Skip to main content
Log in

Mathematical creativity and giftedness: a commentary on and review of theory, new operational views, and ways forward

  • Commentary Paper
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

In this commentary we synthesize and critique three papers in this special issue of ZDM (Leikin and Lev; Kattou, Kontoyianni, Pitta-Pantazi, and Christou; Pitta-Pantazi, Sophocleous, and Christou). In particular we address the theory that bridges the constructs of “mathematical creativity” and “mathematical giftedness” by reviewing the related literature. Finally, we discuss the need for a reliable metric to assess problem difficulty and problem sequencing in instruments that purport to measure mathematical creativity, as well as the need to situate mathematics education research within an existing canon of work in mainstream psychology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Babaeva, J.D. (1999). A Dynamic Approach to Giftedness: theory and practice. High Ability Studies, 10(1), 51–68

  • Balka, D. S. (1974). The development of an instrument to measure creative ability in mathematics. Dissertation Abstracts International, 36(1), 98.

    Google Scholar 

  • Benbow, C. P., & Arjmand, O. (1990). Predictors of high academic achievement in mathematics and science by mathematically talented students: A longitudinal study. Journal of Educational Psychology, 82, 430–441.

    Article  Google Scholar 

  • Brown, S. W., Renzulli, J. S., Gubbins, E. J., Siegle, D., Zhang, W., & Chen, C. (2005). Assumptions underlying the identification of gifted and talented students. Gifted Child Quarterly, 49, 68–79.

    Article  Google Scholar 

  • Caldwell, J. H., & Goldin, G. A. (1979). Variables affecting word problem difficulty in elementary school mathematics. Journal for Research in Mathematics Education, 10, 323–336.

    Article  Google Scholar 

  • Ching, T. P. (1997). An experiment to discover mathematical talent in a primary school in Kampong Air. International Reviews on Mathematical Education, 29(3), 94–96.

    Google Scholar 

  • Coleman, L. J., & Cross, T. L. (2005). Being gifted in school (2nd ed.). Waco, TX: Prufrock Press.

    Google Scholar 

  • Csikszentmihalyi, M. (2000). Becoming adult: How teenagers prepare for the world of work. New York: Basic Books.

    Google Scholar 

  • Davydov, V. (1990). Type of generalization in instruction: Logical and psychological problems in the structuring of school curricula. In J. Kilpatrick (Ed.), Soviet studies in mathematics education (Vol. 2). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970–974.

    Article  Google Scholar 

  • Dodds, R. A., Ward, T. B., & Smith, S. M. (2003). A review of experimental literature on incubation in problem solving and creativity. In M. A. Runco (Ed.), Creativity research handbook (Vol. 3). Cresskill, NJ: Hampton Press.

    Google Scholar 

  • Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dordrecht, Netherlands: Kluwer.

  • Feldhusen, J. F. (2006). The role of the knowledge base in creative thinking. In J. C. Kaufman & J. Baer (Eds.), Creativity and reason in cognitive development. New York, NY: Cambridge University Press.

    Google Scholar 

  • Feldman, D. H., Czikszentmihalyi, M., & Gardner, H. (1994). Changing the world, a framework for the study of creativity. Westport, CT: Praeger Publishers.

    Google Scholar 

  • Hadamard, J. W. (1945). Essay on the psychology of invention in the mathematical field. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Haylock, D. (1985). Conflicts in the assessment and encouragement of mathematical creativity in schoolchildren. International Journal of Mathematical Education in Science and Technology, 16(4), 547–553.

    Article  Google Scholar 

  • Haylock, D. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18(1), 59–74.

    Article  Google Scholar 

  • Haylock, D. (1997). Recognizing mathematical creativity in school children. International Reviews on Mathematical Education, 29(3), 68–74.

    Google Scholar 

  • Heller, J. I., & Hungate, H. N. (1985). Implications for mathematics instruction of research in scientific problem solving. In E. A. Silver (Ed.), Teaching and Learning Mathematical Problem Solving: Multiple research perspectives (pp. 83–112). Hillsdale, NJ: Lawrence Erlbaum.

  • 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, 191–201.

    Article  Google Scholar 

  • Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM—The International Journal on Mathematics Education, 45(this issue). doi:10.1007/s11858-012-0467-1.

  • Kaufman, J. C., & Beghetto, R. A. (2009). Beyond big and little: The four C model of creativity. Review of General Psychology, 13, 1–12.

    Article  Google Scholar 

  • Kim, H., Cho, S., & Ahn, D. (2003). Development of mathematical creative problem solving ability test for identification of gifted in math. Gifted Education International, 18(2), 164–175.

    Article  Google Scholar 

  • Kontoyianni, K., Kattou, M., Pitta-Pantazi, D., & Christou, C. (2011). Unraveling mathematical giftedness. In Proceedings of seventh conference of the European research in mathematics education (Working group 7: Mathematical potential, creativity and talent). Rzeszów: University of Rzeszów.

  • Kozhevnikov, M., Kosslyn, S., & Shephard, J. (2005). Spatial versus object visualizers: A new characterization of visual cognitive style. Memory and Cognition, 33(4), 710–726.

    Article  Google Scholar 

  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Lee, F. L., & Heyworth, R. (2000). Problem complexity: A measure of problem difficulty in algebra by using computer. Education Journal, 28(1), 85–107.

    Google Scholar 

  • Lee, K. H., & Sriraman, B. (2011). Conjecturing via reconceived classical analogy. Educational Studies in Mathematics, 76, 123–140.

    Article  Google Scholar 

  • Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the fifth conference of the European society for research in mathematics education (pp. 2330–2339), Larnaca, Cyprus.

  • Leikin, R., Berman, A., & Koichu, B. (2010). Creativity in mathematics and the education of gifted students. Rotterdam: Sense Publishers.

    Google Scholar 

  • Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM—The International Journal on Mathematics Education, 45(this issue). doi:10.1007/s11858-012-0460-8.

  • Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM—The International Journal on Mathematics Education, 45(this issue). doi:10.1007/s11858-012-0459-1.

  • Lev-Zamir, H., & Leikin, R. (2011). Creative mathematics teaching in the eye of the beholder: Focusing on teachers’ conceptions. Research in Mathematics Education, 13(1), 17–32.

    Google Scholar 

  • Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276.

    Article  Google Scholar 

  • Mann, E. L. (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students. Doctoral dissertation, University of Connecticut.

  • Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30, 236–262.

    Google Scholar 

  • Mason, E., Zollman, A., Bramble, W. J., & O’Brien, J. (1992). Response time and item difficulty in a computer-based high school mathematics course. Focus on Learning in Mathematics, 14(3), 41–51.

    Google Scholar 

  • Mayer, R. E. (1999). Fifty years of creativity research. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 449–460). London: Cambridge University Press.

    Google Scholar 

  • Miller, A. L. (2012). Conceptualizations of creativity: Comparing theories and models of giftedness. Roeper Review, 34, 94–103.

    Article  Google Scholar 

  • Mitchelmore, M. (1993). Abstraction, generalization and conceptual change in mathematics. Hiroshima Journal of Mathematics Education, 2, 45–57.

    Google Scholar 

  • Mitchelmore, M. C., & White, P. (1995). Abstraction in mathematics: Conflict, resolution and application. Mathematics Education Research Journal, 7(1), 50–68.

    Article  Google Scholar 

  • Morgan, S., & Forster, J. (1999). Creativity in the classroom. Gifted Education International, 14, 29–43.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • Niss, M. (1999). Kompetencer og uddannelsesbeskrivelse (Competencies and subject description). Uddannelse, 9, 21–29.

    Google Scholar 

  • Piaget, J. (1977). Recherches sur abstraction reflechissante (Experiments on reflective abstraction) (Vol. 2). Paris: Presses Universitaires de France.

    Google Scholar 

  • Pitta-Pantazi, D., Sophocleous, P., & Christou, C. (2013). Prospective primary school teachers’ mathematical creativity and their cognitive styles. ZDM—The International Journal on Mathematics Education, 45(this issue). doi:10.1007/s11858-012-0475-1.

  • Plucker, J., & Beghetto, R. (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.

    Chapter  Google Scholar 

  • Polya, G. (1954). Mathematics and plausible reasoning: Induction and analogy in mathematics (Vol. II). Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Renzulli, J. S. (1986). The three-ring conception of giftedness: A developmental model for creative productivity. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 51–92). Cambridge: Cambridge University Press.

    Google Scholar 

  • Renzulli, J. S. (2005). The three-ring conception of giftedness: A developmental model for promoting creative productivity. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 246–279). New York, NY: Cambridge University Press.

    Chapter  Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York, NY: MacMillan.

    Google Scholar 

  • Sio, U. N., & Ormerod, T. C. (2007). Does incubation enhance problem solving? A meta-analytic review. Psychological Bulletin, 135(1), 94–120.

    Article  Google Scholar 

  • Skemp, R. K. (1986). The psychology of learning mathematics (2nd ed.). Harmondsworth: Penguin.

    Google Scholar 

  • Sriraman, B. (2004). Reflective abstraction, uniframes and the formulation of generalizations. Journal of Mathematical Behavior, 23, 205–222.

    Article  Google Scholar 

  • Sriraman, B. (2005). Are mathematical giftedness and mathematical creativity synonyms? A theoretical analysis of constructs. Journal of Secondary Gifted Education, 17(1), 20–36.

    Google Scholar 

  • Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM—The International Journal on Mathematics Education, 41, 13–27.

    Article  Google Scholar 

  • Sternberg, R. J. (Ed.). (1999). Handbook of creativity. New York, NY: Cambridge University Press.

    Google Scholar 

  • Tannenbaum, A. J. (2003). Nature and nurture of giftedness. In N. Colangelo & G. A. Davis (Eds.) Handbook of gifted education (3rd edition) (pp. 45–59). Boston: Allyn and Bacon.

  • Taylor, C. (1988). Various approaches to and definitions of creativity. In R. J. Sternberg (Ed.), The nature of creativity (pp. 99–121). New York, NY: Cambridge University Press.

    Google Scholar 

  • Terman, L. M. (1925). Genetic studies of genius. Mental and physical traits of a thousand gifted children (Vol. 1). Stanford, CA: Stanford University Press.

    Google Scholar 

  • Torrance, E. P. (1974). The Torrance tests of creative thinking-norms-technical manual research edition-verbal tests, forms A and B-figural tests, forms A and B. Princeton, NJ: Personnel Press.

    Google Scholar 

  • Treffinger, D. J., Young, G. C., Selby, E. C., & Shepardson, C. (2002). Assessing creativity: A guide for educators. Storrs, CT: The National Research Center on the Gifted and Talented, University of Connecticut.

    Google Scholar 

  • Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: An analysis of high school students’ mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201–221.

    Article  Google Scholar 

  • Wallas, G. (1926). The art of thought. New York, NY: Harcourt, Brace & Jovanovich.

    Google Scholar 

  • Gronlund, N. E. (1981). Measurement and evaluation in teaching. New York, NY: Macmillan.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bharath Sriraman.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sriraman, B., Haavold, P. & Lee, K. Mathematical creativity and giftedness: a commentary on and review of theory, new operational views, and ways forward. ZDM Mathematics Education 45, 215–225 (2013). https://doi.org/10.1007/s11858-013-0494-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-013-0494-6

Keywords

Navigation