This valuable book is less wide ranging than its title. It focuses on gender equity, describing the developing situation around the world in chapters by leading members of the International Organisation for Women in Mathematics Education. They describe work to bring more girls to tackle, to succeed in, and to enjoy more advanced mathematics. The editors, Pat Rogers and Gabriele Kaiser, provide a nicely organised framework and commentary.

The first part of the book describes a number of programmes to help girls get more involved with mathematics; common features are a more diverse and problem centred approach to mathematical activity and single sex classrooms with a supportive, interactive climate. The second part offers a world tour with views from a fair range of culture; inevitably patchy, it serves its thought provoking purpose, showing the wide variety of circumstance and of approaches to changing it.

There is evidence of substantial progress over the last few decades, particularly in the prosperous anglophone countries from which many of the writers come. Indeed, in Britain and elsewhere, there are now important areas of more advanced mathematics in which girls are outperforming boys, as for so long in primary schools. Any complacency is misplaced - for example, there are still very few women mathematics professors and the imbalance in much of science and engineering remains large and stubborn.

The last few sections look at various feminist perspectives on mathematics and on its pedagogy. How should teaching be more female friendly? Should mathematics itself be redefined? These brief contributions are inevitably rather simplistic. For example, the interesting relationship between personal knowledge and absolute knowledge is treated as dichotomy - knowledge is either one or the other. In fact, mathematics has changed and is changing - for example, constructive proof now has increased prestige (partly because of computers), and the relativity of rigour is widely accepted. For education, many of the changes suggested here for girls are widely recommended for all students.

The book is thus of interest beyond its particular field. It provides a case study of how an area of discrimination can be identified and analysed,and of various practical ways in which substantial progress can be made towards ameliorating and later removing a range of serious problems. (Those concerned with ethnic equity may be forgiven for wondering if their challenges will prove more stubborn, noting that these authors seem to spring, predominantly though not exclusively, from prosperous white sections of “advanced” societies). Conversely, though gender is the issue here, many of the changes they seek are important for the better mathematical education of all children.

Two examples will suffice. One of the major themes of reform in mathematical education is “real problem solving” with its explicit attention to learning how to tackle practical problems of real concern, integrating your mathematics with other skills and knowledge. It is true that this kind of situated learning suits most girls more than learning to follow abstract rules; it also suits most boys better. It is now widely accepted as an essential component of a balanced curriculum “diet” - though less widely implemented. Co-operative learning provides a similar story - the need to work well in groups is generally seen as centrally important to both genders. Nonetheless, feminist perspectives have made a real contribution to these issues. Thus the work towards gender equity has both contributed to and gained from the mainstream of reform.

Some fundamental questions of feminism, and of equity in general, are noted but skirted around. For example - are women essentially different, or is it just social conditioning? Such issues fall between the stools of these multiple contributions - perhaps happily so because they can bury progress in theology. For pragmatic purposes, it suffices to say that the “spread” of abilities, or needs, in either group is wider than any essential differences between the group averages; people should thus be treated as individuals, not subject to stereotyping. That message comes through only occasionally; too often, women are discussed as a group.

The final chapter misfires. The editors seem to have had the excellent idea of a broad outward looking epilogue, linking the field to parallel concerns of the kind just mentioned. Perhaps through an excess of respect for the author, the result seems too self indulgent - Desert Island Disks with philosophy instead of music.

But the book is mainly well written and, for all who are concerned with improving mathematics education, well worth reading.

Hugh Burkhardt is currently based at the Universities of Nottingham and California in Berkeley.