수학 학습에 기여하는 기호로서의 다이어그램에 관한 세 가지 관점 = Three Perspectives on Diagrams as Signs Contributing to Learning Mathematics

다국어 초록 (Multilingual Abstract)

Although researchers have studied the contribution of diagrams to learning mathematics based on various perspectives, the meta-analysis of relevant studies is lacking. The purpose of this study is to advance the discussion of epistemological assumptions underlying various approaches to the relationship between diagrams and mathematics learning. To this end, we reviewed theoretical and empirical studies about the contribution of diagrams in mathematics learning, focusing on how they account for the relationship between diagrams as signs and mathematics. The review has led to a proposed framework that categorizes the perspectives on diagrams as signs in pertinent research into structure-based, context-based, and material-based perspectives. We further identified differences in the epistemological background upon which studies from the three perspectives are based and the way the perspectives describe the relationship between diagrams and mathematics learning. The framework was useful identifying the multidimensionality of mathematics learning related to diagrams as well as the use of theoretical lenses by researchers depending on specific aspects of mathematics learning.

국문 초록 (Abstract)

수학 학습 과정에서의 다이어그램의 역할에 관한 연구는 오랫동안 다양한 관점 아래에서 이루어져 왔지만 이러한 다양성에 관한 메타적인 논의는 충분히 이루어지지 않았다. 본 연구는 다이어그램과 수학 학습 사이의 관계에 대한 다양한 접근 방식의 이면에 있는 인식론적인 가정에 관한 체계적인 논의를 진전시키는 데에 목표를 둔다. 이를 위해 수학 학습에서의 다이어그램의 역할에 주목한 이론적·실증적 연구 사례들에 관하여 기호로서의 다이어그램을 바라보는 관점에서의 차이를 중심으로 고찰하였다. 연구 결과 기호로서의 다이어그램과 수학 사이의 관계성을 바라보는 다양한 관점을 구조-기반 관점, 맥락-기반 관점, 그리고 물질- 기반 관점으로 구분하는 틀을 도출하였다. 또한 각 관점의 연구들의 바탕에 놓인 인식론적인 배경과 다이어그램과 수학 학습 사이의 관계를 설명하는 방식에서의 차이를 확인할 수 있었다. 본고에서 제시한 틀은 수학 학습 현상에서의 다이어그램의 역할에 대해 접근하는 데에 있어서 연구자들이 어떠한 이론적 렌즈를 통해 현상의 어떠한 측면에 주목하였는지에 관해 조망할 수 있도록 해준다.

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