In the open-approach method, teachings are required to be open to student's mind. Such requirement can be found in constructivist approach to teaching,which was raised in mid 1980s. Teachers following the open-approach try to orchestrate their lessons by taking advantage of students' thoughts, even when those thoughts are unexpected for the teachers. This seems closely related to the idea of "learning trajectory" that M. Simon has proposed (Simon, 1995). The openness of approaches to one problem is also an important aspect of the open-approach. The class discusses student's various ideas and thoughts, and develops them mathematically through sophistication by the peer group and appropriate advises by the teacher. Thus, the open-approach class may share the common interest with the class that emphasizes mathematical discussion and communication. Furthermore, the evaluation in the open-approach method,where the emphasis is laid on students' ways of mathematical thinking and their creativity rather than correct answers, reflects the common expectation with the research that facilitate students' attitudes and beliefs in problem-solving oriented classes (Nohda, 1993).