교란순열에 대한 역사적 탐색과 교육적 확장에 대한 연구
The Study of Historical Analysis and Educational Extension on Derangement
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초록
본 연구에서 수학사를 활용한 수학탐구활동을 기반으로 연구를 수행하였다. 학교수학 교육에서 중요성이 증대되고 있는 확률과 통계 내용 중에서 순열을 토대로 하였고, 순열의 내용 중 교란순열을 연구주제로 선정하였다. 먼저, 교란순열과 관련된 중등학교 및 대학 수준에서 학습내용에 대한 분석이 이루어졌고, 역사적 발생 순서에 따라 교란순열의 발달과정을 고찰하였다. 이를 기초로 교란순열에 대한 탐구 방향을 교란순열의 수 삼각형으로 결정하고, 중등학교 수준에서 교육적으로 활용할 수 있는 수학탐구활동을 진행하였다. 그 결과, 교란순열의 수 삼각형의 다양한 수학적 사실을 발견하였다. 본 연구 결과의 활용을 통해 수학사의 활용과 새로운 탐구방향의 제시에 유의미한 시사점을 제공할 것으로 기대한다.
Abstract
The study was conducted based on the `method of mathematical exploration thro\-ugh history'. In recent school education, `Probability and Statistics' education has been emphasized, and as a result, the study has conducted a study on permutations. Permutation is used in a variety of fields, and in this study, we looked at the Derangement. The results of this study are as follows. First, analysis was made at current school mathematics level and academic mathematics level for Derangement. Second, the historical development process of derangement was examined. Third, based on this, the research direction of this study was decided to be `Derangement number's triangle(Rencontres number's triangle)', and the inquiry for education expansion was carried out. Fourth, we have presented data on concrete educational expansion by discovering various mathematical facts of the Derangement number's triangle. We hope that the results of this study will provide meaningful implications for the application of mathematics and the presentation of new inquiry directions.
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