A Study On The Mathematical Problem-Posing Performance Of Junior High School Students

Problem posing is an important content of the curriculum reform in mathematics education,it plays an important role in the development of students’ thinking.Unfortunately,it is rarely implemented in actual teaching.There is a need to study students’ mathematical problems-posing performance in order to help their teachers carry out instruction accordingly.Therefore,this study focused on junior high school students and developed a test composed of six problem situations,which were divided into structured situations,semi-structured situations,and free situations according to the structure of problem situations.Meanwhile,they were divided into realistic situations and mathematical situations according to the content of problem situations.Based on this test,the researcher investigated the overall mathematical problem-posing performance of junior high school students and then analyzed the differences in terms of the structure of problem situations,the content of problem situations,student gender and grades.During the formal study,a total of 333 junior high school students from three schools in Chengdu and Chongqing were selected by convenience sampling to complete the test,and then six students were selected for subsequent semi-structured interviews.This study used mixed methods to analyze junior high school students’ mathematical problem-posing performance.Specifically,SPSS 21.0 was used to conduct descriptive statistical analysis and difference analysis on the solvability,reasonability,context,complexity,and readability scores of the mathematical problems proposed by the students.The students’ interview transcripts were used to further investigate their thinking process during the mathematical problem-posing activity.The research conclusions from this study can be summarized as follows:(1)The solvability,reasonability and readability scores of the mathematical problems posed by junior high school students were at a higher level,the context score was at the lowest level,and the complexity score was at a lower level.(2)There were significant differences in each dimension of mathematical problems among the three structures of problem situations,and the differences in each dimension were not completely consistent.In terms of solvability and reasonability scores,only the structured situations were significantly higher than the semi-structured and free situations.In terms of context score,the free situations were significantly higher than the structured and semi-structured situations,and the structured situations were significantly higher than the semi-structured situations.In terms of complexity score,only the free situations were significantly lower than the structured and semi-structured situations.In terms of readability score,the structured situations were significantly higher than the semi-structured and free situations,and the semi-structured situations were significantly higher than the free situations.According to the interviews,junior high school students thought that it was easy to pose mathematical problems in structured situations,but difficult in semi-structured and free situations.(3)The solvability,reasonability,complexity,and readability scores of the mathematical problems posed by junior high school students in realistic situations were significantly higher than those in mathematical situations,but the context score in realistic situations was not significantly higher than that in mathematical situations.(4)There were no significant differences in the solvability,reasonability,context,complexity,and readability scores of problems between male and female students,but the solvability,reasonability,complexity,and readability scores of problems vary across the grades,generally showed an upward trend with the increase of grades.Based on these research conclusions,this study suggested that when carrying out mathematical problem-posing instruction,teachers should create different types of problem situations according to students’ cognitive differences,encourage students to explore independently,promote the development of students’ mathematical thinking,guide students to express mathematical problems in a standardized and accurate manner,and pay attention to students’ understanding of basic knowledge and basic concepts.