Pre-service Mathematics Teachers' Cognition of “Senior High School Students Can Understand Knowledge but cannot Solve Problems”

In senior high school mathematics teaching, many students can understand the knowledge but cannot solve the problems. Existing studies mainly focus on front-line teaching, but no one has explored the cognition of pre-service mathematics teachers to this phenomenon. Whether pre-service mathematics teachers have clear cognition of this phenomenon will greatly affect the quality of mathematics teaching in senior high school in the future. As for the selection of sampling techniques, random sampling was used in this paper, and a total of 30 graduate students and undergraduates from the School of Mathematics and Statistics of Shandong Normal University who want to be senior high school mathematics teachers in the future are selected as the survey objects. As for the selection of investigation method, interview method was used to investigate their understanding of this phenomenon in this paper. The results are as follows: In terms of causes, 93. 33% pre-service mathematics teachers believed that students' grasp of knowledge is not enough, 56. 67% believed that students' thinking is narrow and limited, etc; In terms of countermeasures, 56. 67% believed that students' ability to use knowledge is not enough, and 30% believed that teachers should pay attention to the inspiration of students' ideas and methods, etc. The conclusions of this paper are as follows: (1) For the phenomenon that senior high school students can understand the knowledge but cannot solve the problem, most pre-service mathematics teachers’ cognition have shortcomings in both rationality and comprehensiveness. (2) It is necessary to train pre-service mathematics teachers.