Given that much of these recent math reforms, including these two documents, have been motivated by international comparisons, Foundations for Success coming straight out of those comparisons, it is important to examine these comparisons and consider what they can, and cannot, tell us about mathematics education in the US. This paper will consider some of the literature of international comparisons, looking at how these international comparisons have been drawn upon for these two standards documents, and thinking about what this could mean for US mathematics education. Comparitive studies that have been undertaken on three countries in particular will be the focus of this exploration, because these countries came in at the top of the TIMSS study, and are now often referred to as the top achievers in mathematics: Japan, Singapore, and South Korea.
Because a great amount of emphasis in both standards documents, but particularly in the Achieve standards, is placed on graded curriculum, this exploration will begin with what international comparisons have said about curriculum. The main question to be raised here is, do these top performing countries really follow the challenging curriculum that Achieve claims they do? After looking at these curricular issues, I will then move on to look at other factors that may influence students' mathematics achievement. The question I will be asking then is, what other reason for the top performance of these countries have been identified? Finally, I will look more in depth at one area which has been identified as extremely important in a number of these international comparative studies, charactersitics and preparation of teachers, asking, what difference does the teacher make? The final discussion will tie these questions back to the standards documents to consider how the international comparisons are being used and whether this use is appopriate.