A Case Study Of PCK Between Novice And Expert Teachers In Junior High School

This study mainly applies the concept of Pedagogical Content Knowledge(PCK)of Shulman(1986)and takes four mathematics teachers from a key middle school in Shaanxi Province as the case study.Through classroom observation and semi-structured interviews and other research methods,this paper uses research tools to explore the differences in PCK between math expert teachers and novice teachers in junior middle school.Firstly,it is found that there are significant differences between expert teachers and novices teachers in the six sub-dimensions of PCK through the teaching research of junior high school function.(1)Knowledge of teaching purpose: Through the comparison between the teaching view and the three-dimensional objectives,the study shows that the description of the teaching objectives by the experts is more specific and clear.They set students' cognitive goals based on learning situations,so that students can understand well and improve their abilities as the orientation.(2)Knowledge of mathematical content:According to the analysis of textbooks and the comparison of structure diagrams,it is concluded that experts are far superior to novice teachers in understanding the depth and breadth of mathematical knowledge and the understanding of close relationship between concepts.(3)Knowledge of content organization: Based on the comparison of teaching road-map and teaching design cases,it is proved that the organization and arrangement of experts are more systematic and hierarchical,and they can transform abstract knowledge into concrete knowledge that students can accept easily.They pay attention to the students' learning knowledge while implementing the edification of mathematical ideas and methods,and their experience is far richer than that of novices.(4)Knowledge of student understanding: By the comparison of learning situation analysis and breaking through of key and difficult points,it is found that experts have a deeper understanding of students' cognitive confusion and a better understanding of the psychological characteristics of students in this age.(5)Knowledge of effect feedback: Through the comparison of Flanders interactive analysis system,it is found that experts are more open and guiding in students' interaction,pay more attention to heuristic and questioning,and are good at stimulating students' desire for inquiry.(6)Knowledge of teaching strategies: By comparing the quadrant diagram of the teaching strategy library,it is found that experts are better at organizing cooperative inquiry than novice teachers,and drawing conclusion.Secondly,222 students from four math teachers were surveyed by questionnaire.The results show that there are significant differences between expert teachers and novice teachers in the other five dimensions of PCK,except for the knowledge of teaching purpose.The conclusion is the same as that of the case study.Therefore,This study proposes the following suggestions for the professional development of novice teachers:(1)They should have a deep understanding of the connections between mathematical concepts and build mathematical knowledge into knowledge which is suitable for students to learn.(2)They should have students in mind,think about their cognitive difficulties and doubts from the perspective of students,and guide students to grasp the key points and break through the difficulties.(3)Novice teachers should be organized to learn practical experience and teaching strategies from expert teachers in order to improve their professional level and ability.