Changes in pedagogical content knowledge of secondary mathematics student teachers in Hangzhou during their pre-service teacher education

Abstract

The competence of mathematics teachers and how to prepare competent future mathematics teachers have been hotly debated in recent years; pedagogical content knowledge (PCK) is a critical indictor of that competency (e.g., Ball & Bass, 2000; Ferrini-Mundy & Findell, 2010). This explorative study examines PCK and PCK change and the factors contributing to both among a group of secondary school mathematics student teachers in Hangzhou (the capital of and largest city in Zhejiang Province, China). Changes in PCK are investigated across the final two years of a pre-service secondary mathematics teacher education program. This program is traditional in nature, mainly consisting of mathematics teaching methods courses, teaching practica and advanced mathematics courses.

Student teachers’ performance in three aspects of PCK — the substance of PCK, approaches to PCK and the structure of PCK — were assessed using a combination of quantitative and qualitative measures employed at two distinct stages of the program. At each stage, student teachers’ PCK was examined by a PCK questionnaire, a follow-up interview and three video-based interviews. The factors influencing PCK change were investigated using multiple phases and approaches of data collections. Specifically, rating schemes for each aspect of PCK were developed to evaluate student teachers’ responses and track the changes in their PCK. Interviews were conducted with student teachers at various stages of their professional growth to determine what they considered to be important factors affecting their PCK and changes to their PCK. In addition, observations of student teachers’ teaching practice during their teaching practica, together with interviews involving course instructors, mentor teachers and university teachers were employed to collect supplementary evidence on the impact of those factors.

A quantitative analysis of the PCK questionnaire indicated that the participating student teachers generally did not perform well in PCK items in either stage. The follow-up interviews suggest that the different logic applied by the student teachers when responding to those items, their lack of sensitivity to contextual information, and their misunderstanding of terminology and incorrect assumptions all affected their performance. An additional qualitative analysis, based on three video-based interviews, indicated that student teachers’ overall performances in the three aspects of PCK improved in the second stage. Insights were gained into the major types of changes in PCK through paired responses. These changes were found to be influenced by changes in the student teachers’ knowledge of curriculum, of good examples/tasks/exercises, of clear lesson and teaching goals and of some affiliated affective factors. Other factors, including individual and social contextual factors, prior learning and tutoring experience, practicum experience and preparations for examinations and teaching competitions, are also examined for their direct or indirect impact on PCK.

This study may contribute to current literature on the characteristics of Chinese student teachers’ PCK and PCK changes during the final two years of their pre-service teacher education. It provides a tentative explanation of how institutional and social contextual factors affect PCK and PCK change in different ways. Methodological and practical implications are also discussed.