Children’s Mathematical Thinking in the Primary Years. Edited by Julia Anghileri Cassell 35. - 0 304 33258 5 12.99. - 0 304 33260 7

This book is a collection of chapters by lecturers who contribute to mathematics courses at Homerton College and is edited by the head of the mathematics department.

It is addressed to students, teachers and parents and claims to be jargon-free. This is a difficult aim to aspire to and, although it presents mathematics as accessible, the book would be hard going for most parents.

For students and teachers, however, this is a book which, at least in six of its nine chapters, takes mathematics education beyond what to teach and how to teach it and deals with current issues such as surround the use of calculators, the role of language, mathematical investigations, data handling and the symbolic representation of mathematical processes.

The authors explicitly address their writing to a readership beyond England and Wales through somewhat self-conscious references to the American curriculum and evaluation standards for school mathematics and to the Scottish national guidelines for mathematics 5-14 as well as to mathematics in the national curriculum.

Quotations from these documents are rather obtrusive in the introduction and in the rather bookish first chapter by Julia Anghileri. However, the feeling of plodding is lifted by the excellent chapter by David Whitbread which touches on many themes taken up in more detail by separate later chapters. Whitbread’s writing makes exciting reading for anyone interested in mathematics education and would be particularly stimulating for student teachers.

His overall theme is “emergent mathematics”, a phrase used to reflect the same approach to mathematics as “emergent writing” does to children’s writing. The approach stresses the processes of thinking rather than the product and it encourages children to develop and reflect upon their mathematical strategies. He presents the argument for the value of this approach through examples from research and pertinent personal anecdotes which illustrate well the problems of simply teaching children the procedures for calculating answers.

He also stresses the role of talk, a theme taken up in more detail by Tim Rowland in a chapter on language. Rowland looks first at words used both within an “everyday” and in a specifically mathematical context and then at the language children use to talk about mathematics and the language teachers use in communicating with pupils during mathematical activity.

Julia Anghileri’s second chapter continues the theme of language used by teachers, going into some detail on the words used to describe addition, subtraction, multiplication and division. She shows by examples that what adults regard as alternative ways of saying the same thing (such as “12 divided into 3” and “12 divided by 3”) are not always interpreted by children as meaning the same thing. As in other chapters there are selected references to texts where these points are taken further.

Touching on the use of calculators, Anghileri’s chapter links to the one by Laurie Rousham on calculators in which he describes the CAN (Calculator-Aware Number) curriculum project. This very useful chapter is full of ideas for students, teachers and indeed parents, providing examples of children using calculators in doing mathematics as opposed to using calculators to do the mathematics for them and of children using calculators creatively.

The final three chapters are rather more text-bookish, giving accounts of methods of teaching data handling, algebra and problem-solving, rather than the research-based discussion of the earlier chapters.

Variability is no doubt inevitable in a book written by a closed group, the members of one department. Since the chapters are independent of each other there is no attempt to bring them together or to show how one issue interacts with another. If there is an overall thread it is the reference to Bruner’s three modes of representation - enactive, iconic and symbolic - rather than the explication of constructivism, which is mentioned in the first chapter and only once thereafter. Overall, however, there are sufficient interesting points of view as well as ideas for mathematical activities to make this a useful book for experienced as well as novice primary teachers to dip into.