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Mathematics education in different traditions: A comparative study in Asian and Western countries. Introduction Mathematics is a subject taught in every country of the world, and increasing globalisation is encouraging the assumption of universalism in mathematics education. The increase in journals and books about mathematics teaching, the multitude of conferences in every part of the world, the availability of materials via the World Wide Web, and the activities of multinational computer companies all increase the pressure for adopting similar practices in mathematics teaching around the world. International comparative studies such as SIMS and TIMSS also emphasise a canonical curriculum, since in order for comparisons to be sensibly made, there must be a large amount of uniformity. At the same time, however, the globalisation processes are producing reactions from mathematics educators in many countries who are concerned that regional and local differences in educational approach are being eradicated. This is not just a mathematical ecology argument, about being concerned that the rich global environment of mathematical practices is becoming quickly impoverished. It is also an argument about education, which recognises the crucial significance of any society’s cultural and religious values, socio-historical background and goals for the future, in determining the character of that society’s mathematics education. As research in mathematics education has increased in quantity and scope, we can see developments in areas such as ethnomathematics, and comparative studies such as the SIMS and TIMSS studies, that have produced data indicating that there may be some systematic reasons for differences in achievements and practices between countries. In part these differences can be attributed to the availability of educational resources, to the levels of teacher training and to aspects such as teacher ‘job satisfaction’. However one aspect of difference that is increasing in interest concerns what is euphemistically referred to as the East/West difference. Countries such as Japan, Korea, China, and Singapore consistently show differences in mathematical achievements and practices from countries in Europe, North America and Australasia. Whilst this state of affairs may be both startling and worrying to economically-minded politicians in the West, it is also surprising and intriguing to mathematics educators in both East and West countries. The focus of this interest is on the differences in educational traditions, which have cultural and social implications for the practices of mathematics education. This not a narrow interest in how to improve scores on tests, but a deeper interest about what each tradition can learn from the other, as well as what others can learn of relevance in their own traditional contexts. We all learn by contrast, and contrasts in mathematics education practices can tell us much about the interplay of cultural tradition and modern technological values in the context of mathematics teaching everywhere. This ICMI study should not therefore be seen as a narrow comparison between two small and select groups of countries for their own benefit. This study takes the East/West contrast as a case, to reveal what can be learnt to benefit mathematics education everywhere. It will bring together, both virtually and in reality, a group of scholars already involved with some aspects of this difference, and will encourage the writing of a report that will consider East/West contrasts from multiple perspectives. The challenge will be not just to record differences between countries’ practices, but to account for difference in ways that reveal the nature and role of significant contrasts in values, beliefs, interpretations and evaluations.