미적분학의 기본정리에 대한 역사-발생적 고찰

• 영문명: A study on a genetic history of the fundamental theorem of calculus
• 발행기관: 대한수학교육학회
• 저자명: 한대희
• 간행물 정보: 『수학교육학연구』제9권 1호, 217~228쪽, 전체 12쪽
• 주제분류: 사회과학 > 교육학
• 파일형태: PDF
• 발행일자: 1999.07.31

영문 초록

The fundamental theorem of calculus is the most 'fundamental' content in teaching calculus. Since the aim of teaching the theorem goes beyond simple application of it, it is difficult to teach it meaningfully. Hence, for the meaningful teaching of the fundamental theorem of calculus, this article seeks to find the educational implication of the fundamental theorem of calculus through reviewing the genetic history of it. A genetic history of the fundamental theorem of calculus can be divided into the following five phases: 1. The deductive discovery of the fundamental theorem of calculus 2. Galileo's Law of falling body and the idea of the fundamental theorem of calculus 3. The discovery of the fundamental theorem of calculus and Barrow's proof 4. Newton's mensuration 5. the development of calculus in 19th century and the fundamental theorem of calculus The developmental phases of the fundamental theorem of calculus discussed above provides the three educational implications. First, we can rediscover this theorem through deductive methods and get the ideas of it in relation to kinetic problems. Second, the developmental phases of the fundamental theorem of calculus shows that the value of this theorem lies in the harmony of its theoretical beauty and practicality. Third, Newton's dynamic image of this theorem can be a typical way of understanding the theorem. We have different aims of teaching the fundamental theorem of calculus, according to which the teaching methods can be adopted. But it is self-evident that the simple application of the theorem is just a part of teaching the fundamental theorem of calculus. Hence we must try to put the educational implications reviewed above into practice.

목차

1. 서론

2. 미적분학의 기본정리와 Toeplitz의 연구

3. 미적분학의 기본정리의 역사-발생 과정

4. 미적분학 기본정리의 역사의 교육적 함의

5. 요약 및 제언

참고문헌