Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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Interpretation of Pre-service Teachers' Knowledge by Shulman-Fischbein Framework : For Students' Errors in Plane Figures

평면도형 영역에서 Shulman-Fischbein 개념틀을 활용한 학생의 오류에 대한 예비 교사의 지식 분석

  • Received : 2018.02.12
  • Accepted : 2018.08.21
  • Published : 2018.09.30
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Abstract

This article aims at providing implication for teacher preparation program through interpreting pre-service teachers' knowledge by using Shulman-Fischbein framework. Shulman-Fischbein framework combines two dimensions (SMK and PCK) from Shulman with three components of mathematical knowledge (algorithmic, formal, and intuitive) from Fischbein, which results in six cells about teachers' knowledge (mathematical algorithmic-, formal-, intuitive- SMK and mathematical algorithmic-, formal-, intuitive- PCK). To accomplish the purpose, five pre-service teachers participated in this research and they performed a series of tasks that were designed to investigate their SMK and PCK with regard to students' misconception in the area of geometry. The analysis revealed that pre-service teachers had fairly strong SMK in that they could solve the problems of tasks and suggest prerequisite knowledge to solve the problems. They tended to emphasize formal aspect of mathematics, especially logic, mathematical rigor, rather than algorithmic and intuitive knowledge. When they analyzed students' misconception, pre-service teachers did not deeply consider the levels of students' thinking in that they asked 4-6 grade students to show abstract and formal thinking. When they suggested instructional strategies to correct students' misconception, pre-service teachers provided superficial answers. In order to enhance their knowledge of students, these findings imply that pre-service teachers need to be provided with opportunity to investigate students' conception and misconception.

본 연구는 교사지식 중에서 예비교사의 학생에 대한 지식을 Shulman-Fischbein 개념틀을 이용하여 해석함으로써 우리의 교사교육의 현실에 시사점을 제공하고자 하였다. Shulman-Fischbein 개념틀은 수학의 알고리즘적 SMK, 수학의 형식적 SMK, 수학의 직관적 SMK, 수학의 알고리즘적 PCK, 수학의 형식적 PCK, 그리고 수학의 직관적 PCK의 여섯 가지 요소로 구성되어 있다. 이를 위해 일련의 평면도형 영역의 문제를 다루고 학생의 오개념을 포함한 지필과제를 5명의 예비교사에게 제시하고 그들이 제출한 답변을 분석하였다. 분석 결과 예비교사들은 상당히 강한 SMK를 지니고 있음을 보여주었고, 수학의 형식적 측면을 강조하는 경향을 보였다. 또한 학생들의 오개념 분석 시 학생들의 수준을 깊게 고려하지 않았고, 오개념을 고치기 위한 교수학적 방법을 제안할 때에 구체적이지 못하고 피상적인 답변만을 제시하는 특징을 보여주었다.

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