Browse > Article

Publication Information

Journal of Educational Research in Mathematics
/ v.27, no.1,
2017
, pp.
69-88
More about this Journal

Abstract

One of the most important activities in the process of mathematical modeling is to build models by conjecturing mathematical rules and principles in the real phenomena and to validate the models by considering its validity. Due to uncertainty and ambiguity inherent real-contexts, various strategies and solutions for mathematical modeling can be available. This characteristic of mathematical modeling can offer a proper environment in which creativity could intervene in the process and the product of modeling. In this study, first we analyze the process and the product of mathematical modeling, especially focusing on the students' models and validating way, to find evidences about whether modeling can facilitate students'creative thinking. The findings showed that the students' creative thinking related to fluency, flexibility, elaboration, and originality emerged through mathematical modeling.

Keywords

mathematical modeling; mathematical creativity;

Citations & Related Records

- Reference

1 | Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students. (pp. 129-145). Rotterdam, the Netherlands: Sense Publisher. |

2 | Mann, E. L. (2006). Creativity : The Essence of Mathematics, Journal for the Education of the Gifted, 30(2), 236-260. DOI |

3 | Nadjafikhah, M., Yaftian, N. & Bakhshalizadeh, S. (2012). Mathematical creativity: some definitions and characteristics. Procedia- Social and Behavioural Sciences, 31, 285-291. DOI |

4 | Otte, M. (2011). Evolution, learning, and semiotics from a Peircean point of view, Educational Studies in Mathematics, 77, 313-329. DOI |

5 | Plucker, J. A. & Beghetto, R. A. (2004). Why creativity is domain general, why it looks domain specific, and why the distinction does not matter. In R. J. Sternberg, E. L. Grigorenko, & J. L. Singer (Eds.), Creativity: From potential to realization (pp. 153-167). Washington, DC: American Psychological Association. |

6 | Reiter-Palmon, R., Illies, M. Y., Cross, L. K., Buboltz, C. & Nimps, T. (2009). Creativity and domain specificity: The effect of task type on multiple indexes of creative problemsolving. Psychology of aesthetics, creativity, and the arts, 3(2), 73-80. DOI |

7 | Sheffield, L. J. (2006). Developing mathematical promise and creativity. Research in Mathematics Education, 10(1), 1-11. DOI |

8 | Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem posing and problem solving. ZDM, 29(3), 75-80. DOI |

9 | Sriraman, B. (2005). Are giftedness & creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17, 20-36. DOI |

10 | Sriraman, B., Yaftian, N. & Lee, K. H. (2011). Mathematical creativity and mathematics education, In K. H. Lee, B. Sriraman (eds.) The elements of creativity and giftedness in mathematics (pp. 119-130). Sense publishers. |

11 | Stake, R. (1995). The art of case study research, Thousand Oaks: Sage Publications. |

12 | Yuan, X. & Sriraman, B. (2011). An exploratory study of relationships between students' creativity and mathematical problem-posing abilities, In K. H. Lee, B. Sriraman (eds.) The elements of creativity and giftedness in mathematics (pp. 5-28). Sense publishers. |

13 | 이정연, 이경화(2010). Simpson의 패러독스를 활용한 영재교육에서 창의성 발현 사례 분석, 수학교육학연구, 20(3), 203-219. |

14 | 박만구(2009). 수학교육에서 창의성의 개념 및 신장 방안, 수학교육, 23(3), 803-822. |

15 | 박진형, 김동원(2016). 예 만들기 활동에 의한 창의적 사고 촉진 방안 연구, 수학교육학연구, 26(1), 1-22. |

16 | 이경화(2015). 수학적 창의성: 수학적 창의성의 눈으로 본 수학교육, 서울: 경문사. |

17 | Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instruction and the dialectics between technical and conceptual work. International Journal of Computers and Mathematical Learning, 7, 245-274. DOI |

18 | Blum, W. & Borromeo Ferri, R. (2009). Mathematical Modelling: Can It Be Taught And Learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58. |

19 | Blomhoj, M. & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work - Experiences from an in-service course for upper secondary teachers, ZDM, 38(2), 163-177. DOI |

20 | Blum, W. et al. (2002). ICMI study 14: Applications and modelilng in mathematics education - Discussion document. Educational Studies in Mathematics, 51, 149-171. DOI |

21 | Chamberlin, S. A. & Moon, S. M. (2005). Model-eliciting activities as tool to develop and identify creativity gifted mathematicians. Journal of Secondary Gifted Education, 17(1), 37-47. DOI |

22 | Galbraith, P. & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process, ZDM, 38(2), 143-162. DOI |

23 | Chan, C, M. E. (2008). The use of mathematical modeling tasks to develop creativity, In E. Veikova, A. Andzans, (eds.), Promoting creativity for all students in mathematics education (pp. 207-216). Bulgaria: University of Rousse. |

24 | Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Thousand Oaks, CA: Sage Publications. |

25 | Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics, Educational Studies in Mathematics, 61, 103-131. DOI |

26 | Guin, D. & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematics Learning, 3, 195-227. |

27 | Lesh, R., Middleton, J. A., Caylor, E. & Gupta, S. (2008). A science need: Designing tasks to engage students in modeling complex data, Educational Studies in Mathematics, 68, 113-130. DOI |

28 | Kaiser, G. (2007). Modelling and modelling competencies in school, In P. Galbraith, W. Blum, S. Khan (eds.) Mathematical modelling education, engineering and economics (pp. 110-119). Chechester: Horwood. |

29 | Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. (J. Kilpatrick & I. Wirszup, Eds.; J. Teller, Trans.). Chicago: University of Chicago Press. (Original work published 1968) |

30 | Lesh, R. A., Cramer, K., Doerr, H., Post, T. & Zawojewski, J. S. (2003) Model development sequences. H. Doerr & R. A. Lesh (Eds) Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving (pp. 35-58). Mahwah, NJ: Lawrence Erlbaum. |