Browse > Article

Reanalysis of Realistic Mathematics Education Perspective in Relation to Cultivation of Mathematical Creativity  

Lee, Kyeong-Hwa (Seoul National University)
Publication Information
Journal of Educational Research in Mathematics / v.26, no.1, 2016 , pp. 47-62 More about this Journal
Cultivating mathematical creativity is one of the aims in the recently revised mathematics curricular. However, there have been lack of researches on how to nurture mathematical creativity for ordinary students. Perspective of Realistic Mathematics Education(RME), which pursues education of creative person as the ultimate goal of mathematics education, could be useful for developing principles and methods for cultivating mathematical creativity. This study reanalyzes RME from the points of view in mathematical creativity education. Major findings are followed. First, students should have opportunities for mathematical creation through mathematization, while seeking and creating certainty. Second, it is vital to begin with realistic contexts to guarantee mathematical creation by students, in which students can imagine or think. Third, students can create mathematics in realistic contexts by modelling. Fourth, students create the meaning of 'model of(MO)', which models the given context, the meaning of 'model for(MF)', which models formal mathematics. Then, students create MOs and MFs that are equivalent to the intial MO and MF given by textbook or teacher. Flexibility, fluency, and novelty could be employed to evaluate the MOs and the MFs created by students. Fifth, cultivation of mathematical creativity can be supported from development of local instructional theories by thought experiment, its application, and reflection. In conclusion, to employ the education model of cultivating mathematical creativity by RME drawn in this study could be reasonable when design mathematics lessons as well as mathematics curriculum to include mathematical creativity as one of goals.
Realistic mathematics education; mathematical creativity; mathematization; realistic context; modeling;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 김연식.정영옥(1997). Freudenthal의 수학화 학습 -지도론 연구. 수학교육학연구, 7(2), 1-23.
2 김진호(2003). 학교수준에서의 수학적 창의성에 대한 논의. 교육과학연구, 34(2), 149-165.
3 김진호(2004). 수학적 창의성에 대한 일 논의-창의적인 사람, 창의적인 산물, 창의적인 과정이란 관점으로부터. 수학교육논문집, 18(3), 45-56.
4 성창근.박성선(2012). 수학적 창의성 계발을 위 한 과제와 수업 방향 탐색. 한국초등수학교육학회지, 16(2), 253-267.
5 우정호(2000). 수학 학습-지도 원리와 방법. 서울: 서울대학교 출판부.
6 이경화(2015). 수학적 창의성. 서울: 경문사.
7 정영옥(1997). Freudenthal의 수학화 학습-지도론 연구. 서울대학교 대학원 박사학위 논문.
8 정영옥(1999). 현실적 수학교육에 대한 고찰. 수학교육학연구, 9(1), 81-109.
9 정영옥(2005). 교과과정 개발을 위한 기초로서의 개발연구에 대한 고찰. 수학교육학연구, 15(3), 353-374.
10 한정민.박만구(2010). 수학적 창의성 관점에서 본 교사의 발문 분석. 한국초등수학교육학회지, 14(3), 865-884.
11 황우형.최계현.김경미.이명희(2006). 수학교육과 수학적 창의성. 수학교육논문집, 20(4), 561-574.
12 Bobis, J., & Bobis, E. (2005). The empty number line: Making children's thinking visible. In Coupland, M., Anderson, J., & Spencer, T. (Eds.). Proceedings of the twentieth biennial conference of the Australian association of mathematics teachers, 66-72.
13 Bobis, J. (2007). The Empty Number Line: A Useful Tool or Just Another Procedure?. Teaching Children Mathematics, 13(8), 410-413.
14 Brendel, E. (2004). Intuition pumps and the proper use of thought experiments. Dialectica, 58(1), 89-108.
15 Freudenthal, H. (1968). Why to teach mathematics so as to be useful. Educational studies in mathematics, 1(1), 3-8.   DOI
16 교육부(2015). 2015 개정 수학과 교육과정. 교육부 고시 제2015-74호 [별책8].
17 김도한.황혜정.김창일.정영옥.박만구. 고호경.김선희.한혜숙.한세호.김현아.장미라.정은선(2010). 창의 중심의 수학 수업 내실화 및 평가 방안 연구. 서울: 한국과학창의재단.
18 Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Kluwer Academic Publishers.
19 Freudenthal, H. (1981). Major problems of mathematics education. Educational studies in mathematics, 12(2), 133-150.   DOI
20 Freudenthal, H. (1991). Revisiting Mathematics Education: China Lectures. Dordrecht: Kluwer Academic Publishers.
21 Hanna, R. (2002). Mathematics for humans: Kant's philosophy of arithmetic revisited. European Journal of Philosophy, 10(3), 328-352.   DOI
22 Gravemeijer, K. (1993a). Modelling two-digit addition and subtraction with an empty number line. Teaching and learning mathematics in contexts, 51-61.
23 Gravemeijer, K. (1993b). The empty number line as an alternative means of representation for addition and subtraction. Innovation in mathematics education by modelling and applications, 141-159.
24 Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical thinking and learning, 1(2), 155-177.   DOI
25 Klein, A. S., Beishuizen, M., & Treffers, A. (1998). The empty number line in Dutch second grades: Realistic versus gradual program design. Journal for Research in Mathematics Education, 443-464.
26 Klein, A. S., Beishuizen, M., & Treffers, A. (2002). The empty number line in Dutch second grade. Lessons learned from research, 41-44.
27 Otte, M. F., Campos, T. M., & Abido, A. S. (2013). Plato, Pascal, and the dynamics of personal knowledge. Educational Studies in Mathematics, 82(3), 397-415.   DOI
28 Prediger, S., Gravemeijer, K., & Confrey, J. (2015). Design research with a focus on learning processes: an overview on achievements and challenges. ZDM, 47(6), 877-891.   DOI
29 Van den Heuvel-Panhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour. Freudenthal Institute CD-rom for ICME9, 1-32.
30 Van Den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9-35.   DOI
31 Van Oers, B. (2002). The mathematization of young children's language. In Symbolizing, modeling and tool use in mathematics education (pp. 29-58). Springer Netherlands.
32 Van den Heuvel-Panhuizen, M. (2008). Learning from "didactikids": An impetus for revisiting the empty number line. Mathematics Education Research Journal, 20(3), 6-31.   DOI
33 Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic mathematics education. In Lerman, S. (Ed.). Encyclopedia of mathematics education (pp. 521-525). Springer Netherlands.