직관적ㆍ형식적 탐구 기반의 문제해결식 접근법에 따른 수학 문제해결 지도 방안 탐색
A Study on the Mathematical Problem Solving Teaching based on the Problem solving approach according to the Intuitive and the Formal Inquiry
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초록
수학 문제해결은 학교수학의 주요 관심사가 되어 왔고, 학생들의 수학 문제해결 능력을 길러 줄 수 있는 방안을 모색하는 것은 수학교육 연구자들의 주요 연구 대상이 되어 왔다. 본 연구에서는 문제해결을 통해 학생들이 수학적 개념을 이해하고, 개념과 관련된 절차적이고 형식적인 원리를 탐구하며, 이를 실세계 상황에 적용할 수 있는 학교 현장 중심의 문제해결 지도 방안을 탐색해 보았다. 이를 위해 문제해결 교육의 필요성과 역사를 살펴보았고, 문제해결 지도 방안의 이론적 토대를 구축하기 위해 문제해결에 관한 연구와 그간의 문제해결 모델을 고찰하였다. 본 연구에서는 문제해결식 접근법에 따른 문제해결 지도 방안으로 직관적 탐구 단계와 형식적 탐구 단계를 바탕으로 이들의 상호 보완 및 균형을 추구하도록 구성하였다. 또, 적용 단계를 통해 문제해결 과정에서 경험한 수학적 원리를 활용하도록 문제를 만들어 해결해 보거나 실생활에 적용하는 활동으로 구성하였다. 특히 직관적 탐구 단계를 통해 개념적 이해가 가능하도록 하였고, 형식적 탐구 단계를 통해 절차적 이해가 가능하도록 제안하였다.
Abstract
Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.
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