베이즈 통계학의 교수학적 분석과 학교수학에서의 적용 가능성 탐색 = A Didactic Analysis of Bayesian Statistics: Can It Be Applied to School Mathematics?

국문 초록 (Abstract)

본 연구는 현대 사회에서 그 실용적 가치를 인정받고 있는 베이즈 통계학에 대한 교수학적 분석을 시도하여 그 교육적 의의를 확인하고, 나아가 학교수학에 이를 적용하는 방안을 탐색하기 위한 목표로 수행하였다. 먼저, 교수학적 분석의 일환으로 베이즈 통계학의역사-발생적 분석, 수학적 분석, 철학적 분석을 시도하였다. 그리고 초등학생과 중학생을 대상으로 베이즈 통계학의 관점이 반영된 과제를 적용한 선행연구를 분석하여, 학교수학에서 베이즈 통계학을 지도하기 위해서 무엇을 고려해야 할지를 살펴보았다. 연구결과, 베이즈 통계학의 핵심 아이디어는 데이터에 의해 확률이 갱신된다는 점, 그리고 그 믿음 갱신 규칙의 일관성은 확률을 믿음의 정도로서 주관적인 것으로 정의하는 데서 비롯된다는 점이라는 사실을 알 수 있었다. 또한, 위험 맥락과 같이 일상에서의 예측과 연결지을 수 있는 자연스러운 맥락에서 표본공간의 변화를 시각적으로 표현함으로써 초등학생과 중학생 수준에서 비형식적으로 이러한 아이디어를 이해할 수 있음을 확인하였다.

다국어 초록 (Multilingual Abstract)

This study aims to explore the pedagogical significance of Bayesian statistics, which is increasingly recognized for its practical value in modern society, and to further explore avenues for its application in school mathematics. As part of the didactic analysis, the study attempts historico-genetic, mathematical, and philosophical analyses of Bayesian statistics. In addition, it examines previous studies applying Bayesian perspectives in tasks for elementary and middle school students to identify considerations for teaching Bayesian statistics in school mathematics. The results show that the core ideas of Bayesian statistics lie in the updating of probabilities by data and the consistency of belief updating rules, which follows from defining probability as a subjective measure of belief. Moreover, it is confirmed that these ideas can be informally understood at the elementary and middle school levels by visually representing changes in sample space in contexts, such as risk, which can be linked to predictions in everyday life.

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