Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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A Concretization and Application of Deductive Problem Making Method

연역적 문제만들기 방법의 구체화와 활용

  • Received : 2023.11.27
  • Accepted : 2023.12.22
  • Published : 2023.12.31
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Abstract

The development of mathematical problem solving ability and the making(transforming) mathematical problems are consistently emphasized in the mathematics curriculum. However, research on the problem making methods or the analysis of the characteristics of problem making methods itself is not yet active in mathematics education in Korea. In this study, we concretize the method of deductive problem making(DPM) in a different direction from the what-if-not method proposed by Brown & Walter, and present the characteristics and phases of this method. Since in DPM the components of the problem solving process of the initial problem are changed and problems are made by going backwards from the phases of problem solving procedure, so the problem solving process precedes the formulating problem. The DPM is related to the verifying and expanding the results of problem solving in the reflection phase of problem solving. And when a teacher wants to transform or expand an initial problem for practice problems or tests, etc., DPM can be used.

수학과 교육과정에서 수학 문제해결력 신장, 수학 문제만들기 등이 꾸준히 강조되고 있다. 본 연구에서는 Brown & Walter가 제안한 what-if-not 방법과는 다른 방향의 문제만들기 방법을 연구하였다. 여기서 다루는 문제만들기 방법에서는 출발점 문제의 문제해결 과정을 분석하여 그 구성 요소들을 변화시키며, 얻어진 변화를 바탕으로 문제해결 과정을 역으로 거슬러 올라가면서 새로운 문제, 즉 출발점 문제를 변형시킨 문제를 만들었다. 이러한 순서로 문제를 만들면, 문제해결 과정으로부터 새로운 변형된 문제가 유도될 수 있다. 즉, 문제해결 과정이 문제에 선행하게 되며, 본 연구에서는 이러한 문제만들기 방법을 연역적 문제만들기라고 명명하였다. 특히, 연역적 문제만들기의 다양한 사례들, 특징들을 구체적으로 제시하였으며, 치환을 이용하여 로그가 포함된 방정식으로부터 지수, 무리식, 삼각함수가 포함된 방정식 등을 만드는 과정을 소개하였다. 연역적 문제만들기는 문제해결의 반성 단계에서 문제해결 결과를 검증하고 확장하는 활동과 관련될 수 있으며, 수학 교사가 개념 정착, 복습 등과 같은 교수학적 목적에 따라 기존 문제를 변형시킬 때도 활용할 수 있을 것으로 기대된다.

Keywords

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