Educational Studies in Mathematics

, Volume 73, Issue 2, pp 159–179 | Cite as

Working like real mathematicians: developing prospective teachers’ awareness of mathematical creativity through generating new concepts

  • Atara Shriki


This paper describes the experience of a group of 17 prospective mathematics teachers who were engaged in a series of activities aimed at developing their awareness of creativity in mathematics. This experience was initiated on the basis of ideas proposed by the participants regarding ways creativity of school students might be developed. Over a period of 6 weeks, they were engaged in inventing geometrical concepts and in the examination of their properties. The prospective teachers’ reflections upon the process they underwent indicate that they developed awareness of various aspects of creativity while deepening their mathematical and didactical knowledge.


Creativity in mathematics Prospective mathematics teachers 


  1. Ashby, F. G., Isen, A. M., & Turken, U. (1999). A neuropsychological theory of positive affect and its influence on cognition. Psychological Review, 106(3), 529–550.CrossRefGoogle Scholar
  2. Beghetto, R. A., & Kaufman, J. C. (2009). Do we all have multicreative potential? ZDM Mathematics Education, 41, 39–44.CrossRefGoogle Scholar
  3. Beswick, K. (2005). Preservice teachers’ understanding of relational and instrumental understanding. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th international conference on the Psychology of Mathematics Education (PME), Vol. 2 (pp. 161–168). Melbourne, Australia.Google Scholar
  4. Brown, S. I., & Walter, M. I. (1990). The art of problem posing (2nd ed.). Hillsdale: Lawrence Erlbaum.Google Scholar
  5. 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.Google Scholar
  6. Church, E. B., & Ravid, F. (2003). Setting the state for learning. Scholastic Parent & Child, 11, 38–42.Google Scholar
  7. Csikszentmihalyi, M. (1999). Applications of a system perspective for the study of creativity. In R. Sternberg (Ed.), Handbook of creativity (pp. 313–335). Cambridge: Cambridge University Press.Google Scholar
  8. Csikszentmihalyi, M., Rathunde, K., & Whalen, S. (1993). Talented teenagers: The roots of success and failure. Cambridge: Cambridge University Press.Google Scholar
  9. Cunningham, R. (2004). Problem posing: An opportunity for increasing student responsibility. Mathematics and Computer Education, 38(1), 83–89.Google Scholar
  10. Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dodrecht: Kluwer Academic.Google Scholar
  11. Fredrickson, B. L., & Branigan, C. (2001). Positive emotions. In T. J. Mayne & G. A. Bonanno (Eds.), Emotions—Current issues and future directions (pp. 123–151). New York: Guilford Press.Google Scholar
  12. Goldin, G. A. (2008). The affective dimension of mathematical inventiveness. In R. Leikin (Ed.) Proceedings of the 5th international conference on creativity in mathematics and the education of gifted students (pp. 1–14).Google Scholar
  13. Hadamard, J. (1945). The psychology of invention in the mathematical field. New York: Dover.Google Scholar
  14. Haylock, D. W. (1987). A framework for assessing mathematical creativity in schoolchildren. Educational Studies in Mathematics, 18(1), 59–74.CrossRefGoogle Scholar
  15. Hensley, R. B. (2004). Curiosity and creativity as attributes of information literacy. Reference & User Services Quarterly, 44(1), 31–36.Google Scholar
  16. Hong, E., & Aqui, Y. (2004). Cognitive and motivational characteristics of adolescents gifted in mathematics: Comparisons among students with different types of giftedness. Gifted Child Quarterly, 48(3), 191–201.CrossRefGoogle Scholar
  17. John-Steiner, V. (2000). Creative collaboration. Oxford: Oxford University Press.Google Scholar
  18. Lavy, I. & Shriki, A. (2006). Computerized project-based-learning approach as means for supporting professional development of mathematics pre-service teachers. In Q. Douglas (Ed.) Proceedings of the 3rd International Conference on the Teaching of Mathematics at the undergraduate level (ICTM), (CD format) 6 pages. Istanbul, Turkey.Google Scholar
  19. Lavy, I. & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. In W. Jeong-Ho, P. Kyo-Sik, L. Hee-Chan & S. Dong-Yeop (Eds.), Proceedings of the 31th international conference on the Psychology of Mathematics Education (PME) (pp. 129–136). Seoul, South Korea, III.Google Scholar
  20. Lavy, I., & Shriki, A. (2008). Investigating changes in prospective teachers’ views of a ‘good teacher’ while engaging in computerized project-based learning. Journal of Mathematics Teacher Education, 11(4), 259–284.CrossRefGoogle Scholar
  21. Lortie, D. C. (1975). Schoolteacher. Chicago: The University of Chicago Press.Google Scholar
  22. Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236–260.Google Scholar
  23. Milgram, R. M., & Livne, N. L. (2005). Creativity as a general and a domain-specific ability: The domain of mathematics as an exemplar. In J. C. Kaufman & J. Baer (Eds.), Creativity across domains: Faces of the muse (pp. 187–204). Mahwah: Lawrence Erlbaum.Google Scholar
  24. Movshovitz-Hadar, N. (2008). Intellectual courage and mathematical creativity. In R. Leikin (Ed.), Proceedings of the 5th international conference on creativity in mathematics and the education of gifted students (pp. 173–185).Google Scholar
  25. NCTM - National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.Google Scholar
  26. Neumann, C. J. (2007). Fostering creativity—A model for developing a culture of collective creativity in science. EMBO Reports, 8(3), 202–206.CrossRefGoogle Scholar
  27. Pehkonen, E. (1997). The state-of-art in mathematics creativity. International Review on Mathematical Education, 29, 63–66.Google Scholar
  28. Perry, B. D. (2001). Curiosity: The fuel of development. Early Childhood Today, 15, 22–24.Google Scholar
  29. Pink, D. H. (2005). A whole new mind—Moving from the information age to the conceptual age. New York: Penguin.Google Scholar
  30. Plucker, J., & 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. 153–168). Washington, DC: American Psychological Association.CrossRefGoogle Scholar
  31. Polya, G. (1954). Mathematics and plausible reasoning. Princeton: Princeton University Press.Google Scholar
  32. Reid, A., & Petocz, P. (2004). Learning domains and the process of creativity. Australian Educational Researcher, 31(2), 45–62.Google Scholar
  33. Shriki, A. (2005). What do teachers know about creativity? Unpublished paper, Kesher-Ham – Israel National Center of Mathematics, Technion (In Hebrew).Google Scholar
  34. Shriki, A. (2008). Towards promoting creativity in mathematics of pre-service teachers: The case of creating a definition. In R. Leikin (Ed.) Proceedings of the 5th international conference on creativity in mathematics and the education of gifted students (pp. 201–210).Google Scholar
  35. Silver, E. A. (1997). Fostering creativity through instruction in mathematical problem solving and problem posing. International Review on Mathematical Education, 29, 75–80.Google Scholar
  36. Simon, M. (1994). Learning mathematics and learning to teach: Learning cycles in mathematics teacher education. Educational Studies in Mathematics, 26, 71–94.CrossRefGoogle Scholar
  37. Starko, A. J. (2001). Creativity in the classroom: Schools of curious delight. Mahwah: Lawrence Erlbaum.Google Scholar
  38. Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, XVII(1), 20–36.Google Scholar
  39. Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM Mathematics Education, 41, 13–27.CrossRefGoogle Scholar
  40. Sternberg, R. J., & Lubart, T. I. (1996). Investing in creativity. American Psychologist, 51, 677–688.CrossRefGoogle Scholar
  41. Sternberg, R. J., & Lubart, T. I. (2000). The concept of creativity: Prospects and paradigms. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 93–115). New York: Cambridge University Press.Google Scholar
  42. Taylor, S. J., & Bogdan, R. (1998). Introduction to qualitative research methods. New York: Wiley.Google Scholar
  43. Torrance, E. P. (1974). Torrance tests of creative thinking: Norms-technical manual. Lexington: Ginn.Google Scholar
  44. Weisberg, R. W. (1993). Creativity: Beyond the myth of genius. New York: Freeman.Google Scholar
  45. Wilson, M., & Cooney, T. J. (2002). Mathematics teacher change and development. In G. C. Leder, E. Pehkonene & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127–147). Dordrecht: Kluwer Academic.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Oranim Academic College of EducationKiryat TivonIsrael

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