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고등학교 미적분학 지도에서의 수학사 활용에 관한 연구

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Author(s)
조미숙
Issued Date
2006
Abstract
Calculus has been applied to various fields, such as natural science, statistics and economics. Nevertheless, most student don't understand fully what the calculus is because they don't understand the concept of limit, which is the basic of calculus, and they have to study in test-oriented environment. To solve these problems, a lot of interesting teaching methods should be developed. So, this thesis tried to find how mathematical history can be applied to the calculus in high school.
First, the application of mathematical history and the effect were surveyed through the preceding studies. With these, the development of teaching and learning materials in classes related to the role of teachers was discussed, and the background of the calculus was researched with the mathematicians' ideas as the origin of calculus. Moreover, the examples on the application of mathematical history in high school mathematics were developed.
The example which were made on the basis of mathematical contents and questions, will be applied to the preparation in teaching calculus and the mensuration by parts. This example will help teachers solve the problems in teaching calculus and improve the quality in mathematics education and the effect in learning. In this thesis, two examples regarding the application of mathematical history were presented.
To enhance the teaching skill through the application of mathematical history, the following studies on the teaching and learning materials with mathematical history, and various teaching methods applied to real classes should be developed.
Alternative Title
A study on the applications of mathematical history in teaching high school calculus
Alternative Author(s)
Jo, Mi Suk
Affiliation
조선대학교 교육대학원
Department
교육대학원 수학교육
Advisor
安永濬
Awarded Date
2006. 2
Table Of Contents
표 및 그림 목차 = ⅲ
ABSTRACT = ⅳ
제 1 장 서론 = 1
제 2 장 수학교육에서의 수학사 활용 = 4
1. 수학사 활용의 필요성 = 5
2. 수학사 활용의 효과 = 10
3. 수학사 활용의 방법적 측면 = 12
4. 수학사 활용에서의 교사의 역할 = 14
제 3 장 미적분학의 수학사적 배경 = 16
1. 적분학 = 16
1) 적분개념의 기원 = 16
2) Archimedes의 평형법 = 18
3) Kepler의 포도주 통의 부피 측정 = 21
4) Cavalieri의 불가분량법 = 22
2. 미분학 = 25
1) 미분개념의 기원 = 25
2) 무한소의 개념 = 29
3) Newton의 유율법 = 32
4) Leibniz의 미분학 = 33
제 4 장 고등학교 미적분학 지도에서의 수학사 활용 예시안 = 37
1. 예시안 1 : 미적분학 단원의 사전 준비학습 = 37
1) 예시안의 개발 방향 = 37
2) 예시안 분석 및 설명 = 41
2. 예시안 2 : 구분구적법 = 48
1) 예시안의 개발 방향 = 48
2) 예시안 분석 및 설명 = 50
제 5 장 결론 = 56
참고문헌 = 58
Degree
Master
Publisher
조선대학교 교육대학원
Citation
조미숙. (2006). 고등학교 미적분학 지도에서의 수학사 활용에 관한 연구
Type
Dissertation
URI
https://oak.chosun.ac.kr/handle/2020.oak/4430
http://chosun.dcollection.net/common/orgView/200000232785
Appears in Collections:
Education > Theses(Master)(교육대학원)
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