Primary mathematics teachers’ pedagogical content knowledge of the teaching of quadrilaterals

Abstract

Teacher’s pedagogical content knowledge is essential in bringing about effective learning. Different models have been developed in recent studies (e.g., Shulman, 1987; Peterson, 1988; Leinhardt et al., 1995; Marks, 1990; Cochran et al., 1993). Deriving from these models, an analytical framework of four components, namely, subject matter knowledge, knowledge of students’ understanding, curriculum knowledge, and knowledge of instructional strategies is developed in this study. The aim of this study is to explore primary school mathematics teachers’ pedagogical content knowledge in the teaching of quadrilaterals. The subjects included 8 primary mathematics teachers with different experience in teaching from a Hong Kong school. The teachers were interviewed. In the interviews, they were presented scenarios constructed out of common tasks of teaching mathematics. The scenarios were designed in order to explore three things: (1) What the mathematics teachers seemed to know about quadrilaterals and the teaching and learning of quadrilaterals in classroom; (2) What actions the mathematics teachers would take in responding to each scenario; and (3) How the mathematics teachers weave together different kinds of knowledge in making interpretations and choice. Other interview questions focused on teacher’s knowledge of students’ understanding, curriculum knowledge, knowledge of instructional strategies and subject matter. The results show that the four components of pedagogical content knowledge are interrelated. The lack of one of the components may have a negative impact on the holistic development of pedagogical content knowledge. However, the teachers in this study were confi- dent with what they had learnt during their schooling and did not realize that their subject matter knowledge was not sufficient for their teaching. They even did not consider whether their concepts about quadrilaterals were right or not. Such lack of awareness of their weaknesses will probably imply difficulties in providing an enhanced environment for their students’ learning.