학교수학에서 인수분해의 지도
Teaching Factorization in School Mathematics
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Abstract
This paper focuses on two problems in the 10th grade mathematics, the rational zero theorem and the content(the integer divisor) of a polynomial. Among 138 students participated in the problem solving, 58 of them (42 %) has used the rational zero theorem for the factorization of polynomials. However, 30 of 58 students (52 %) consider the rational zero theorem is a mathematical fake(false statement) and they only use it to get a correct answer. There are three different types in the textbooks in dealing with the content of a polynomial with integer coefficients. Computing the greatest common divisor of polynomials, some textbooks consider the content of polynomials, some do not and others suggest both methods. This also makes students confused. We suggests that a separate section of the rational zero theorem must be included in the text. As for the content of a polynomial, we consider the polynomials are contained in the polynomial ring over the rational numbers. So computing the gcd of polynomials, guide the students to give a monic(or primitive) polynomial as an answer.
참고문헌 (29)
- 교육부, "고등학교 수학과 교육과정 해설" (1992), 대한교과서주식회사
- 교육부, "제 7 차 수학과 교육과정" (1997), 대한교과서주식회사
- 한국교육과정평가원, "수학과 교육과정 개정 시안 및 수준별 수업활성화 방안" (2005), 한국교육과정평가원
- 강행고, "수학 10-가" (2001), 동화사
- 김수환, "수학 10-가" (2001), 지학사
- 박규홍, "수학 10-가" (2001), 교학사
- 박배훈, "수학 10-가" (2001), 범문사
- 박세희, "수학 10-가" (2001), 동아서적
- 박윤범, "수학 10-가" (2001), 대한교과서
- 신현승, "수학 10-가" (2001), 천재교육
- 양승갑, "수학 10-가" (2001), 금성출판사
- 우정호, "수학 10-가" (2001), 대한교과서
- 이광복, "수학 10-가" (2001), 새한교과서
- 임재훈, "수학 10-가" (2001), 두산
- 장건수, "수학 10-가" (2001), 지구문화사
- 최봉대, "수학 10-가" (2001), 중앙교육진흥연구소
- 최상기, "수학 10-가" (2001), 고려출판
- Auslander, M, "Unique factorization in regular local rings", Proceeing in Natl. Acad. Sci. U. S. A., 42, pp.36~38
- Burton,D.M, "History of Mathematics" (1995), Wm. C. Brown Publishers
- Choi,S, "The divisor class group of surfaces of embedding dimension 3", Journal of Algebra, 119, pp.162~169 (1988)
- Collins, W, "Glencoe Algebra 2" (2007), McGraw-Hill
- Eisenbud,D, "Recent progress in commutative algebra, Algebraic Geometry - Arcta 1974", Proc. pure math, 29, pp.111~128 (1975)
- Hartshorne,R, "Teaching geometry according to Euclid", Notices of the American Mathematical Society, 47(4) (2000)
- Heath,T.L, "The thirteen books of Euclid's Elements" (1926), Cambridge University Press
- Huneke,C, "An algebraist commuting in Berkeley", Mathematical Intelligencer, 11(1) (1989), Springer-Verlag
- Larson, R, "Algebra 2" (2007), McDougal Littell
- Lasker,E, "Zur Thoerie der Modulin and ideale", Math. Ann, 60, pp.20~116 (1905)
- Lipman,J, "Rational singularities with application to algebraic surfaces and unique factorizations", IHES, 36, pp.195~279 (1969)
- Mordell,L.J, "A chapter in the theory of numbers-An inaugural lecture" (1947), Cambridge University Press