School Mathematics (대한수학교육학회지:학교수학)

The Korea Society of Educational Studies in Mathematics (대한수학교육학회)
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A Study on the Qualitative Differences Analysis between Multiple Solutions in Terms of Mathematical Creativity

수학적 창의성 관점에서 다중해법 간의 질적 차이 분석

  • Received : 2017.08.10
  • Accepted : 2017.09.19
  • Published : 2017.09.30
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Abstract

Tasks of multiple solutions have been said to be suitable for the cultivation of mathematical creativity. However, studies on the fact that multiple solutions presented by students are useful or meaningful, and students' thoughts while finding multiple solutions are very short. In this study, we set goals to confirm the qualitative differences among the multiple solutions presented by the students and, if present, from the viewpoint of mathematical creativity. For this reason, after presenting the set of tasks of the two versions to eight mathematically gifted students of the second-grade middle school, we analyzed qualitative differences that appeared among the solutions. In the study, there was a difference among the solution presented first and the solutions presented later, and qualitatively substantial differences in terms of flexibility and creativity. In this regard, it was concluded that the need to account for such qualitative differences in designing and applying multiple solutions should be considered.

다중해법 문제는 수학적 창의성 함양에 적합하다고 알려져 왔다. 그런데 학생들이 제시한 다중해법들이 모두 유용하거나 의미 있는지, 학생들이 다중해법을 찾아 나가면서 어떤 사고를 하는지에 대한 연구는 매우 부족하다. 본 연구는 학생들이 제시한 다중해법 간에 질적 차이가 존재하는지, 존재한다면 수학적 창의성의 관점에서 어떤 차이인지를 확인하는 데 목표를 둔다. 이를 위해 영재교육원에 재원 중인 중학교 2학년 학생 8명에게 두 가지 버전의 과제를 제시한 후, 해법 간에 나타난 질적 차이를 분석하였다. 연구 결과, 처음에 제시한 해법과 나중에 제시한 해법 간에 차이가 있었으며, 유연성과 독창성 면에서 질적으로 상당한 차이가 나타났다. 이에 다중해법 문제를 설계하고 적용함에 있어 이와 같은 질적 차이를 고려할 필요가 있음을 결론으로 제시하였다.

Keywords

References

  1. 도종훈(2007). 개방형 문제를 어떻게 만들 것인가?: 두 개의 개방형 문제 제작 사례를 중심으로. 한국학교수학회논문집. 10(2). 221-235
  2. 박진형, 김동원(2016). 예 만들기 활동에 의한 창의적 사고 촉진 방안 연구. 수학교육학연구, 26(1). 1-22
  3. 신희영, 고은성, 이경화. (2007). 수학영재교육에서의 관찰평가와 창의력평가. 학교수학, 9(2), 241-257.
  4. 우정호, 정영옥, 박경미, 이경화, 김남희, 나귀수, 임재훈(2006). 수학교육학 연구방법론. 서울: 경문사.
  5. 이경화(2015). 수학적 창의성: 수학적 창의성의 눈으로 본 수학교육, 서울: 경문사.
  6. 이대현(2014). 다양한 해결법이 있는 문제를 활용한 수학적 창의성 측정 방안 탐색. 학교수학, 16(1), 1-17.
  7. 이정연, 이경화(2010). Simpson의 패러독스를 활용한 영재교육에서 창의성 발현 사례 분석, 수학교육학연구, 20(3), 203-219.
  8. 하수현, 이광호(2014). Leikin의 수학적 창의성 측정 방법에 대한 고찰. 한국초등수학교육학회지, 18(1), 83-103.
  9. 황우형, 최계현, 김경미, 이명희(2006). 수학교육과 수학적 창의성. 수학교육 논문집, 20(4), 561-574.
  10. Ervynck, G. (1991). Mathematical Creativity. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 42-53). Dordrecht: Springer Netherlands.
  11. Guilford, J. P. (1967). The nature of human intelligence. New York: McGraw-Hill.
  12. Hashimoto, Y. (1997). The methods of fostering creativity through mathematical problem solving. ZDM, 29(3), 86-87. https://doi.org/10.1007/s11858-997-0005-8
  13. Haylock, D. W. (1987). A framework for assessing mathematical creativity in schoolchildren. Educational Studies in Mathematics, 18, 59-74. https://doi.org/10.1007/BF00367914
  14. Haylock, D. (1997). Recognising mathematical creativity in schoolchildren. ZDM, 29(3), 68-74. https://doi.org/10.1007/s11858-997-0002-y
  15. Kaufman, J. C., & Beghetto, R. A. (2009). Beyond big and little: The four c model of creativity. Review of general psychology, 13(1), 1. https://doi.org/10.1037/a0013688
  16. Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. Creativity in mathematics and the education of gifted students, 9, 129-145.
  17. Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference?. Zdm, 45(2), 183-197. https://doi.org/10.1007/s11858-012-0460-8
  18. Leikin, R., & Levav-Waynberg, A. (2008). Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers' knowledge. Canadian Journal of Science, Mathematics, and Technology Education, 8(3), 233-251. https://doi.org/10.1080/14926150802304464
  19. Levav-Waynberg, A., & Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. Journal of Mathematical Behavior, 31, 73-90. https://doi.org/10.1016/j.jmathb.2011.11.001
  20. Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255-276. https://doi.org/10.1007/s10649-007-9104-2
  21. Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30, 236-262. https://doi.org/10.4219/jeg-2006-264
  22. Pehkonen, E. (1997). Introduction to the concept "open-ended problem". In Pehkonen, E.(Ed.), Use of Open-Ended Problems in Mathematics Classroom (pp.7-11). Helsinki University
  23. Sheffield, L. J. (2009). Developing mathematical creativity-questions may be the answer. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 87-100). Rotterdam: Sense Publishers.
  24. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 29(3), 75-80. https://doi.org/10.1007/s11858-997-0003-x
  25. Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17, 20-36. https://doi.org/10.4219/jsge-2005-389
  26. Sriraman, B., Haavold, P., & Lee, K. (2014). Creativity in mathematics education. In Encyclopedia of Mathematics Education (pp. 109-115). Springer Netherlands.
  27. Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville, IL: Scholastic Testing Service.
  28. Treffinger, D. J. (1989). From potentials to productivity: Designing the journey to 2000. Gifted Child Today, 17-21.
  29. Treffinger, D. J. (1991). School reform and gifted education-Opportunities and issues. Gifted Child Quart. 35(1), 6-11. https://doi.org/10.1177/001698629103500101