Approaches to the Teaching of Creative and Non-Creative Mathematical Problems

  • Mei-Shiu ChiuEmail author


This study investigated the approaches to teaching by three fifth-grade teachers’ of creative and non-creative mathematical problems for fractions. The teachers’ personal constructs of the two kinds of problems were elicited by interviews through the use of the repertory grid technique. All the teaching was observed and video-recorded. Results revealed that the teachers had slightly distinctive constructs of creative and non-creative problems, and professed a greater preference for creative problems. Based on the teachers’ creations of problems in classrooms and related features, the study identified three types of teaching approaches: liberal, reasoning, and skill approaches. The liberal approach appeared to indicate the most appropriate teaching methods for creative problems.

Key words

classroom practice creative mathematics teaching repertory grid technique 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baroody, A.J. (1993). Problem solving, reasoning, and communication, K-8: Helping children think mathematically. NY, NY: Macmillan.Google Scholar
  2. Biggs, J. (2001). Enhancing learning: A matter of style or approach? In R.J. Sternberg & L. Zhang (Eds.), Perspectives on thinking, learning, and cognitive styles (pp. 73–102). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  3. Boaler, J. (1998). Open and closed mathematics: Student experiences and understanding. Journal for Research in Mathematics Educations, 29(1), 41–62.CrossRefGoogle Scholar
  4. Charmaz, K. (2000). Grounded theory: Objectivist and constructivist methods. In N.K. Denzin & Y.S. Lincoln (Eds.), Handbook of qualitative research (2nd ed.) (pp. 509–535). Thousand Oaks, CA: Sage.Google Scholar
  5. De Corte, E., Verschaffel, L., & Op’t Eynde, P. (2000). Self-regulation: A characteristic and a goal of mathematics education. In M. Boekaerts, P.R. Pintrich & M. Zeidner (Eds.), Handbook of Self-regulation (pp. 687–726). San Diego, CA: Academic Press.CrossRefGoogle Scholar
  6. Department for Education and Employment (2000). National curriculum. Retrieved September 21, 2001 from the World Wide Web:
  7. Fryer, M. (1996). Creative teaching and learning. London: Paul Chapman.Google Scholar
  8. Fuchs, L.S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C.L., Owen, R., & Schroeter, K. (2003). Enhancing third-grade students’ mathematical problem solving with self-regulated learning strategies. Journal of Educational Psychology, 95(2), 306–315.CrossRefGoogle Scholar
  9. Gao, L., & Watkins, D. (2001). Identifying and assessing the conceptions of teaching of secondary school physics teachers in China. British Journal of Educational Psychology, 71, 443–469.CrossRefGoogle Scholar
  10. Hayes, N. (2000). Doing psychological research: Gathering and analyzing data. Buckingham, UK: Open University Press.Google Scholar
  11. International Association for the Evaluation of Educational Achievement (2005). TIMSS 2003 user guide for the international database. Chestnut Hill, MA: TIMSS & PIRLS International Study Centre.Google Scholar
  12. Jausovec, N. (1994). Metacognition in creative problem solving. In M.A. Runco (Ed.), Problem finding, problem solving, and creativity (pp.77–95). Norwood, NJ: Ablex Publishing Corporation.Google Scholar
  13. Jin, S. (1998). Career counseling and guidance. Taipei, Taiwan: Dong-Wha. (in Chinese)Google Scholar
  14. Jonassen, D.H. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45(1), 65–94.CrossRefGoogle Scholar
  15. Kelly, G.A. (1955). The Psychology of personal constructs (volume one): A theory of personality. New York: W. W. Norton & Company.Google Scholar
  16. Lehrer, R. & Franke, M.L. (1992). Applying personal construct psychology to the study of teachers’ knowledge of fractions. Journal for Research in Mathematics Education, 23(3), 223–241.CrossRefGoogle Scholar
  17. Lilly, F.R. & Bramwell-Rejskind, G. (2004). The dynamics of creative teaching. Journal of Creative Behavior, 38(2), 102–124.Google Scholar
  18. McLeod, D.B. (1988). Affective issues in mathematical problem-solving: Some theoretical considerations. Journal for Research in Mathematics Education, 19(2), 134–141.CrossRefGoogle Scholar
  19. McLeod, D.B. (1994). Research on affect and mathematics learning in the JRME: 1970 to the present. Journal for Research in Mathematics Education, 25(6), 637–647.CrossRefGoogle Scholar
  20. Miles, M.B. & Huberman, A.M. (1994). Qualitative data Analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA: Sage.Google Scholar
  21. Ministry of Education in Taiwan (2000). The national curriculum outline for Taiwanese school mathematics. Retrieved September 27, 2001 from the World Wide Web: (in Chinese)
  22. National Council of Teachers of Mathematics (1995). Assessment standard for school mathematics. Reston, VA: The National Council of Teachers of Mathematics.Google Scholar
  23. Nitko, A.J. (1996). Educational assessment of students (2nd ed.). Englewood Cliffs, NJ: Merrill.Google Scholar
  24. Organization for Economic Co-operation and Development (2005). Retrieved January 29 2005 from the World Wide Web:
  25. Pape, S.J. Bell, C.V. & Yetkin, I.E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics, 53(3), 179–202.CrossRefGoogle Scholar
  26. Pope, M.L. & Denicolo, P.M. (2001). Transformative education: Personal construct approaches to practice and research. London: Whurr.Google Scholar
  27. Puustinen, M. & Pulkkinen, L. (2001). Models of self-regulated learning: A review. Scandinavian Journal of Educational Research, 45(3), 269–286.CrossRefGoogle Scholar
  28. Scott, G., Leritz, L.E. & Mumford, M.D. (2004). Types of creativity training: Approaches and their effectiveness. Journal of Creative Behavior, 38(3), 149–179.Google Scholar
  29. Shaw, M.L.G. (1980). On becoming a personal scientist: Interactive computer elicitation of personal models of the world. London: Academic Press.Google Scholar
  30. Stipek, D., Salmon, J.M., Givvin, K.B., Kazemi, E., Saxe, G. & MacGyvers, V.L. (1998). The value (and convergence) of practices suggested by motivation research and promoted by mathematics education reformers. Journal for Research in Mathematics Education, 29(4), 465–488.CrossRefGoogle Scholar
  31. Strauss, A. & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park, CA: Sage.Google Scholar
  32. Strauss, A. & Corbin, J. (1998). Grounded theory methodology: An overview. In N.K. Denzin & Y.S. Lincoln (Eds.), Strategies of qualitative inquiry (pp. 158–183). Thousand Oaks, CA: Sage.Google Scholar
  33. Stright, A.D., Neitzel, C., Sears, K.G. & Hoke-Sinex, L. (2001). Instruction begins in the home: Relations between parental instruction and children’s self-regulation in the classroom. Journal of Educational Psychology, 93(3), 456–466.CrossRefGoogle Scholar
  34. Vermeer, H.J., Boekaerts, M. & Seegers, G. (2000). Motivational and gender differences: Sixth-grade students’ mathematical problem-solving behavior. Journal of Educational Psychology, 92(2), 308–315.CrossRefGoogle Scholar
  35. Wilkinson, J. (1995). Direct observation. In G.M. Breakwell, S. Hammond & C. Fife-Schaw (Eds.), Research methods in psychology (pp. 224–238). London: Sage.Google Scholar
  36. Zimmerman, B.J. (1989). A social cognitive view of self-regulated academic learning. Journal of Educational Psychology, 81(3), 329–339.CrossRefGoogle Scholar

Copyright information

© National Science Council, Taiwan 2007

Authors and Affiliations

  1. 1.Department of EducationNational Chengchi UniversityTaipeiRepublic of China

Personalised recommendations