# 대칭성을 고려한 방정식의 해법 지도

• Accepted : 2015.11.12
• Published : 2015.11.30

#### Abstract

Based on Lagrange's general theory of algebraic equations, by applying the solution of the equation using the relationship between roots and coefficients to the high school 1st grade class, the purpose of this study is to recognize the significance of symmetry associated with the solution of the equation. Symmetry is the core idea of Lagrange's general theory of algebraic equations, and the relationship between roots and coefficients is an important means in the solution. Through the lesson, students recognized the significance of learning about the relationship between roots and coefficients, and understanded the idea of symmetry and were interested in new solutions. These studies gives not only the local experience of solutions of the equations dealing in school mathematics, but the systematics experience of general theory of algebraic equations by the didactical organization, and should be understood the connections between knowledges related to the solutions of the equation in a viewpoint of the mathematical history.

#### References

1. 고영미․이상욱 (2014). 라그랑주의 방정식론. 한국수학사학회지, 27(3), 165-182. Koh, Y. M., Ree, S. W. (2014). Lagrange and Polynomial Equations. Journal for History of Mathematics, 27(3), 165-182. https://doi.org/10.14477/jhm.2014.27.3.165
2. 교육과학기술부 (2008). 2007 고등학교 교육과정 해설 (5) 수학. 교육인적자원부. Ministry of Education, Science and Technology (2008). The 2007 Revised curriculum Guide for high Schools (5) Mathematics. MEST.
3. 김경희․김부윤 (2000). 유리계수 다항방정식의 해법에 대한 고찰. 한국수학교육학회지 시리즈 E <수학교육 논문집>, 10, 351-379. Kim, K. H., Kim, B. Y. (2000). A study on the solution of polynomial equations with rational coefficients. Communications Mathematics Education, 10, 351-379.
4. 김응태․박승안 (2012). 현대대수학. 서울: 경문사. Kim, E. T., Park, S. A. (2012). Modern Algebra. Seoul: KYUNGMOON PUBLISHERS.
5. 남진영․박선용 (2002). 대칭성의 관점에서 본 '문제해결' 및 '군' 개념지도. 대한수학교육학회지 <수학교육학연구>, 12(4), 509-521. Nam, J. Y., Park. S. Y. (2002). Problem solving and teaching 'group concept' from the point of symmetry. Journal Educational Research in Mathematics, 12(4), 509-521.
6. 서울대학교 국정도서편찬위원회 (2003). 고급수학. 교육인적자원부. Seoul National University Compilation Committee of National book (2003). Advanced Mathematics. Ministry of Education & Human Resources Development.
7. 성기원 (1998). n차 방정식의 근과 계수의 관계에 대한 연구. 석사학위논문, 홍익대학교. Seong, G. W. (1998). The relation between the roots and the coefficients of polynomial equations. Master's Thesis, Hongik University.
8. 이대현 (2004). 방정식의 해법에 관한 소고. 한국수학사학회지, 17(1), 61-68. Lee, D. H. (2004). A study on solution of equations. Journal for History of Mathematics, 17(1), 61-68.
9. Freudenthal, Hans (1973), Mathematics as an Educational Task. Dordrecht: D. Reidel Pub. Co.
10. Gowers, Timothy, June Barrow-Green, Imre Leader (2014). The Princeton Companion to Mathematics1 (금종해 외 28명 역), 서울: 승산. (원저 2008년 출판) Keum, J. H. et al. (2014). The Princeton Companion to Mathematics1 (translation of the book by Gowers, Timothy, June Barrow-Green, Imre Leader. Princeton University Press, 2008). Seoul : Seungsan.
11. Hungerford, Thomas W. (2006). Abstract Algebra : An Introduction, Cleveland: Books/Cole.
12. Klein, Felix C. (2012). 19세기 수학의 발전에 대한 강의 (한경혜 역). 서울: 나남. (원저 1967년 출판) Han, G. H. (2012). Vorlesungen uber die Entwicklung der Mathematik im 19. Jahrhunder (translation of the book by Klein, Felix C.. 1967). Seoul : Nanam Publishing House.
13. Kleiner, Israel (2012). 추상대수학의 역사 (김부윤․정영우 역). 서울: 경문사. (원저 2007년 출판) Kim, B. Y., Chung, Y. W. (2012). A History of Abstract Algebra (translation of the book by Israel Kleiner. Birkhäuser Boston, 2007). Seoul : KYUNGMOON PUBLISHERS.
14. Ronan, Mark (2007). 몬스터 대칭군을 찾아서 (심재관 역). 서울 : 살림Math. (원저 2006년 출판) Sim, J. G. (2007). Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics (translation of the book by Mark Ronan. Oxford University Press, 2006). Seoul : SalimMath.
15. The Inter-IREM Commision (1997). History of Mathematics Histories of Problems. Paris: Ellipses.
16. Wely. H. (1952). Symmetry. Princeton University Press.
17. 片野善一郎 (2011). 수학사를 활용한 교재 연구 (김부윤․정영우 역), 서울: 경문사. (원저 1992년 출판) Kim, B. Y., Chung, Y. W. (2011). A Study on the textbooks using Mathematical History (translation of the book by Zenichiro Katano. Meijitosho Shuppan Corporation, 1992). Seoul : KYUNGMOON PUBLISHERS.