Openness and Types of Problems
In the open-ended approach proposed by Shimada, emphasis was placed on the problem whose end was not closed to one answer. He and his colleagues intended to organize class by making use of multiple correct answers positively.In the open-approach method, the meaning of openness is considered broadly than the open-ended approach. Here, in addition to the problem whose end was open, the problem that produces multiple correct solutions and the problem that produces multiple problems are included. By this extension, the difficulty of constructing the open problem is overcome. Moreover, it becomes possible to provide more opportunities for students with different abilities and needs to participate in the class. After getting multiple solutions by his/her own, it also becomes possible to lead students to sum up their solutions from the view point of mathematical ideas (Nohda, 1983).