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Developing Understanding in Primary Mathematics key stages 1 amp; 2 Edited by Andrew Davis and Deidrie Pettitt Falmer Press pound;12.95 0 7507 0358 X.

It is suggested that the intended audience for Developing Understanding in Primary Mathematics is the reflective primary teacher. However, given the quantity of information currently in schools and the pressures on teachers' time, this book is more likely to be of interest and value to those teachers who have the responsibility for co-ordinating mathematics in school and who wish to stimulate discussions during school-based staff development.

In Chapter four, a number of open-ended investigations which build on the constructivist theme of the book are suggested for Inset. These offer teachers the opportunity to work together in groups to re-examine their understanding of mathematical concepts. The sub-title "Key Stages 1 amp; 2" might attract teachers who are looking for support with the early stages of mathematics in the national curriculum but actual references to anything specifically related to the national curriculum or key stages 1 and 2 are non-existent. This is not necessarily a fault and it may even be a relief, but it could mislead potential readers.

The book carries extensive discussions of the role of stories, drama, pattern, games and drawings in the development of young children's understanding of mathematics. The chapter "Children Drawing" may be of interest in helping teachers to respond to different features of infant art, but the relationship with mathematics is tenuous.

In discussing the role of stories and drama as techniques for the development or consolidation of mathematical skills, the authors are limited by the essentially open-ended nature of these techniques. They discuss the place of dramatic play in general terms and suggest a number of ideas for use in the classroom but they cannot be more precise. How these ideas develop in individual classrooms depends on the interaction between teachers and pupils. There is always the danger that in unskilled hands both the drama and the mathematics could be trivialised. The chapters on constructing patterns and games are more conventionally linked to mathematics and include useful ideas to help teachers extend their teaching beyond the use of commercial schemes.

There are two fundamental messages from the authors. One relates to the role of the teacher as an essential ingredient in helping children to build on their existing skills and to realise their potential. The other emphasises the importance of talking and listening at the early stages of mathematical development and stresses the need to ensure that children understand and use appropriate vocabulary. In this respect it is disappointing that any mathematics educator in Britain could write of teachers using "the American ploy of asking children how they arrived at answers and if anyone else could suggest another way". Surely these are now standard questions which teachers use to help children clarify their own thinking.

Finally, syntax: certain sections would have benefited from much more vigorous editing. I was continually stopped by long convoluted sentences with numerous qualifying clauses which took time to disentangle. This interfered with the assimilation of some stimulating thoughts.

Marion Devine is Senior Researcher, Scottish Council for Research in Education.

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