near panic in the capital: modern Dutch invasions tend to be more benign. What distinguishes Julia Anghileri's collection is the way she interleaves chapters from five British "top guns" in mathematical education with contributions from five equally distinguished Dutch educators.
Margaret Brown's survey of influences on the teaching of number in England provides a picture of repeated political interference that would be unthinkable in the Netherlands. There, curriculum is developed through what Koeno Gravemeijer, in a powerful chapter, calls "a dialectic between theory and practice". Though some of the changes that have rippled through maths teaching since the National Numeracy Strategy was introduced could be viewed as taking us closer to a continental model, not all have been assimilated or fully understood before being implemented.
Meindert Beishuizen has done more than anyone to alert this country to the potential of the empty number line, but hardly has it had time to approach sacred cow status than he is provocatively asking whether real mastery of place-value methods (such as decomposition) might not be preferable to low-level mastery of sequential ones, even if number-line based. Real mastery of any approach is likely to be better, but which is easier to master, sequential or split-tens models? We do not have a glorious history of success with place-value approaches.
What we do is increasingly prescribed from the centre, whereas the Dutch enjoy considerable freedom. But their schools work from very detailed, government-approved textbooks at a time when British teachers are being exhorted to move away from over-reliance on texts. Crucially, they see the maths curriculum as a "work under construction", subject to a constant process of research, trial and improvement by practitioners and researchers (who in Holland are not above getting involved in the writing of texts for teachers).
Dutch texts have to be government-approved before they can be used in schools. Ian Thompson asks whether the time has arrived when we too should have official approval of all mathstexts, though he does not answer his own question.
It certainly works for the Dutch. One reason why the Netherlands has greater freedom from political interference is that their methods have elevated them to premier league status in international comparisons of arithmetic: unlike us, they are up there with Japan and Singapore.
This book confirms that educational research has sharpened its focus and is increasingly willing to get its hands dirty at classroom level, which makes it of immediate use and relevance to classroom teachers. Many chapters exemplify this.
Mike Askew reflects on learning and teaching but shifts the perspective to that of the pupil, pointing out that although we talk about the "daily maths lesson" as if it were a uniform experience, what is experienced by pupils can be very different.
Kenneth Ruthven, in another powerful chapter, argues for a "new numeracy", including a fresh attempt to make our curriculum calculator-friendly. (It is certainly hard for teachers to develop all the calculator skills listed in the numeracy strategy Framework if they are not allowed to start until Year 5 - no wonder the calculator paper is done so badly at key stage 2.) Ruthven puts forward an exciting new model: a division procedure employing not one but two empty number lines, arranged vertically side by side, allowing the user to keep track of two simultaneous counts, rather as some calculators show a double count when using the constant function. This could help develop understanding of both multiplication and division. He admits it needs trialling and development of the type called for by Askew and Gravemeijer; an exciting prospect for teachers who want new ways to inject meaning and understanding into calculator and non-calculator division. I cannot wait to try it out.
This book is for anyone who wants to understand the background to recent developments, or gain an insight into where we might go next: it is likely to be influential. In 1667, popular outcry against the conduct of the war, together with the outbreak of plague, forced Charles II to surrender to the Dutch. Though it raises as many questions as it answers, this book confirms that while the state of the art has moved on, we have some way to go. Has the time come to surrender to Dutch influence again?
Laurie Rousham is numeracy consultant in Suffolk