A Study On The Cognitive Level Of Junior And Senior High School Students In Solving Open-Ended Mathematic Problems

The open-ended mathematic problem is an important role of the new curriculum reform. After systematic reviewing its concept, characteristics, classification and educational values, we conducted a detailed survey on the cognitive level of high school students in open-ended mathematic problems, exploring its rules and effective solutions, and providing references for quality-oriented education.A survey of students'performance on solving the open-ended mathematic problem was conducted through questionnaires and individual interviews to 253 students from two schools in Shanghai. 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 mathematic problems. Secondly, we divided the students into six grades as PU, UM, M, MR, R, RE, and described their performance through interview and case study. Finally, we used statistical method for the overall performance. The major findings are follows:1. The students need a high level of thinking ability in the open-end mathematic problem solving, so they develop the ability through solving the open-ended mathematic problems.2. The students' performance was highly and positively correlates with the scores of mathematics. The basic knowledge and basic skills play an important role in solving the open-ended mathematic problems.3. There was not always difference in the ability of solving open-ended mathematic problems between the students in junior high school and the students in senior high school. There was no difference in the ability of solving open-ended mathematic problems between the students in key junior high school and the students in key senior high school. The students' ability to solve the open-ended mathematic problems are proportional to the grade of his grade in ordinary high school.4. Whether he had done the same questions had no influence on the student's performance in solving the open-end mathematic problems. It elucidates that there are no fixed thinking mode and type in solving open-ended problems. It is a long time that the teacher cultivate the students' divergent thinking and creative thinking through solving the open-ended problems.5. There was no gender difference in the ability of solving the open-ended mathematic problems.