The author supposes that mathematics teachers in Japan tend to develop their lessons by children's questions which reflect their ideas, understanding, etc. Child-centered problem solv- ing lesson, which are realized by a sequence of their questions, is one of the standards of "good problem solving lesson" in Japan. In the videos, famous mathematicians such as Field medalists, appeared as commentators of lessons. It was interesting for mathematics educators that they appraised these lessons, because children's habit of posing questions fostered their creativity. On the other hand, they also pointed out that children would learn how often they make mistakes in posing new ques- tions by themselves.