수학적 귀납법 단원의 과제 설계를 통한 교사 공동체의 학습: 공동학습형 연구공동체의 활동 사례를 중심으로 = Learning of Teacher Community Through Designing of Mathematical Induction Tasks: A Case of a Co-learning Inquiry Community

국문 초록 (Abstract)

수학적 귀납법은 그 안에 내포된 추론 구조와 표현의 형식성 때문에 교수학적 변환, 특히, 학습과제 설계의 어려움을 일으키는 것으로 알려져 왔다. 본 연구는 이러한 어려움을 지원하고 교사 공동체의 학습을 이끌기 위해 교사와 연구자가 참여한 공동학습형 연구공동체를 구성하였으며, 수학적 귀납법에 대한 과제를 공동으로 설계하였다. 그리고 그 과정 속에서 어떤 지식이 개발되어 가는지 설명함으로써 과제 설계가 교사 공동체의 학습에 어떤 영향을 미치는지를 분석하였다. 연구 결과, 교사 공동체는 교수전략으로서 증명계획 전략을 도출하였고, 수열의 귀납적 정의와 조작의 역할을 재발견하면서 학생들이 명제함수의 재귀성을 인식할 수 있도록 하는 과제를 설계하였다. 이를 통해 수학적 귀납법의 논리적 구조에 관한 지식, 수학적 귀납법에 대한 학생의 이해와 어려움에 관한 지식, 수학적 귀납법의 학습 과정의 각 과정을 돕는 교수학적 방법에 관한 지식을 개발하였음을 확인할 수 있었다.

다국어 초록 (Multilingual Abstract)

Mathematical induction has been known to be difficult topic for didactic transposition, especially for tasks designs, due to the formality of reasoning structures and expressions embedded in them. This study organized a co-learning inquiry community with teachers and researchers to overcome these difficulties and to lead the learning of teacher community. A series of activities consisting of tasks design, implementation, and reflection were conducted. Then the learning of teacher community was analyzed by describing which knowledge elements were developed. As a result, teacher community drew a proof-planning activity as a didactic strategy and designed tasks that enable students to recognize the recursibility of the proposition function as they rediscover the roles of inductive definitions of sequence and operations. Through this, teacher community developed the knowledge of the logical structure of mathematical induction, knowledge of students understanding and difficulties about learning mathematical induction, and knowledge of didactic strategies which support the learning process of mathematical induction.

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