An Analysis of the Relationship between Teachers' Pedagogical Content Knowledge and Teaching Practice: Focusing on the Area of Plane Figure

평면도형의 넓이에 대한 교사의 교수학적 내용 지식과 수업 실제 분석

The purpose of this study was to analyze teachers' pedagogical content knowledge (PCK) about area of plane figure and how it was actualized in instruction. As an exploratory, qualitative, and comparative case study, 2 fifth-grade teachers were selected. Semi-structured interviews with the leachers were conducted in order to explore their PCK with regard to the area of plane figure. A total of 14 mathematics instructions were videotaped and transcribed. Teachers' PCK and classroom teaching practices were analyzed in detail into 3 categories: (a) knowledge of mathematics contents, (b) knowledge of students' understanding, and (c) knowledge of instructional methods. As such, this paper provided a detailed description on each teacher's PCK and her teaching practice. The results showed that teachers' PCK had a significant impact on instruction. The teacher who had rich knowledge about the area of plane figure was able to encourage students to understand the concept of area and to or explore the principles behind formula calculating various areas of plane geometry. The results demonstrated the importance of individual components of PCK as well as that of overall level of PCK. Different aspects of teaching practices were observed as to how the teachers had internalized PCK. On the basis of a close relationship between teachers' PCK and their teaching practice, this paper finally raised several implications for teachers' professional development for effective mathematics instruction.

교사의 지식은 효과적인 수업을 위해 필수적이며, 교수 학습에 직접적인 영향을 끼친다. 이에 본 연구는 평면도형의 넓이에 대한 수학 내용에 대한 지식 학습자의 이해에 대한 지식 교수 방법에 대한 지식으로 교사의 교수학적 내용 지식(PCK)을 알아보고, 이에 관한 수업 실제를 상세하게 분석하여, 교사의 PCK와 수업 실제와의 관계를 살펴보았다. 분석 결과 교사가 가진 PCK의 전반적인 특성에 따라 수업의 구현 양상이 다양하게 나타났는데 특히, 평면도형의 넓이와 관련하여 세부적인 PCK의 요소를 교사가 어떻게 내면화했는지에 따라 수업의 초점이 달랐다. 이러한 연구 결과를 토대로, 본 연구는 PCK의 중요성을 피상적으로 강조하기보다는 PCK 와 수업 실제 간의 면밀한 관계를 분석하여 효과적인 수업 구현을 위한 시사점을 도출하였다.