Results from the Third International Mathematics and Science Study (TIMSS) suggested that the nature of mathematics teaching in Japan is different from that commonly seen in the United States. Although the TIMSS focused on the eighth-grade level, other studies suggest that a similar difference also exists at the elementary school level. My recent seven-month visit to Japan, which included observations of more than 50 lessons, seems to confirm this difference. For example, Japanese lessons often focus on a single fundamental problem. Also, students’ solutions are shared and analyzed critically, and teachers often appear to stand aside during the class discussion. I would like to discuss one factor that may contribute to the difference in performance between Japanese students and students in the United States. That factor is teachers’ anticipation of students’ thinking.