Exploring the impact of mathematics teachers' pedagogical content knowledge on student achievement: A 'H-V' perspective case study

The Pedagogical Content Knowledge（PCK） of teachers has attracted the attention of many educators and plays an indispensable role in their classroom teaching. The purpose of this study is to investigate the PCK of mathematics teachers with different experiences and explore the impact of PCK on student achievement. The study adopted a mixed study design, with participants consisting of two middle school mathematics teachers with different teaching experiences and their students. Interviews, questionnaire surveys, classroom observations, and statistical analysis of student grades are used as data source tools to conduct content analysis, descriptive statistics, and inference analysis on the data. The "H" perspective is a horizontal comparison of the PCK of different teachers and the achievement of students in different classes, while the "V" perspective is a vertical comparison of the achievement of students in the same class. The horizontal research results show that there is a significant difference in PCK between the two teachers, and there is also a significant difference in student performance in the class they teach. The vertical research results show that after improving the level of PCK, the achievement of students taught by teachers with short teaching experience have significantly improved, while the achievement of students taught by teachers with long teaching experience have not improved significantly. It also provides suggestions for further improving research.