| Problem solving is one of the main research fields of mathematics education.The importance of metacognition in the process of mathematics problem solving has also attracted the attention of many researchers.This study attempted to combine mathematical problem solving with metacognition,and took high school mathematics excellent students and normal students as the research object to study the process of mathematical problem solving and metacognitive performance.After recording and analyzing the students’ problem-solving process in detail,this paper tried to compare the problem-solving process and metacognitive monitoring,and tried to find the difference through case study.This study selected two cases of high school students,through the investigation of their problem-solving process,trying to answer:（1）what are the differences between excellent students and normal students in the problem-solving process?（2）What are the differences between excellent students and ordinary students in metacognitive monitoring in problem solving?This study mainly used the think aloud method to detect the problem-solving process of two cases,supplemented by observation and interview to make up for the limitations of the think aloud method.After reading the literature,the researcher determined the theoretical framework to investigate the problem-solving process and metacognitive monitoring,and then carried out the research process.The research showed that:（1）In the problem-solving process,the case of excellent student spent more time in the planning and testing phase,while the case of normal student used more time in the analysis and exploration phase;（2）In the aspect of metacognitive monitoring,the case of excellent student had more verification behavior,and the effect of his metacognitive monitoring behavior was better;（3）The performance of the two cases in metacognitive monitoring also had different characteristics. |
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