About mathematics education in the United States it is a sad (but true) commonplace that it is demonstrably inferior to that in many other countries. Given the consensus that mathematics, science and engineering expertise will allow countries to dominate the world in the future, the conclusion that the United States will not be able to compete is a valid one. South Korea is one country that consistently ranks far higher than the United States, so it is logical that any attempt by American educators to understand the differences and reduce them begin with a study of how mathematics education is done in South Korea.

There are some good points in this volume, but the variation in quality and value of the material is strikingly similar to what one finds in compilations written by a collection of American mathematical educators. Some of it is extremely tedious to read and not terribly informative. Other sections are very informative, specifically those on standards, national curriculum and some of the learner based activities.

After reading the sections on the contents of the curriculum as well as the goals and how their achievement is measured, one of the conclusions that I reached was that in many ways the higher level of mathematics achievement is not based on a more extensive or deeper curriculum, but on other factors such as the national uniformity of the curriculum and the consequent smaller variability in the skills of the students as they arrive at the next level. American teachers are generally forced to teach to the middle of the skill range of their students, boring the bright while the weaker fall further behind. If that range is narrowed, then all have a chance of reaching a level of competence and the teacher can spend less time in aiding the weaker students, leaving more time to present new material.

When I was in the K–12 system there were many instances when transfer students arrived and struggled for months to learn what we were doing. I personally experienced this in my first year of junior high, which at the time was seventh grade. We were still doing basic arithmetic in sixth grade and we were overwhelmed when we started mathematics in seventh grade and were combined with students from other elementary schools. Together, we formed the bottom fourth of our mathematics class and I did not recover my previous high standing in mathematics until ninth grade.

“National will” is a concept that has been improperly used through the course of history, yet that does not mean that it does not have value. In this book you can learn some of the reasons why South Korea has such national high achievements in mathematics and why the United States trails. I was particularly struck by the national standards of assessment, something I detested when I had to be a part of it when I was teaching full-time. The way the Koreans described it, assessment there was nothing like the nonsensical game playing that the American assessment process seemed to degenerate into.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing *The Journal of Recreational Mathematics*. In his spare time, he reads about these things and helps his daughter in her lawn care business.