A Case Study Of High School Students' Problem Posing Ability

Since 1990s, problem posing has been an important research topic in the field of mathematics education. Problem posing is the need of both mathematics and mathematics education. Problems are the heart of mathematics without which mathematics doesn't exist and problem posing is indispensible to the development of mathematics. Problem posing acts as the means of promoting problem solving and strengthening interaction between the teacher and students. Therefore, it is of importance to foster students' problem-posing abilities in high school mathematics teaching.A questionnaire survey was conducted with two hundred students from one rural and one city middle school and a part of them were interviewed.The following conclusions are arrived at:(1) Senior high school students hold positive opinions on problem posing. However, generallyspeaking, their problem posing ability and the posed mathematical problems are of low level;(2) Students' problem posing performance is not affected by hints of negating attributes;(3) Students from different cultural background show different problem posing abiliyies. There are greater proportion of the city students than rural ones who hold that problem solving is more important than problem posing. But there are greater proportion of the rural students than that of city ones who first solve the problem before posing new problems. The city students pose more types of new problems than rural students do.(4) Given a problem, the boy students pose more types of new problems than those of girl students, but the girl students pose more problems which just change the data of the original problem. (5) Students' consciousness of problem posing in the situation of plane geometry is more intense than in other situation. When the given problem is open-ended, students' consciousness is also intense. A few students posed many good new problems, some of which are original, showing quite good problem posing ability. But most of students fail to pose original and valid problems.