Browse > Article

A Case Study on Utilizing Invariants for Mathematically Gifted Students by Exploring Algebraic Curves in Dynamic Geometry Environments  

Choi, Nam Kwang (DeaJean Science High School)
Lew, Hee Chan (Korea National University of Education)
Publication Information
Journal of Educational Research in Mathematics / v.25, no.4, 2015 , pp. 473-498 More about this Journal
Abstract
The purpose of this study is to examine thinking process of the mathematically gifted students and how invariants affect the construction and discovery of curve when carry out activities that produce and reproduce the algebraic curves, mathematician explored from the ancient Greek era enduring the trouble of making handcrafted complex apparatus, not using apparatus but dynamic geometry software. Specially by trying research that collect empirical data on the role and meaning of invariants in a dynamic geometry environment and research that subdivide the process of utilizing invariants that appears during the mathematically gifted students creating a new curve, this study presents the educational application method of invariants and check the possibility of enlarging the scope of its appliance.
Keywords
Mathematically gifted students; level-1 invariants; level-2 invariants; types of creating curves utilizing invariants;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 김진호, 김용대, 서보억(2011). 3대 작도 문제 해결을 위한 곡선과 기구. 서울: 교우사.
2 김향숙, 박진석, 도석수, 윤삼열, 김영미, 이세룡, 정성곤, 배옥향, 이혜경, 박혜정(2007). 창의성 신장을 위한 문제일반화. 서울: 경문사.
3 남선주(2006). 역동적 기하 환경에서 분석법을 활용한 증명학습에 관한 연구. 한국교원대학교 대학원 석사학위 논문.
4 류희찬(2004). 수학교육에서 탐구형 소프트웨어의 활용과 의미. 청람수학교육, 14, 1-15.
5 류희찬, 윤옥교(2013). 역동적 기하 환경에서 비례를 이용한 중학교 함수의 작도. 학교수학 13(1), 19-36.
6 류희찬, 제수연(2009). 역동적 기하 환경에서 파푸스의 분석법을 이용한 이차곡선의 작도활동에서 나타난 학생들의 수학적 발견과 정당화. 한국교원대학교 교육연구원, 25(4), 168-189.
7 유윤재(2010). 수학영재교육. 서울: 교우사.
8 윤옥교(2014). 역동적 기하 환경에서 비례에 기반한 함수와 이차방정식 작도 문제 해결 과정 연구. 한국교원대학교 박사학위논문.
9 장혜원(1997). 중학교 기하 영역 중 작도 단원에 관한 고찰. 대한수학교육학회 논문집 7(2), 327-336.
10 조정수, 이은숙(2013), 역동기하 환경에서 "끌기(Dragging)"의 역할에 대한 고찰, 학교수학 15(2), 481-501.
11 진만영, 김동원, 송민호, 조한혁(2012). 원뿔곡선의 수학사와 수학교육. 한국수학사학회지. 25(4), 83-99.
12 Arzarello, F., Olivero, F., Paola, D., & Robutti, O.(2002). A Cognitive Analysis of Dragging Practices in Cabri Environments. ZDM, 34(3), 66-72.
13 Baccaglini-Frank, A., Mariotti, M. A., & Antonini, S.(2009). Different perceptions of invariants and generality of proof in dynamic geometry. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, 2, 89-96.
14 Baccaglini-Frank, A. & Mariotti, M.A.,(2010). GeneratingConjectures through Dragging in DynamicGeometry: the Maintaining Dragging Model.International Journal of Computers forMathematical Learning 15(3), 225-253.   DOI
15 Drijvers, P., Kieran, C., Mariotti, M. A., Ainley, J., Andresen, M., Chan, Y. C., Dana-Picard, T., Gueudet, G., Kidron, I., Leung, A., & Meagher, M.(2010). Integrating technology into mathematics education : Theoretical perspectives. In C. Hoyles & JB. Lagrange (Eds.), Mathematics education and technology-Rethinking the terrain. pp. 89-132. New York: Springer.
16 Falcaede, R., Laborde, C., & Mariotti, M. A.(2007). Approaching functions; Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317-333.   DOI
17 Jones, K.(2000). Providing a foundation for deductive reasoning: Students' interpreations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1), 55-85.   DOI
18 Laborde, C.(2003). Technology used as a tool for mediating knowledge in the teaching of mathematics: The case of Cabri-geometry. In W.-C. Yang, S. C. Chu, T. de Alwis, & M. G. Lee (Eds.), Proceedings of the 8th Asian Technology Conference in Mathematics(1), 23-38.
19 Laborde, C., & Laborde, J. M. (1995). What about a learning environment where Euclidean concepts are manipulated with a mouse? In A. di Sessa, C. Hoyles, R. Noss (Eds.), Computers and exploratory learning. 241-262.
20 Leung, A.(2008). Dragging in a dynamic geometry environment through the lens of variation. International Journal of Computers for Mathematical Learning, 13, 135-157.   DOI
21 Olivero, F. (2002). The proving process within a dynamic geometry environment. Doctoral thesis. Bristol: University of Bristol.
22 Leung, A.(2012). Discernment and reasoning in dynamic geometry environments. Paper presented at the 12th International Congress on Mathematical Education, Seoul, Korea.
23 Leung, A., Baccaglini-Frank, A., Mariotti, M. A.(2013). Discernment of invariants in dynamic geometry environments. Educational Studies in Mathematics, 84(3). 439-460.   DOI
24 Marrades, R., & Gutierrez, A.(2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational studies in mathematics, 44(1-2), 87-125.   DOI
25 Tall, D.(1995). Cognitive developments, representations and proof. Paper presented at the conference Justifying and Proving in School Mathematics, Institute of Education, London, pp. 27-38.
26 Weisberg, R. W. (2006). Creativity: Understanding Innovation in Problem Solving, Science, Invention, and the Arts. NJ: John Wiley & Sons. (김미선 역). 서울: 시그마프레스.