A Study On The Cognitive Level Of Grade One High School Students In Solving Open-Ended Mathematic Problems

The open-ended mathematic problem is an innovative product of the new curriculum reform. It strengthens students' overall mathematic ability and realizes the goal of the reform. After systematic reviewing its concept, characteristics, classification and educational values, we conducted a detailed survey on the cognitive level of grade one high school students in open-ended problems, exploring its rules and effective solutions, and providing references for quality-oriented education. Based on open-ended mathematical problem theory, a survey of students' performance on solving the open-ended mathematical problem was conducted through questionnaires and individual interviews to 201 students from Baixiang high school. According to students' responses of the questionnaires, we firstly used SOLO Taxonomy as a framework for analyzing the results, and built five levels for solving the open-ended problems. Secondly, we divided the students into four grades as P-U, U-M, M-R, R-E, and described their performance through interview and case study. Finally, we used statistical method for the overall performance. The major findings are as follows:(1) The overall cognitive level of students in solving open-ended problems is not high. There are 52.24% students in U-M. They could get three or more solutions, but their poor logic limited them into fragmented answers. Only 9.45% of students arrived the R-E grade, presenting a narrow space of students ability in abstract generalization and innovation. The drawbacks of traditional teaching mode, the imperfect structure of students' knowledge and the low quality of thinking may be the main facts.(2) There was gender difference in the ability of solving open-ended problems. Boy students were better performed than girl students due to different learning methods they applied.(3) The students' performance was highly and positively correlates with the scores of mathematics, which proved open-ended problems played a key role in students' academic performance.According to the results mentioned above, some suggestions for the teaching of the open-ended problem are given at the end of this thesis, which are explained by two teaching cases: (1) Teachers should cultivate students positive emotions and attitudes of exploring open-ended problem; (2) Teachers should be good at digging the basic knowledge and skills from the open-ended problem so that it can be skilfully integrated with the "Two Basics"; (3) Students can identify and learn the differences between different grades through multi-level questions, cooperation and communication.