중등 수학교과서가 다루는 수학사의 비판과 대안
Study on Criticism and Alternative on the History of Mathematics Described in the Secondary School Mathematics Textbooks
1
조회
0
다운로드
6
인용
0
참고문헌
키워드
초록
본 논문의 목적은 중등 수학교과서에 기술되어 있는 수학사의 주요 문제점을 알아보고, 그리고 중등 수학교과서에수학문화의 전이가 반영되어야함을 주장하는데 있다. 교과서에서 다루는 수학사는 기축시대와 고대 그리스에서 고대이집트, 고 바빌로니아, 그리고 이슬람 수학을 제외한 유럽으로의 수학문화의 전이가 반영되어 있다. 우리는 이를 알아보고 수학사적 문제의 대안을 제시하였다.
Abstract
The purpose of this article is to discuss some of the most commonly repeated misconceptions on the history of mathematics described in the secondary school mathematics textbooks, and recommend that we should include mathematical transculture in the secondary school mathematics. School mathematical history described in the texts reflects the axial age, and deals with mathematical transculture from the ancient Greek into Europe excluding the ancient Egypt, Old Babylonia, and Islamic mathematics. We discuss about them through out the secondary school textbooks and give some alternatives for the historical problems.
참고문헌 (210)
- 고호경, "중학교 수학③" (2012), 교학사
- 2009 개정 교육과정에 따른 수학과 교육과정 연구, "교육과학기술부", ~ (2011)
- 교육부, "초등수학 5-1" (2015), ㈜천재교육
- 김서령, "중학교 수학①" (2012), 천재교육
- 김서령, "중학교 수학②" (2012), 천재교육
- 김용운, "수학의 흐름" (1975), 배영사
- 김용운, "수학의 흐름" (1985), 전파과학사
- 김용운, "재미있는 수학여행 3" (1991), 김영사
- 김용운, "중국수학사" (1996), 민음사
- 김용운, "한국 수학사" (2012), 살림Math
- 김원경, "중학교 수학②" (2012), 비상교육
- 김원경, "고등학교 수학I" (2014), 비상교육
- 김창동, "고등학교 미적분I" (2014), ㈜교학사
- 김창동, "고등학교 미적분II" (2014), ㈜교학사
- 김창동, "고등학교 기하와 벡터" (2014), ㈜교학사
- 김창동, "고등학교 수학II" (2014), ㈜교학사
- 류희찬, "중학교 수학①" (2013), 천재교과서
- 류희찬, "중학교 수학②" (2013), 천재교과서
- 류희찬, "중학교 수학③" (2013), 천재교과서
- 류희찬, "고등학교 수학I" (2014), 천재교과서
- 류희찬, "고등학교 수학II" (2014), 천재교과서
- 류희찬, "고등학교 기초수학" (2014), 천재교과서
- 러시아 과학 아카데미 철학연구소, "세계철학사1" (2008), 중원문화
- 박종률, "예술(음", 미)과 수학 통합 교수 학습자료 개발, 2013
- 박제남, "현대대수학" (2013), 경문사
- 박제남, "황금비와 수학교육 담론", 수학교육 논문집, 28(2), pp.281~302 (2014), 한국수학교육학회
- 박제남, "초등학교 수학 교과서가 다루는 수학사의 보완 방안 -수학문화의 전이를 중심으로-", 수학교육 논문집, 28(4), pp.493~511 (2014), 한국수학교육학회
- 박제남, "4천년 역사의 흔적" (2004), 교우사
- 손주영, "이집트역사" (2011), 가람기획
- 신준국, "중학교 수학③" (2012), 두배의느낌
- 이광연, "고등학교 미적분II" (2014), 지학사
- 우정호, "중학교 수학②" (2012), 두산동아
- 우정호, "중학교 수학③" (2012), 두산동아
- 우정호, "고등학교 기하와 벡터" (2014), 두산동아
- 이강섭, "고등학교 수학I" (2014), ㈜미래엔
- 이강섭, "고등학교 수학II" (2014), ㈜미래엔
- 이종우, "기하학의 역사적 배경과 발달" (1998), 경문사
- 이정우, "세계철학사1" (2014), 도서출판 길
- 이준열, "중학교 수학③" (2012), 천재교육
- 이준열, "고등학교 수학II" (2014), 천재교육
- 이준열, "고등학교 기초수학" (2014), 천재교육
- 정상권, "중학교 수학①" (2012), ㈜금성출판사
- 정상권, "고등학교 미적분II" (2014), ㈜금성출판사
- 정수용, "수학교과서 속 수학자들에 대한 비판적 분석: 융합적 협업으로서 다문화교육 관점에서", 교과교육학연구, 18(2), pp.441~470 (2014), 교과교육연구소
- 정해남, "예비수학교사를 위한 수학사 활용 방안", 한국수학사학회지, 25(3), pp.141~157 (2012), 한국수학사학회[DOI]
- 한경혜, "수학과 교수-학습에서 수학사 활용의 교육적 함의", 한국수학사학회지, 19(4), pp.31~62 (2006), 한국수학사학회
- 김영록, "고등학교 미적분II" (2014), (주)좋은책신사고
- 황선욱, "고등학교 기하와 벡터" (2014), 좋은책신사고
- 황선욱, "고등학교 수학I" (2014), 좋은책 신사고
- 허민, "중학교 수학①" (2012), 대교
- 허민, "중학교 수학③" (2012), 대교
- Aaboe, A., "Episodes from the early history of mathematics" (1998), MAA
- Aaboe, A, "al-Kashi's iteration method for the determination of sin1°", Scripta Math, 20, pp.24~29 (1954)
- Al-Khalili, J., "The house of wisdom : How Arabic science saved ancient knowledge and gave us the Renaissance" (2010), Penguin Books
- Anderson, M., "Sherlock Holmes in Babylon" (2004), MAA
- Aristoteles, "Politika" (2009), 도서출판 숲
- Aristoteles, "Politica(Oxford Classical Text)" (1957), Oxford Univ. Press
- Armstrong, K., "축의 시대" (2010), 교양인
- Armstrong, K., "The great transformation" (2007), Anchor
- Baragar, A., "Constructions using a compass and twice-notched straightedge", Amer. Math. Monthly, 109, pp.151~164 (2002)
- Bashmakova, I., "The beginnings and evolution of algebra" (2000), MAA
- Beard, C., "The Fibonacci drawing board-design of the great pyramid of Giza", Fibonacci Quarterly, 6, pp.66~68 (1968)
- Berggren, J. L., "Episodes in the mathematics of medieval Islam" (1986), Springer
- Bernal, M., "블랙 아테나, 제1권" (2011), 소나무
- Bernal, M., "Black Athena, Vol. I" (1987), Rutgers Univ. Press
- Bernal, M., "블랙 아테나, 제2권" (2012), 소나무
- Bernal, M., "Black Athena, Vol. II" (1991), Rutgers Univ. Press
- Bernal, M., "Animadversions on the origines of western science", Isis, 83, pp.596~607 (1992)
- Bernal, M, "Response to Robert Palter", Hist. Sci, 32, pp.445~468 (1994)
- Bold, B., "Famous problems of geometry and how to solve them" (1969), Dover
- Bonnard, A., "그리스인 이야기1" (2011), 책과함께
- Bonnard, A., "Civilisation Grecque, Vol. 1" (1954), Les Editions de L’aire
- Bonnard, A., "그리스인 이야기2" (2011), 책과함께
- Bonnard, A., "Civilisation Grecque, Vol. 2" (1957), Les Editions de L’aire
- Boyer, B., "A history of mathematics" (1991), John Wiley
- Bradly, R., "Euler, D’Alembert and the logarithm function, Leonhard Euler: Life, work and legacy" (2007), Elsevier
- Bressoud, D, "Was calculus invented in India?", College Math. J, 33, pp.2~13 (2002)
- Broug, E., "Islamic geometric patterns" (2011), Thames & Hudson
- Brown, E, "Square roots from 1; 24, 51, 10 to Dan Shanks", College Math. J, 30, pp.82~95 (1999)
- Burton, D., "The history of mathematics" (2007), McGraw-Hill
- Cajori, F., "History of the exponential and logarithmic concepts", Amer. Math. Monthly, 20(3), pp.5~14 (1913)
- Cajori, F., "A history of mathematical notations, Vol. I" (1928), The Open Court Pub. Com
- Cajori, F., "A history of mathematics" (1991), AMS
- Chace, A., "The Rhind mathematical papyrus" (1979), NCTM
- Chang, W., "Trisecting angles in Pythagorean triangles", Amer. Math. Monthly, 121, pp.625~631 (2014)
- "Chinese Text Project"[URL]
- Clagett, M., "Ancient Egyptian science, A source book Vol. 3: Ancient Egyptian mathematics" (1999), APS
- Corbin, H., "이슬람 철학사" (1997), 서광사
- Corbin, H., "Histoire de la philosopbie Islamique" (1964), Gallimard
- Couprie, D., "How Thales was able to"predict"a solar eclipse without the help of alleged Mesopotamian wisdom", Early Science and medicine, 9(4), pp.321~337 (2004)
- Curchin, I., "Hero of Alexandria’s numerical treatment of division in extreme and mean ratio and its implications", Pheonix, 35(2), pp.129~133 (1981)
- Dahan-Dalmedico, A., "History of mathematics" (2010), MAA
- Derbyshire, J., "Unknown quantity" (2006), Joseph Henry Press
- Descartes, R., "The Geometry of René Descartes with a facsimile" (1954), Dover
- Dunham, W., "Journey through genius" (1991), Penguin Books
- Durant, W., "문명이야기, 그리스 문명 2-1" (2011), 민음사
- Durant, W., "The story of civilization vol II.: The life of Greece" (1939), Simon & Schuster
- Elam, K., "Geometry of design" (2011), Princeton Architectural Press
- Engels, H., "Quadrature of the circle in ancient Egypt", Historia Mathematica, 4, pp.137~140 (1977)
- Euclid., "The thirteen books of the elements" (1956), Dover
- Eves, H., "Great moments in mathematics before 1650" (1983), MAA
- Eves, H., "An introduction to the history of mathematics" (1990), The Saunders Series
- Fowler, D., "The mathematics of Plato’s academy, A new construction" (2003), Clarendon Press
- Friberg, J., "Unexpected links between Egyptian and Babylonian mathematics" (2005), World Scientific
- Friberg, J., "A remarkable collection of Babylonian mathematical texts" (2007), Springer
- Friberg, J., "Amazing traces of a Babylonian origin in Greek mathematics" (2007), World Scientific
- Fritz, K, "The discovery of incommensurability by Hippasus of Metapontum", Annals of Math, 46, pp.242~264 (1945)
- Gandz, S., "he origin of the term “algebra”", Amer. Math. Monthly, 33, pp.437~440 (1926)
- Gandz, S., "The sources of al-Khowārizmī’s algebra", Osiris, 1, pp.263~277 (1936)
- Gandz, S., "The origin and development of the quadratic equations in Babylonian, Greek, and early arabic algebra", Osiris, 3, pp.405~557 (1937)
- Gast, K., "Le Corbusier, Paris-Chandigarh" (2000), Birkhauser
- Gillings, R., "Mathematics in the time of the pharaohs" (1982), Dover
- Gonzalez-Velasco, E., "Journey through mathematics" (2011), Springer
- Grabiner, J, "Descartes and problem-solving", Math. Mag, 68, pp.83~97 (1995)
- Gutas, D., "그리스 사상과 아랍문명" (2013), 글항아리
- 8th-10th Centuries), "Greek thought, Arabic culture: The Graeco-Arabic Translation Movement in Baghdad and Early ʻAbbāsid Society (2nd-4th", pp.1998, Gutas, D.
- Hahn, A., "Basic calculus : From Archimedes to Newton to its role in science" (1998), Springer
- Hambidge, J., "The elements of dynamic symmetry" (1920), Yale Univ. Press
- Hambidge, J., "Dynamic symmetry : The Greek vase" (1920), Yale Univ. Press
- Hambidge, J., "The Parthenon and the other Greek temples" (1924), Yale Univ. Press
- Heath, T., "Diophantus of Alexandria" (1910), Cambridge Univ. Press
- Heath, T., "Mathematics in Aristotle" (1949), Clarendon Press
- Heath, T., "A history of Greek mathematics, I : From Thales to Euclid" (1981), Dover
- Heath, T., "A history of Greek mathematics, II : From Aristarchus to Diophantus" (1981), Dover
- Heath, T, "The work of Archimedes" (2002), Dover
- Heath, T., "Aristarchus of Samos : The ancient Copernicus" (2004), Dover
- Heidarzadeh, T., "A history of physical theories of comets-From Aristotle to Whipple" (2008), Springer
- Herodotos, "역사" (2012), 도서출판 숲
- Herodotus, "Herodoti historiae, 2vol(Oxford Classical Text)" (1927), OUP
- Ho̷yrup, J., "Lengths, widths, surfaces, A portrait of Old Babylonian algebra and its kin" (2002), Springer
- Hughes, H., "Gerard of Cremon’s translation of Al-Khwarizmi’s al-jabr : A critical edition", Mediaeval Studies, 48, pp.211~263 (1986)
- Iamblichus, "On the Pythagorean way of life(Text, Translation, and Notes : J. Dillon and J. Hershbell)" (1991), Scholars Press
- Jepson, C., "Making square from Pythagorean triangles", College Math. J, 29(4), pp.284~288 (1998)
- Karpinski, L., "Robert of Chester’s Latine translation of the algebra of Al-Khowarizmi" (1915), MacMillan Company
- Katz, V, "Ideas of calculus in Islam and India", Math. Mag, 68, pp.163~174 (1995)
- Katz, V, "The mathematics of Egypt, Mesopotamia, China, India, and Islam, A source book" (2007), Princeton Univ. Press
- Katz, V., "A history of mathematics : An introduction" (2009), Addison-Wesley
- Kitto, H., "그리스 문화사" (2004), 탐구당
- Kitto, H., "The Greeks" (1951), Penguin Books
- Klein, F., "19세기 수학의 발전에 대한 강의" (2012), 나남
- Klein, F., "Vorlesungen über die entwicklung der mathematik Im 19" (1926), Springer
- Kline, M., "Mathematical thought from ancient to modern times, Vol. 1" (1972), Oxford Univ. Press
- Lay-Yong, L., "Circle measurements in ancient China", Historia Mathematica, 13, pp.325~340 (1986)
- Livio, M., "The golden ratio" (2002), Broadway Books
- Livio, M., "신은 수학자인가?" (2009), 열린과학
- Livio, M., "Is god a mathematician?" (2009), Simon & Schuster
- Lorch, R., "Greek-Arabic-Latin: The transmission of mathematical texts in the middle ages", Science in Context, 14, pp.313~331 (2001)
- Lumpkin, B., "The Egyptians and Pythagorean triples", Historia Mathematica, 7, pp.186~187 (1980)
- Lyons, J., "The house of wisdom" (2009), Bloomsbury Press
- Mardia, K., "Omar Khayyam, René Descartes and solutions to algebraic equations", International Congress in Commemorating Hakim Omar Khayyam Neyshabouri.(900th Death Anniversary 9) (2009)
- Markowsky, G, "Misconceptions about the golden ratio. College Math", College Math. J, 23, pp.1~19 (1992)
- Martin, J, "The Helen of geometry", College Math. J, 41, pp.17~28 (2010)
- Martin, T., "고대 그리스의 역사" (2011), 가람기획
- Martin, T., "Ancient Greece" (1996), Yale Univ. Press
- Mendelssohn, K., "The riddle of the pyramids" (1974), Thames and Hudson
- Merzbach, U., "A history of mathematics" (2011), Wiley
- Miatello, L., "The design of the Snefru pyramids at Dahshur and the Netjerikhet pyramid at Saqqara", PalArch’s Journal Archaeology of Egypt, 2005, pp.1(1), 1~11
- Mohanty, S., "Pythagorean Numbers", Fibonacci Quarterly, 28(1), pp.31~42 (1990)
- Nahin, P., "The story of " (1998), Princeton Univ. Press
- Neugebauer, O., "The exact sciences in antiquity" (1957), Dover
- Newton, I., "The principia" (1999), Univ. of California Press
- Ngo, V., "Who cares if has a solution?", College Math. J, 29(2), pp.141~144 (1998)
- Ore, O., "Number theory and its history" (1976), Dover
- Osserman, R., "Mathematics of the Gateway Arch", AMS Notices, 57(2), pp.220~229 (2010)
- Ostermann, A., "Geometry by its history" (2012), Springer
- Panchenko, D., "Thales’s prediction of a solar eclipse", J . for The History of Astronomy, 25, pp.275~288 (1994)
- Palter, R, "Black Athena, Afro-centrism, and the history of science. Hist", Hist. Sci, 31, pp.227~287 (1993)
- Paton, W. R, "The Greek anthology (BOOKS XIII-XVI)" (1979), Harvard Univ. Press
- Phillips, G, "Archimedes the numerical analyst", Amer. Math. Monthly, 88(3), pp.165~169 (1981)
- Pliny, "Natural history" (1967), Harvard Univ. Press
- Platon, "Timaios" (2000), 서광사
- Platon., "Platonis Opera, Tomus IV(Oxford Classical Text)" (1902), Oxford Univ. Press
- Platon., "Menon" (2009), 이제이북스
- Platon, "Platonis Opera, Tomus III(Oxford Classical Text)" (1903), Oxford Univ. Press
- Platon, "Phaedrus" (2011), 문예출판사
- Platon., "Platonis Opera, Tomus II(Oxford Classical Text)" (1910), Oxford Univ. Press
- Platon, "Theaetetos" (2013), 이제이북스
- Platon, "Platonis Opera, Tomus I(Oxford Classical Text)" (1995), Oxford Univ. Press
- Plutarch., "Parallel lives(플루타르크 영웅전I)" (2014), 동서문화사
- Plutarch., "Plutarch’s lives, Vol.1" (1906), Modern Library
- Proclus, "The complete works of Plutarch: Essays and miscellanies, Vol. III" (1909), Crowell
- Ptolemy, "Almagest" (1998), Princeton Univ. Press
- Querejeta, M., "On the eclipse of Thales, cycles and probability", Culture And Cosmos, 15, pp.5~16 (2011)
- Rashed, R, "Problems of the transmission of Greek scientific thought into Arabic: Examples from mathematics and optics", His. Sci, 27, pp.199~209 (1989)
- Rashed, R., "Classical mathematics from Al-Khwarīzmī to Descartes" (2015), Routledge
- Robert, J., "로마에서 중국까지" (2000), 이산
- Robert. J., "De Rome à la Chine" (1993), Les Belles Lettres
- Robins, G., "The Rhind mathematical papyrus" (1987), Dover
- Robson, E., "Neither Sherlock Holmes nor Babylon : A reassessment of Plimpton 322", Historia Mathematica, 28, pp.167~206 (2001)
- Robson, E., "Words and pictures: New light on Plimpton 322", Amer. Math. Monthly, 109, pp.105~120 (2002)
- Robson, E., "Mathematics in ancient Iraq" (2008), Princeton Univ. Press
- Rosen, F, "The algebra of Mohammed ben Musa" (1923), ULAN Press
- Rossi, C., "Architecture and mathematics in ancient Egypt" (2003), Cambridge Univ. Press
- Sontag, S., "해석에 반대한다" (2013), 이후
- Sontag, S., "Against interpretation" (1965), FSG
- Stephenson, F., "Thales’s prediction of a solar eclipse", J. for the History of Astronomy, 28, pp.279~282 (1997)
- Stillwell, J., "Mathematics and history" (2010), Springer
- Struik, D, "A source book in mathematics, 1200-1800" (1986), Princeton Univ. Press
- Suzuki, J., "A history of mathematics" (2002), Prentice Hall
- Suzuki, J., "Mathematics in historical context" (2009), MAA
- Thomas, I, "Greek mathematics II" (1993), Harvard Univ. Press
- Thomas, I, "Greek mathematics I" (2006), Harvard Univ. Press
- Trachtenber, M., "Architecture: From prehistory to post-modernism" (2002), Prentice Hall
- Van Brummelen, G., "The mathematics of the heavens and the earth : The early history of trigonometry" (2009), Princeton Univ. Press
- Van De Mieroop, M., "A history of ancient Egypt" (2011), Wiley-Blackwell
- van der Waerden, B. L., "A history of algebra" (1985), Springer
- Varadarajan, V., "Algebra in ancient and modern times" (1998), AMS
- Veljan, D, "The 2500-year-old Pythagorean theorem", Math. Mag, 73(4), pp.259~272 (2000)
- Wells, D., "The penguin dictionary of curious and interesting numbers" (1997), Penguin Books
- Whitman, E., "Some historical notes on the cycloid", Amer. Math. Monthly, 50(5), pp.309~315 (1943)
