Browse > Article

A Historical Analysis of Barrow's Theorem and Its Educational Implication  

Park, SunYong (Department of Mathematics Education, Yeungnam University)
Publication Information
Journal for History of Mathematics / v.26, no.1, 2013 , pp. 85-101 More about this Journal
This study is to analyse the characteristics of Barrow's theorem on the historical standpoint of hermeneutics and to discuss the teaching-learning sequence for guiding students to reinvent the calculus according to historico-genetic principle. By the historical analysis on the Barrow's theorem, we show the geometric feature of the theorem, conjecture the Barrow's intention in dealing with it, and consider the epistemological obstacles undergone by Barrow. On a basis of this result, we suggest a purposeful and meaning-oriented teaching-learning way for students to realize the sameness of the 'integration' and 'anti-differentiation', and point out the shortcomings and supplement point in current School Mathematic Calculus.
Barrow's theorem; epistemological obstacles; historico-genetic principle;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 김남희 외, 수학교육과정과 교재연구, 경문사, 2011.
2 고종숙, 수학 바로 보기, 여울, 2004.
3 민세영, 역사발생적 수학 학습-지도 원리에 관한 연구, 서울대학교 박사학위 논문, 2002.
4 정연준, 미적분의 기본정리에 대한 교수학적 분석, 서울대학교 박사학위 논문, 2010.
5 정연준, 이경화, 부정적분과 정적분의 관계에 관한 고찰, 학교수학 11(2009), No. 2, pp. 301-316.
6 한경혜, 수학사 도입의 이론적 근거 - 역사 발생 원리와 해석적 방법론, Proceeding of HPM2012 Book 1 (2012), pp. 59-72.
7 Baron, M. E., The Origins of the Infinitesimal Calculus, Dover Publications, Inc., New York, 1969.
8 Bell, J. L., The Continuous and the Infinitesimal in Mathematics and Philosophy, Polimetrica, International Scientific Publisher, Monza-Milano (Italy), 2006.
9 Boyer, C. B., The History of the Calculus and Its Conceptual Development, Dover Publications, Inc., New York, 1949.
10 Boyer, C. B., 김경화 역, 미적분학사: 그 개념의 발달, 교우사, 2004. (원저는 1949년 출판).
11 Brousseau, G., Theory of Didactical Situations in Mathematics Education, Kluwer Academic Publishers, 1997.
12 Child, J. M.,"The Lectiones Geometricae of Isaac Barrow", Monist 26(1916), No. 2, pp. 251-267.   DOI
13 Child, J. M., The Geometrical Lectures of Isaac Barrow, Open Court Publishing Co., 1916.
14 Child, J. M., The Geometrical Lectures of Isaac Barrow (Lecture X), The Treasury of Mathematics (H. O. Midonick Ed.), Philosophical Library, New York, 1965, pp. 106-115.
15 Coolidge, J. L.,"The Story of Tangents", The American Mathematical Monthly 58(1951), Issue 7, pp. 449-462.   DOI   ScienceOn
16 Courant, R., Differential and Integral Calculus, Vol. 1, Interscience Publishers-John Wiley & Sons, Inc., 1988.
17 Edwards, C. H., The Historical Development of the Calculus, Springer-Verlag, New York, 1979.
18 Feingold, M.,"Newton, Leibniz and Barrow Too: An Attempt at a Reinterpretation", Isis 84(1993), No. 2, pp. 310-338.
19 Flashman, M. E.,"Historical Motivation for a Calculus Course: Barrow' s Theorem", Vita Mathematica (R. Calinger Ed.) MAA Notes 40(1996), pp. 309-315.
20 Gonzalez-Velasco, E. A., Journey Through Mathematics, Springer, New York, 2012.
21 Jahnke, H. N., The use of original sources in the classroom: empirical research findings, History in Mathematics Education (J. Fauvel, & J. V. Maanen Eds.), Kluwer Academic Publishers, Dordrecht, 2000, pp. 291-328.
22 Jankvist, U. T.,"A categorization of the whys and hows of using history in mathematics education,"Educational Studies in Mathematics 71(2009), No. 3, pp. 235-261.   DOI
23 Kline, M., Mathematical Thought from Ancient to Modern Times, Oxford University Press, New York, 1972.
24 Mahoney, M. S., Barrow's mathematics: between ancients and moderns, Before Newton: The Life and times of Isaac Barrow (M. Feingold Ed.), Cambridge University Press, New York, 1990, pp. 179-249.
25 More, L. T., Isaac Newton: A biography, Dover Publications, New York, 1962.
26 Struik, D. J., A Source Book in Mathematics: 1200-1800, Harvard University Press, 1969.
27 Radford, L.,"Historical formation and student understanding of mathematics,"History in Mathematics Education (J. Fauvel, & J. V. Maanen Eds.), Kluwer Academic Publishers, Dordrecht, 2000, pp. 143-170.
28 Sierpinska, A., Understanding in Mathematics, The Palmer Press, Washing, DC, 1994.
29 Stewart, J., Calculus-Early Transcendentals, Belmont, Brooks & Cole., CA, 2008.
30 Whiteside, D. T.", Isaac Newton: Birth of aMathematician,"Notes and Records of the Royal Society of London 19(1964), pp. 53-62.   DOI