A Case Study On Senior Middle School Students' Problem Posing In The Context Of Analytic Geometry

Problem posing, a popular research field in mathematics education in the recent decade, is drawing the attention of researchers in mathematics education and mathematics teachers in our country. Given the context of the analytic geometry, the subjects are asked to pose various problems using the "what-if-not" strategy. The answers provided by the senior middle school students reveal their problem posing ability, the extent to which they grasp the relevant concepts of conic sections and the main steps of the posing process of a good mathematics problem.The answers of the subjects reveal that senior middle school students are able to pose a variety of new mathematics problems using the "what-if-not" strategy under the situation of analytic geometry; that the problems posed by the students consist of two types, namely keeping and changing problem questions, each of which consists of two subcategories, namely changing the data and changing the type of curves; that most problems posed by the subjects are of low levels, merely changing the data or problem question without attempt to generalize the data or curves and that quite a lot of students are ignorant of the incompatibility of the new data while changing the data or curves and thus posing invalid problems.It is found from the interviews that most of students are interested in the problem posing activity and hope the teacher will provide them more opportunity of problem posing and that problem posing activity has such educational value as making the students reflect on what they have learnt and thus deepening their unstanding of relevant concepts.