Asia Pacific Education Review

, Volume 7, Issue 1, pp 51–61 | Cite as

Cultivating divergent thinking in mathematics through an open-ended approach

  • Oh Nam KwonEmail author
  • Jee Hyun Park
  • Jung Sook Park
Article and Report


The purpose of this study was to develop a program to help cultivate divergent thinking in mathematics based on open-ended problems and to investigate its effect. The participants were 398 seventh grade students attending middle schools in Seoul. A method of pre- and post-testing was used to measure mainly divergent thinking skills through open-ended problems. The results indicated that the treatment group students performed better than the comparison students overall on each component of divergent thinking skills, which includes fluency, flexibility, and originality. The developed program can be a useful resource for teachers to use in enhancing their students’ creative thinking skills. An open-ended approach in teaching mathematics suggested in this paper may provide a possible arena for exploring the prospects and possibilities of improving mathematical creativity.

Key Words

mathematical creativity divergent thinking open-ended approach 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Becker, J. P., & Shimada, S. (Eds.) (1997).The open-ended approach: A new proposal for teaching mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  2. Brown, S. (2001).Reconstructing school mathematics. New York: Peter Lang Publishing.Google Scholar
  3. Cohen, J. (1988).Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  4. Ervynck, G. (1991). Mathematical creativity. In D. Tall. (Ed.),Advanced mathematical thinking (pp.42–53). Netherlands: Kluwer Academic Publishers.Google Scholar
  5. Freedman, R. (1994).Open-ended questioning: A handbook for educators. Don Mills, OH: Addison-Wesley.Google Scholar
  6. Hadamard, J. (1945).An essay on the psychology of invention in the mathematical field. New York: Dover Publication.Google Scholar
  7. Haylock, D. W. (1987). A framework for assessing mathematical creativity in school children.Educational Studies in Mathematics, 18, 59–74.CrossRefGoogle Scholar
  8. Haylock, D. (1997). Recognizing mathematical creativity in schoolchildren.Zentralblatt fur Didaktik der Mathematik, 27(2), 68–74.CrossRefGoogle Scholar
  9. Gravemeijer, K., & Doorman, M. (1999). Context problem in realistic mathematics education: A calculus course as an example.Educational Studies in Mathematics, 39, 111–129.CrossRefGoogle Scholar
  10. Guilford, J. (1967).The nature of human intelligence. New York: McGraw-Hill.Google Scholar
  11. Krutetskii, V.A. (1976).The psychology of mathematical abilities in school children. The Univ. of Chicago Press.Google Scholar
  12. London, R. (1993). A curriculum of nonroutine problems.Paper represented at the Annual Meeting of the American Educational Research Association, Atlanta, GA, April. (ERIC Document Reproduction Service No. ED359213)Google Scholar
  13. Marilyn Burns Education Associates. (1996).Problem-solving lessons. Sausalito: Math Solutions Publications.Google Scholar
  14. Nohda, N. (1995). Teaching and evaluating using “open-ended problems” in classroom.Zentralblatt fur Didaktik der Mathematik, 27(2), 57–61.Google Scholar
  15. Nohda, N. (2000). Teaching by open-approach method in Japanese mathematics classroom.Proceeding of the 24th conference of the international Group for the Psychology of Mathematics Education, Hiroshima, Japan, July 23–27, volume 1–39–53.Google Scholar
  16. Pehkonen, E. (1995). Using open-ended problem in mathematics.Zentralblatt fur Didaktik der Mathematik, 27(2), 67–71.Google Scholar
  17. Poincaré, H. (1948).Science and method. New York: Dover.Google Scholar
  18. Sawada, T. (1997). Developing Lesson Plans. In J. Becker, & S. Shimada (Eds.),The open-ended approach: A new proposal for teaching mathematics. (p. 23–35). National Council of Teachers of Mathematics.Google Scholar
  19. Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing.Zentralblatt fur Didaktik der Mathematik, 27(2), 68–74.Google Scholar

Copyright information

© Education Research Institute 2006

Authors and Affiliations

  1. 1.Department of Mathmatics EducationSeoul National UniversitySeoulKorea

Personalised recommendations