중학교 수학교과서에 나타난 수학사 활용 조사 및 학습지도방안 연구 : - 확률?통계 단원을 중심으로 -

다국어 초록 (Multilingual Abstract)

ABSTRACT

A Study of Application and Teaching Plans of History of Mathematics in Mathematics Textbooks of Middle School
- focusing on probability and statistics

Min Kyung Song
Major in Mathematics Education
Department of Education
Graduate School of Education
Woosuk University


The objective of this research come up with teaching plans using history of mathematics through analyzed the application of history of mathematics in mathematics textbooks and selected chapters incomplete in applying history of mathematics.
Specific subjects for inquiry according to the purpose of the research are as follows.

1. To discuss the necessity, effectiveness and introduction of the classes using history of mathematics.
2. To investigate the application of history of mathematics in mathematics textbooks in middle schools.
3. To review the preceding researches about the effectiveness and teaching plans of the classes using history of mathematics.
4. To select chapters incomplete in teaching plans using history of mathematics after analyzing textbooks and preceding researches.
5. To suggest the material and teaching plans of history of mathematics related to the selected chapters.

In this paper, the teaching plans using history of mathematics will be introduced and the reason why history of mathematics is necessary in math education will be shown.

The results are as follows.

The chapter of statistics was chosen as the incomplete in applying history of mathematics through the preceding researches. The research suggests the material and teaching plans of history of mathematics related to the probability of statistics.

There are suggestions for the effective education of probability and statistics using history of mathematics.

1. It is necessary to introduce history of mathematics and to develop textbooks using history of mathematics.
2. The education environment for using history of mathematics should be improved.
3. The history of mathematics related to probability and statistics should be discovered.
4. It is necessary to educate teachers for the appropriate education of statistics.

목차 (Table of Contents)

• 목 차
• ABSTRACT ⅳ
• Ⅰ. 서 론 1
• A. 연구의 필요성 및 목적 1
• B. 연구 문제 2
• C. 연구의 제한점 3
• Ⅱ. 이론적 배경 4
• A. 수학과의 성격 4
• B. 역사 발생적 원리 5
• C. 수학교육에서 수학사 도입의 필요성과 효과 7
• D. 수학사를 활용한 지도법 11
• Ⅲ. 연구방법 14
• A. 연구목표 14
• B. 연구대상 14
• C. 연구절차 15
• Ⅳ. 연구결과 및 분석 16
• A. 교과서의 수학사 내용 16
• B. 선행연구 조사 20
• C. 교과서와 선행연구 분석 28
• D. 통계단원의 수학사 관련자료 및 학습지도방안 제시 29
• (1) 도수분포와 그래프 29
• (a) 통계의 역사 30
• (b) 통계 자료 왜곡 사례 31
• (2) 확률과 그 기본성질 34
• (a) 갈릴레이의 주사위 문제 35
• (b) 드 메레의 문제 38
• (3) 대푯값과 산포도 42
• (a) 파푸스와 산술평균, 기하평균, 조화평균의 관계 42
• (b) 고대의 평균 45
• (c) 통계의 발달과정 46
• (d) 아헨발 48
• Ⅴ. 결론 및 제언 50
• 참고 문헌 53