모델링 과정에서 지각적, 인지적, 메타인지적 활동의 상호작용에 관한 사례연구 = An Analysis of the Interaction of Perceptive, Cognitive, and Metacognitive Activities on the Middleschool Students' Modeling Activity

다국어 초록 (Multilingual Abstract)

In this article, we classify the middleschool students' mathematical modeling activities with three types as following: perceptive activity, cognitive activity, and metacognitive activity. And we research model development process through the interaction of perceptive, cognitive, and metacognitive activities. We report three results of our case study as following: First, students understanded the context of the modeling tasks on the base of their own experience and constructed the tasks with perceptive activity operating tool. Second, students developed various models with reorganizing cognitive activity which think and reason about perceptive activity-based model. Third, students were able to create generalizable and reusable models through metacognitive activities. This study revealed that the possible contribution of modeling activity as following: Students are able to understand abstractive mathematical knowledge as connecting between realistic activity and abstractive activity.

국문 초록 (Abstract)

본 연구에서는 모델링 과정의 활동을 세 가지 활동-지각적 활동, 인지적 활동, 메타인지적 활동-으로 구분하여 이 활동들의 상호작용으로 모델을 개발하는 과정을 중학교 학생들을 대상으로 사례연구 방법으로 조사하였다. 연구결과 학생들은 자신의 경험에 기반하여 과제상황을 이해하였고, 도구를 조작하는 지각적인 활동을 하면서 상황을 구조화하였다. 또한 지각적 활동에 기반하여 개발한 모델에 대해 사고하고 추론하는 인지적 활동을 재조직하면서 모델을 개발하였다. 아울러 메타인지적 활동을 통해 모델을 수정하고 정교화하여 일반화 가능한 모델을 개발하였다. 본 연구로부터 모델링 활동은 물리적 세계에서의 지각적인 활동과 추상적인 수학 활동을 연결함으로써 추상적인 수학 지식을 학생들이 이해하기 쉽게 지도할 수 있는 방법이라는 시사점을 얻을 수 있었다.

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