A Study On The Thinking Characteristics Of Senior One Students In Solving Open-ended Mathematics Problems

In recent years，according to the importance of mathematical open-ended problems to theBasic Education Curriculum Reform,the thesis not only descrips the Concept，characteristics，classification and education value of mathematical open-ended problems but also do adetailed survey about the thinking characteristics of solving mathematical open-endedproblems among students in senior one in order to find out the thinking regularities of solvingmathematical open-ended problems and the effective way to cultivate students’ mathematicalthinking ability，which Provides reference for the implementation of quality education.The research selected270Senior one stuednts in Zijin high school of HeYuanGuangdong Province as the Objects. Self test volume and interview are applied to survey thestudents’ thinking characteristics of solving open mathematical problems.The research mainlyfocuses on two areas：First，the research analyzed the students’ answers and established fivelevels to solve open-ended mathematical problems according to the theory of multipleintelligences，Solo classification theory and constructivist theory as a theoretical basis.Second， We divided the students into four grades as prestructural， unistructural，multistructural，relational，extended abstract. Finally，we used statistical method for theoverall performance.The major findings are as follows:1.Solving Open-ended mathematical problems requires high-level thinking skills. Usingopen-ended mathematical problems contributes to the formation of students’ thinking abilityat all levels.2.The overall cognitive level of senior one students in ZiJin High School are at thepoorer level among the above five grades，only a few students achieve a higher level.3. In the real life issues, students have a certain degree of divergent thinking ability, thereason is that they learned a lot of related information through the Internet, mobile phones andother media. But they lack of associate and abstract thinking.4. The logic and rigorous thinking of students in the formula derivation needs to beimproved.5. Part of the students’ thinking stiff and rigid in the image study，not further expansion of associate and abstract. There are also part of the students’ thinking in this respect is veryactive and wide.6The students’ performance was correlates with the scores of mathematics. The perfectstructure of the students’ knowledge plays an important part in it.7. There was few gender difference in the ability of solving open-ended problems.8. Developing students’ mathematical thinking ability and improving the level ofstudents’ mathematical thinking is a long process.