1 |
Sriraman, B. (2004). Reflective abstraction, uniframes and formulation of generalizations. Journal of Mathematical Behavior, 23(2), 205-222.
DOI
|
2 |
Tall, D. (2011). Looking for the bigger picture. For the Learning of Mathematics., 31(2), 17-18.
|
3 |
Wagner, R. (2013). A historically and philosophically informed approach to mathematical metaphors. International Studies in the Philosophy of Science, 27(2), 109-135.
DOI
|
4 |
Yerushalmy, M., & Gilead, S. (1997). Solving equations in a technological environment. Mathematics Teacher, 90(2), 156-162.
|
5 |
Zazkis, R., Liljedahl, P., & Chernoff, E. J. (2007). The role of examples in forming and refuting generalizations. ZDM Mathematics Education, 40(1), 131-141.
|
6 |
교육과학기술부(2011). 수학과 교육과정. 교육과학기술부 고시 제 2011-261호 [별책 8].
|
7 |
교육부(2015). 수학과 교육과정. 교육부 고시 제 2015-74호 [별책 8].
|
8 |
류희찬․조완영․이정례․선우하식․이진호․손홍찬․신보미․조정묵․이병만․김용식․임미선․선미향․유익승․한명주․박원균․남선주․김명수․정성윤(2014). 고등학교 수학 I. 서울: 천재교과서.
|
9 |
우정호(2007). 학교수학의 교육적 기초(증보판 2판). 서울대학교 출판부.
|
10 |
우정호․민세영․정연준(2003). 역사발생적 수학교육 원리에 대한 연구(2): 수학사의 교육적 이용과 수학교사 교육. 학교수학, 5(4), 555-572.
|
11 |
이경화(2010). 교수학적 변환 과정에서 은유와 유추의 활용. 수학교육학연구, 20(1), 57-71.
|
12 |
Allaire, P. R., & Bradley, R. E. (2001). Geometric approaches to quadratic equations from other times and places. Mathematics Teacher, 94(4), 308-319.
|
13 |
Amir-Moez, A. R. (1962). Khayyam's solution of cubic equations. Mathematics magazine, 35(5), 269-271.
DOI
|
14 |
Common Core State Standards Initiative(CCSSI). (2010). Common Core State Standards For Mathematics. U.S.A.
|
15 |
Atiyah, M. (2001). Mathematics in the 20th Century: geometry versus algebra. Mathematics Today, 37(2), 46-53.
|
16 |
Berggren, J. L. (1986). Episodes in the mathematics of medieval Islam. New York: Springer-Verlag.
|
17 |
Boyer, C. B., & Merzbach, U. C. (1991). A history of mathematics (2nd ed). New York: McGraw-Hill.
|
18 |
Dikovic, L. (2009). Applications geogebra into teaching some topics of mathematics at the college level. Computer Science and Information Systems, 6(2), 191-203.
DOI
|
19 |
Connor, M. B. (1956). A historical survey of methods of solving cubic equations. Unpublished master's dissertation, University of Richmond, Virginia.
|
20 |
Coxford, A. F. (1995). The case for connections. In P. A. House & A. F. Coxford (Eds.), Connecting mathematics across the curriculum (pp. 3-12). Reston, VA: National Council of Teachers of Mathematics.
|
21 |
English, L. D. (Ed.). (2004). Mathematical and analogical reasoning of young leaders. Mahwah, NJ: Lawrence Erlbaum Associates.
|
22 |
Erez, M. M., & Yerushalmy, M. (2006). "If you can turn a rectangle into a square you can turn a square into a rectangle..." young students experience the dragging tool. International Journal of Computers for Mathematics Learning, 11(3), 271-299.
|
23 |
Eves, H. (1958). Omar Khayyam's Solution of Cubic Equation. Mathematics Teacher 51, 285-286.
|
24 |
Guilbeau, L. (1930). The History of the Solution of the Cubic Equation. Mathematics News Letter, 5(4), 8-12.
|
25 |
Eves, H. (1995). 수학의 역사(이우영, 신항균 역). 서울: 경문사. (원저는 1953년에 출판).
|
26 |
Georgia Department of Education(GDE). (2014). Common Core Georgia Performance Standards Frameworks of Mathematics, CCGPS Coordinate Algebra Unit 6: Connecting Algebra and Geometry through Coordinates. U.S.A.
|
27 |
Grabiner, J. (1995). Descartes and problem-solving. Mathematics Magazine, 68(2), 83-97.
DOI
|
28 |
Healy, L., & Hoyles, C. (2001). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235-256.
DOI
|
29 |
Henning, H. B. (1972). Geometric solutions to quadratic and cubic equations. Mathematics Teacher, 65, 113-119.
|
30 |
Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal of Research in Mathematics Education, 32(2), 195-222.
DOI
|
31 |
Hoyles, C., Noss, R., & Pozzi, S. (1999). Mathematizing in practice. In C. Hoyles, C. Morgan, & G. Woodhouse (Eds.), Rethinking the mathematics curriculum (pp. 48-62). London: Falmer Press.
|
32 |
Jones, K. (2002). Research on the use of dynamic geometry software. MicroMath, 18(3), 18-20.
|
33 |
Kasir, D. S. (1931). The Algebra of Omar Khayyam. Columbia University, NY.
|
34 |
Katz, V. J. (1997). Algebra and its teaching: An historical survey. Journal of Mathematical Behavior, 16(1), 25-38.
DOI
|
35 |
Laborde, C. (1998). Relationship between the spatial and theoretical in geometry: The role of computer dynamic representations in problem solving. In J. D. Tinsley & D. C. Johnson (Eds.), Information and communications technologies in school mathematics (pp. 183-195). London, UK: Chapman & Hall.
|
36 |
Khayyam, O. (2008). An essay by the uniquely wise 'ABEL FATH BIN AL-KHAYYAM on algebra and equations. Translated by R. Khalil & Reviewed by W. Deeb. UK: RG1 4QS.
|
37 |
Knuth, E. J. (2000). Understanding connections between equations and graphs. Mathematics Teacher, 93(1), 48-53.
|
38 |
Krantz, S. G. (2010). An episodic history of mathematics: Mathematical culture through problem solving. The Mathematical Association of America.
|
39 |
Laborde, C. (2010). Linking geometry and algebra through dynamic and interactive geometry. In Z. Usiskin, K. Andersen, & N. Zotto (Eds.), Future curricular trends in school algebra and geometry (pp. 217-230). Charlotte, NC: Information Age Publishing.
|
40 |
Lakoff, G., & Nunez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.
|
41 |
Mardia, K. V. (1999). Omar Khayyam, Rene Descartes and solutions to algebraic equations. Presented to Omar Khayyam Club, London. Retrieved from http://www1.maths.leeds.ac.uk/-sta6kvm/omar.pdf.
|
42 |
Law, H. L. (2003). The comparison between the methods of solution for cubic equations in Shushu Jiuzhang and Risalah fil-barahin a'la masail ala-Jabr wa'l-Muqabalah. Mathematical Modley, 30(2), 91-101.
|
43 |
Lee, K. H., & Sriraman, B. (2011). Conjecturing via reconceived classical analogy. Educational Studies in Mathematics, 76, 123-140.
DOI
|
44 |
Lumpkin, B. (1978). A mathematics club project from Omar Khayyam. Mathematics Teacher, 71(9), 740-744.
|
45 |
Maryland Department of Education(MDE). (2013). Maryland Common Core State Curriculum Unit Plan for Geometry. Geometry Unit 4: Connecting Algebra and Geometry through Coordinates. U.S.A.
|
46 |
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author. 류희찬, 조완영, 이경화, 나귀수, 김남균, 방정숙 공역(2007). 학교수학을 위한 원리와 규준. 서울: 경문사.
|
47 |
Mena, R. (2009). First course in the history of mathematics (pp.123-125). Unpublished paper, California State University. Retrieved from http://web.csulb.edu/-rmena/History/Complete%20Notes%20303%20 with%20exercises.pdf.
|
48 |
Mitchelmore, M. C. (2002). The role of abstraction and generalisation in the development of mathematical knowledge. In D. Edge, & B. H. Yeap (Eds.), Mathematics education for knowledge-based era (Proceedings of the 2nd East Asia Regional Conference on Mathematics Education and the 9th Southeast Asian Conference on Mathematics Education) (pp. 157-167). Singapore: Association of Mathematics Educators.
|
49 |
National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author. 구광조, 오병승, 류희찬 공역(1992). 수학교육과정과 평가의 새로운 방향. 서울: 경문사.
|
50 |
Polya, G. (2005). 어떻게 문제를 풀 것인가? -수학적 사고와 방법-(우정호 역). 서울: 경문사. (원저는 1956년에 출판).
|
51 |
Sangwin, C. (2007). A brief review of GeoGebra: dynamic mathematics. MSOR Connections, 7(2), 36-38.
DOI
|
52 |
Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press.
|