| A questionnaire on open-ended problem and open-ended teaching was given to 192 students of two schools include Grade three of Junior school and Grade three of senior high school in Xi'an city. Then, all the students were given a test to do open-ended problem of computational estimation. Also, 6 teachers from four schools and 20 students from one school were interviewed. Aimed at realizing the situation on that open-ended problem is used in the west of China, which is important to the students' creative spirit and ability. In addition, we can understand the attitude of both students and teachers to open-ended problem, the students' ability to work out open-ended problem as well. The research can provide some references for teaching in class and course reform. What's more, it can provide some bases for teacher training. Finally, the following conclusions were obtained:(1)There appear only a few open-ended problems on math papers in National University Entrance Examination, So some of the math teachers in high school do not pay much attention to this kind of problem and do not teach or never teach it. Though they think it can reflect the students' level of learning mathematics objectively.(2)The premise of learning math well is interest. Some bad students are sometimes more capable of doing these open-ended problems than those top students. Some students are losing interest in doing these flexible problems, though they are interested in them.(3)The students of science subject classes in Grade three of senior high school are less capable than those in Grade three of junior school at doing the open-ended problem. There is a very clear gap between the students of art subject classes and the students in Grade three of Junior school.On the basis of the findings of this study, this author proposed some useful suggestions to senior teachers. In the end, some further research questions for further studies can also be founded in the last chapter of this thesis.
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