Dynamic growth of collective pedagogical content knowledge via mathematics teacher collaboration : a case study in a primary school

Abstract

The aim of this study is to explore how lesson study may act as a form of professional development in helping primary mathematics teachers to develop their collective pedagogical content knowledge in teaching mathematics. According to Shulman (1986, 1987), pedagogical content knowledge is of special interest because it is a knowledge that links content and pedagogy. Pedagogical content knowledge includes four components, namely, subject matter knowledge, knowledge of students understanding, curriculum knowledge, and knowledge of instructional strategies. Pedagogical content knowledge is the essential element for effective teaching. Strong claims have been made about the benefits of lesson study and it is a comprehensive approach to examine practice for teachers (Stigler and Hiebert, 1999; Fernandez et al., 2003). In lesson study, teachers have to identify a lesson study goal and content area and then meet to discuss their observations and ideas for how to improve the lesson. Through the collaborative planning and examination of actual lessons, teachers’ subject matter knowledge, knowledge of students understanding, curriculum knowledge, and knowledge of instructional strategies are involved. In this study, the term “Collective Pedagogical Content Knowledge” (Collective PCK) is created to describe the pedagogical content knowledge that is explicitly developed and shared by the teachers from lesson study group with evidence provided in their pre-lesson preparation meetings as well as post-lesson evaluation meetings. A school-based staff development project of lesson study led by the mathematics panel chair and supported by the school principal is reported. The mathematics topic is focused on the teaching of quadrilaterals. Data collected from in-depth interviews with teachers, observations of research lessons, field notes of teachers’ meeting and documents of lesson study artefacts such as meeting agendas and lesson plans. The metaphor “seed events” is used to describe critical events in the lesson study, which provide a nursery for the development of the collective pedagogical content knowledge. The concept of “Seed Event” was created in the analysis of the data collected from the implementation of the lesson study plans. Seed events are real episodes captured from the preparation meetings and actual research lessons. Seed events provide real episodes that all of the team members are exposed to. As a result, every peer observer can have a real picture of the seed events and this lead to a more objective reflection among the participants. Through the discussion of a seed event, the team members learn something collectively, make suggestions for actions in the following research lessons which are further evaluated and developed. Since those events have different levels of development, the term "seed" events is used to represent the growth of the events. It was found that teachers paid most attention on the sharing of teaching strategies. Teachers were willing to try different approaches in handling the teaching of quadrilaterals. Some seed events about teaching strategies have been tried out 4 times throughout the whole project. The teaching strategies have been improved according to the shared pedagogical content knowledge. It was also found that teachers’ awareness of students’ misconception was not enough in the preparation meetings. As a result, some seed events about students’ misconception were captured from the research lessons. This indicated that students’ misconception mainly related to teacher conception of students’ understanding. Improving teachers’ awareness was another highlight of the collective pedagogical content knowledge shared by the team. Deeper reflection and constructive evaluation for teachers’ misconception was found in preparation meetings. The whole team of panel provided a proper platform for teachers overcome their fear and difficulty themselves. In tracing the development of seed events, variety of growth of the collective pedagogical content knowledge shared by the team becomes explicit.