Howard, I got to hear James Stigler and Harold Stevenson present about their case studies--in conjunction with TIMSS-- in Washington in February. They said exactly what you stated--in the higher scoring countries, instruction focuses much more on important mathematical concepts than do the typical 8th grade mathematic lessons in the US. A panel of mathematic educators, mathematics professors and mathematicians was given scripts of lessons from several countries. All cultural references were removed so that they couldn't tell from which country a lesson was taken. They were asked to judge the lessons as to whether or not there was any important mathematics being taught. Not one of the US scripts was found to contain any significant mathematics. Most of the US lessons focused on basic arithmetic and required students to solve many problems. The Japanese lessons, on the other hand, contained a small number of problems which required higher level mathematics. The videos--which are available on the Internet--are quite striking in the difference between the US lessons and the Japanese lessons. Interestingly enough, when Stigler and Stevenson asked US teachers if they had heard of the NCTM Standards, a large number (75%?) said they had. 50% said that they were applying the standards in the lesson being observed. Many of them cited their use of manipulatives or cooperative small groups as evidence of their teaching to the Standards. Those familiar with the Standards and math reform in general know that these can be mere trappings and that the Standards call for much, much more . The TIMSS report, however, says in several places that the teaching in the higher scoring countries is much more in line with the NCTM Standards and the kind of teaching being called for by math reformers in this country than is the US teaching. Clearly, the TIMSS is NOT an indictment of the NCTM Standards! The Standards aren't really being applied in the majority of classes in this country. When asked what the point of their lessons were, the Japanese educators said they wanted their students to understand something. The US educators said they wanted their students to be able to do something. This isn't an indicator of something wrong, but it is an interesting difference.