The benchmark test comparing students in various countries is called PISA (the program for international student assessment) which focuses on mathematics, reading, and science. For the last few decades, students from the U.S. have scored in the middle of developed countries and behind many Asian countries. There are several possible reasons for this.
1. Some countries do not test a cross-section of their students, but only those in the upper percentiles. For instance, the Chinese scores come from Hong Kong and Shanghai, which are not representative of the rural regions.
2. Most countries are not as economically diverse as the U.S. Studies have shown a strong correlation between socioeconomic status and academic achievement. Some states in the U.S. typically perform as well as their Asian counterparts, but poorer states do not fare as well.
3. Most Asian countries (as well as some northern European countries) are much more racially homogenized than the U.S. The U.S. will have a significant number of ESL (English as a second language) students taking the test which has an impact on reading skills.
4. The U.S. does not have a national curriculum, and in many states the curriculum varies from school to school. Since the population in the U.S. is more mobile than the typical Asian country, students often move in the middle of the school year and the result can be "gaps" in their learning.
5. Finally, many Asian countries have begun to develop a strong middle class. This has happened within the last 2-3 generations. Parents see the importance of education to help their children to succeed. This is reminiscent of the "American Dream" where every generation was to do better than the previous generation. In the U.S. there is not as much emphasis on academics, especially in the lower socioeconomic classes.