The international New Math developments between about 1950 through 1980, are regarded by many mathematics educators and education historians as the most historically important development in curricula of the twentieth century. It attracted the attention of local and international politicians, of teachers, and of parents, and influenced the teaching and learning of mathematics at all levels-kindergarten to college graduate-in many nations. After garnering much initial support it began to attract criticism. But, as Bill Jacob and the late Jerry Becker show in Chapter 17 of this book, some of the effects became entrenched.

This volume, edited by Professor Dirk De Bock, of Belgium, provides an outstanding overview of the New Math/modern mathematics movement. Chapter authors provide exceptionally high-quality expositions and analyses of the rise of the movement, and of subsequent developments, within a range of nations. The first few chapters show how the initial leadership came from mathematicians in European nations and in the United States of America. The background leaders in Europe were Caleb Gattegno and members of a mysterious group of mainly French pure mathematicians, who since the 1930s had published under the name of (a fictitious) Nicolas Bourbaki. These Bourbakists emphasized the need for a strictly deductive approach to mathematics starting from basic structures such as groups, rings, fields, and vector spaces.

In the United States, there emerged, during the 1950s (and as David Roberts shows, in Chapter 2 of this book, even before that) various attempts to improve U.S. mathematics curricula and teaching, especially in secondary schools and colleges. This side of the story climaxed in 1957 when the Soviet Union succeeded in launching Sputnik, the first satellite. There was a national outcry that the nation had obviously fallen behind in mathematics and science education. One result was that the USA agreed to help finance a major international conference which was held at Royaumont, in France, in 1959. A Euclid must go demand, expressed by the Bourbakist leader Jean Dieudonne in a keynote address, reverberated around the world, but the main message coming from Royaumont was much more than that. This book pays due attention to the rise (between 1957 and about 1970) and the decline of the movement in both Europe and the United States-and especially to opposition coming from many mathematicians.

Chapters 1 and 3 in this volume (both by Dirk De Bock) make clear that from the outset the New Mathematics had European and North American origins-and the emphases were different. There were further meetings emanating from Royaumont and, gradually, the messages were heard, and to different extents, put into practice in many other nations around the world. This book attends to the various narratives in a wide range of those nations. As such, it provides essential reading for all mathematicians, mathematics educators, curriculum theorists, and others interested in curriculum diffusion.

Undoubtedly, this is a landmark publication in education. The foreword was written by Professor Bob Moon, one of a few other scholars to have written on the New Math from an international perspective. The final epilogue chapter, by Professor Geert Vanpaemel, a historian, draws together the overall thrust of the volume, and makes links with the general history of curriculum development, especially in science education, including recent globalization trends.