Situation C: "Posing advanced problems."After all presentations were made, Mr. Tsubota let the students go back to the original game situation and decide the winner by using someone's proposed way. The students said that they liked simpler ones, and finally decided to use "area" to make comparison. They measured the "areas" of their own scattered marbles and decided the winner. At the same time, it became apparent that in some cases the "area" did not give reasonable measures for the purpose of comparing the degree of scattering. At the end of the class, the teacher and the students recognized that the "area"method needed to be revised further and reflected on today's class. The teacher concluded the class by saying, "Today, we learned how to measure and compare ambiguous objects.