**5. Limitations**

First, post-hoc retrospective data did not allow for rigorous causal inference research. This study was based on the administration data of student performance and teacher questionnaires. The teacher data were only questionnaire data collected at the same time point. Matching the student and teacher data only enabled the analysis of the correlation between individual teacher characteristics and student performance based on cross-sectional data. If feasible, the best way is to track the evaluation and collect baseline data, process data, and outcome data, to compose longitudinal data for causal inference. Second, it should be noted that the survey measures teachers' perception that they are prepared in terms of content knowledge and pedagogical content knowledge, which may be accurately related to their actual perception or there may be biases. Third, the detailed student information was not collected and controlled. Since the 2016–2019 senior high school graduates involved in this study had left school, it was difficult to contact them to do the questionnaires again. If feasible, variables such as students' characteristics and parental background should be controlled in the model, making the estimates more accurate.
