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Comprehending the Symbols of Definite Integral and Teaching Strategy  

Choi, Jeong-Hyun (Daeryun High School)
Publication Information
Journal for History of Mathematics / v.24, no.3, 2011 , pp. 77-94 More about this Journal
This study aims to provide a teaching strategy accommodating the symbols of the definite integral and guiding students through the meaning of notations in area and volume calculations, based on characterization as to how students comprehend the symbols used in the Riemann sum formula and the definite integral, and their interrelationship. A survey was conducted on 70 high school students regarding the historical background of integral symbols and the textbook contents designated for the definite integral. In the following analysis, the comprehension was qualified by 5 levels; students in higher levels of comprehension demonstrated closer relation to the history of integral notations. A teaching strategy was developed accordingly, which suggested more desirable student understanding on the concept of definite integral symbols in area and volume calculations.
Definite Integral; the Symbols of Definite Integral;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Oberg, T., An investigation of undergraduate calculus student's conceptual understanding of the definite integral. Doctoral Dissertation, The University of Montana. 2000.
2 Harel, G. & Kaput, J., The role of conceptual entities and their symbols in building advanced mathematical concept. In D. Tall(Ed.), Advanced mathematical thinking. Dordrecht: Kluwer Academic Publishers, 류희찬, 조완영, 김인수 (공역) (2002), 고등수학적 사고. 서울 : 경문사. 1991.
3 Knobloch, E., Leibnitz's rigorous foundation of infinitesimal geometry by means of Riemannian sums. Synthese, vol. 133(1-2), 2002. 59-73.   DOI
4 Malet, A., From indivisibles to infinitesimals : studies on seventeenth-century mathematizations of infinitely small quantities, Universitat Autonoma de Barcelona, Servei de Publications. 1996.
5 이성무. 수학교육에서 기호의 의미와 도입에 대한 고찰. 경성대학교 교육대학원 석사논문. 2007.
6 Eves, H., Great Moments in Mathematics, 수학의 위대한 순간들, 허민 . 오혜영 옮김, 경문사. 1994
7 Eves, H., An introduction to the history of mathematics, 수학사, 이우영 . 신항균 옮김, 경문사. 1995
8 정창택. 역사발생적 원리에 의한 적분단원의 재구성에 관한 연구. 경남대학교 교육대학원 석사논문. 2006.
9 허학도. 직사각형 넓이의 공식의 이해와 인식론적 장애. 서울대학교 대학원 석사학위논문. 2006.
10 Dubinsky, E., Reflective abstraction in advanced mathematical thinking. In D. Tall(Ed.), Advanced mathematical thinking. Dordrecht: Kluwer Academic Publishers, 류희찬, 조완영, 김인수 (공역) (2002), 고등수학적 사고. 서울 : 경문사. 1991.
11 정연준 . 강현영. 정적분의 무한소 해석에 대한 고찰. 학교수학, 10(3), 2008. 375-399.
12 Gray, E. M. & Tall, D. O., Duality, Ambiguity and Flexibility: A Process View of Simple Arithmetic, The Journal for Research in Mathematics Education, 26(2), 1994. 115-141.
13 우정호 . 박교식 . 박경미 . 이경화 . 김남희 . 임재훈 . 이정아 . 김민경. 고등학교 적분과 통계. 서울 : (주) 두산동아. 2009.
14 김선희 . 이종희. 수학기호와 그 의미에 대한 고찰 및 도입 방법. 학교수학, 4(4), 2002. 539-554.
15 김용운 . 김용국. 수학사의 이해, 서울 ; 우성. 1997.
16 신보미. 고등학생들의 정적분 개념 이해. 학교수학 11(1), 2009. 93-110.