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Psychological and Neuroscientific Perspectives on Mathematical Creativity and Giftedness

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Creativity and Giftedness

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

Creativity and giftedness have long been linked together in the literature, particularly where giftedness is conceived, not in the analytically focused sense of schoolhouse giftedness (e.g. Renzulli 1978), but in the sense of creative-productive giftedness that emphasizes the generation and production of ideas. Creativity has a well-established foundation in the psychological literature, and a growing body of work derived from neuroscientific approaches. How do these contrasting psychological and neuroscientific approaches inform our understanding of creativity as a component of giftedness in general? How is giftedness manifest in mathematics in the creative-productive sense? What do psychology and neuroscience tell us about the process of fostering mathematical giftedness specifically?

In this chapter, we examine first general aspects of creativity and giftedness, noting that Treffinger’s (2004) five themes provide a framework for understanding the connection between creativity and giftedness. Having established that creativity and giftedness are connected through these five themes, we then turn attention first to a psychological view of factors that are important for understanding mathematical creativity and giftedness, followed by a neuroscientific examination of the same.

The chapter concludes with the notion that mathematical creativity and giftedness can be thought of as a special case of the intersection of creativity and giftedness more generally, and that creativity and giftedness – mathematical or otherwise – can be characterized by a series of dualities. Elements of the person, the cognitive processes employed, the outcome and the environment associated with mathematical creativity and giftedness are unique to this domain, and the blending of psychological and neuroscientific approaches offers the best means for understanding and fostering this ability.

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References

  • Arden, R., Chavez, R. S., Grazioplene, R., & Jung, R. E. (2010). Neuroimaging creativity: A psychometric view. Behavioural Brain Research, 214(2), 143–156.

    Article  Google Scholar 

  • Baer, J. M. (1998). The case for domain specificity of creativity. Creativity Research Journal, 11(2), 173–177.

    Article  Google Scholar 

  • Baer, J. M. (2010). Is creativity domain specific? In J. C. Kaufman & R. J. Sternberg (Eds.), The Cambridge handbook of creativity (pp. 321–341). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Baer, J. M. (2012). Domain specificity and the limits of creativity theory. The Journal of Creative Behavior, 46(1), 16–29.

    Article  Google Scholar 

  • Baer, J. M., & Kaufman, J. C. (2005). Bridging generality and specificity: The amusement park theoretical (APT) model of creativity. Roeper Review, 27(3), 158–163.

    Article  Google Scholar 

  • Barron, F. X. (1955). The disposition toward originality. The Journal of Abnormal and Social Psychology, 51(3), 478.

    Article  Google Scholar 

  • Beaty, R. E., & Silvia, P. J. (2012). Why do ideas get more creative across time? An executive interpretation of the serial order effect in divergent thinking tasks. Psychology of Aesthetics Creativity and the Arts, 6(4), 309–319.

    Article  Google Scholar 

  • Beaty, R. E., Benedek, M., Wilkins, R. W., Jauk, E., Fink, A., Silvia, P. J., … Neubauer, A. C. (2014). Creativity and the default network: A functional connectivity analysis of the creative brain at rest. Neuropsychologia, 64, 92–98.

    Google Scholar 

  • Benedek, M., Jauk, E., Fink, A., Koschutnig, K., Reishofer, G., Ebner, F., & Neubauer, A. C. (2014). To create or to recall? Neural mechanisms underlying the generation of creative new ideas. NeuroImage, 88, 125–133.

    Article  Google Scholar 

  • Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development, 78(1), 246–263.

    Article  Google Scholar 

  • Cooper, N. R., Croft, R. J., Dominey, S. J., Burgess, A. P., & Gruzelier, J. H. (2003). Paradox lost? Exploring the role of alpha oscillations during externally vs. internally directed attention and the implications for idling and inhibition hypotheses. International Journal of Psychophysiology, 47(1), 65–74.

    Article  Google Scholar 

  • Cooper, N. R., Burgess, A. P., Croft, R. J., & Gruzelier, J. H. (2006). Investigating evoked and induced electroencephalogram activity in task-related alpha power increases during an internally directed attention task. Neuroreport, 17(2), 205–208.

    Article  Google Scholar 

  • Cropley, A. J. (1994). Creative intelligence: A concept of ‘true’ giftedness. European Journal for High Ability, 5(1), 6–23.

    Article  Google Scholar 

  • Cropley, D. H. (2015). Creativity in engineering: Novel solutions to complex problems. San Diego: Academic.

    Google Scholar 

  • Cropley, D. H., & Kaufman, J. C. (2012). Measuring functional creativity: Non-expert raters and the creative solution diagnosis scale. The Journal of Creative Behavior, 46(2), 119–137.

    Article  Google Scholar 

  • Cropley, A. J., & Urban, K. K. (2000). Programs and strategies for nurturing creativity. In F. J. M. K. A. Heller, R. J. Sternberg, & R. F. Subotnik (Eds.), International handbook research and development of giftedness and talent (pp. 481–484). Oxford: Pergamon.

    Google Scholar 

  • Cropley, D. H., Kaufman, J. C., & Cropley, A. J. (2011). Measuring creativity for innovation management. Journal of Technology Management & Innovation, 6(3), 13–30.

    Article  Google Scholar 

  • Delcourt, M. A. (1993). Creative productivity among secondary school students: Combining energy, interest, and imagination. Gifted Child Quarterly, 37(1), 23–31.

    Article  Google Scholar 

  • Dietrich, A. (2004). The cognitive neuroscience of creativity. Psychonomic Bulletin & Review, 11(6), 1011–1026.

    Article  Google Scholar 

  • Dietrich, A., & Kanso, R. (2010). A review of EEG, ERP, and neuroimaging studies of creativity and insight. Psychological Bulletin, 136(5), 822–848.

    Article  Google Scholar 

  • Fink, A., & Neubauer, A. C. (2006). EEG alpha oscillations during the performance of verbal creativity tasks: Differential effects of sex and verbal intelligence. International Journal of Psychophysiology, 62(1), 46–53.

    Article  Google Scholar 

  • Fink, A., & Benedek, M. (2014). EEG alpha power and creative ideation. Neuroscience & Biobehavioral Reviews, 44, 111–123.

    Article  Google Scholar 

  • Fink, A., Koschutnig, K., Hutterer, L., Steiner, E., Benedek, M., Weber, B., … Weiss, E. M. (2014). Gray matter density in relation to different facets of verbal creativity. Brain Structure and Function, 219(4), 1263–1269.

    Google Scholar 

  • Finke, R. A., Ward, T. B., & Smith, S. M. (1992). Creative cognition. Boston: MIT Press.

    Google Scholar 

  • Gonen-Yaacovi, G., de Souza, L. C., Levy, R., Urbanski, M., Josse, G., & Volle, E. (2013). Rostral and caudal prefrontal contribution to creativity: a meta-analysis of functional imaging data. Frontiers in Human Neuroscience, 7, 465–486.

    Google Scholar 

  • Gross, M. U. M. (2004). Exceptionally gifted children. London: Routledge.

    Google Scholar 

  • Guilford, J. P. (1950). Creativity. American Psychologist, 5, 444–454.

    Article  Google Scholar 

  • Guilford, J. P. (1959). Three faces of intellect. American Psychologist, 14(8), 469–479.

    Article  Google Scholar 

  • Howard-Jones, P. A., Blakemore, S.-J., Samuel, E. A., Summers, I. R., & Claxton, G. (2005). Semantic divergence and creative story generation: An fMRI investigation. Cognitive Brain Research, 25(1), 240–250.

    Article  Google Scholar 

  • Isaksen, S. G., Lauer, K. J., & Ekvall, G. (1999). Situational outlook questionnaire: A measure of the climate for creativity and change. Psychological Reports, 85(2), 665–674.

    Article  Google Scholar 

  • Isaksen, S. G., Lauer, K. J., Ekvall, G., & Britz, A. (2001). Perceptions of the best and worst climates for creativity: Preliminary validation evidence for the situational outlook questionnaire. Creativity Research Journal, 13(2), 171–184.

    Article  Google Scholar 

  • Kaufman, J. C. (2009). Creativity 101. New York: Springer Publishing Company.

    Google Scholar 

  • Kaufman, J. C., Plucker, J. A., & Russell, C. M. (2012). Identifying and assessing creativity as a component of giftedness. Journal of Psychoeducational Assessment, 30(1), 60–73.

    Article  Google Scholar 

  • Ludwig, A. M. (1998). Method and madness in the arts and sciences. Creativity Research Journal, 11(2), 93–101.

    Article  Google Scholar 

  • Murphy, M. C., & Dweck, C. S. (2009). A culture of genius: How an organization’s lay theory shapes people’s cognition, affect, and behavior. Personality and Social Psychology Bulletin, 36(3), 283–296.

    Article  Google Scholar 

  • Naglieri, J. A., & Kaufman, J. C. (2001). Understanding intelligence, giftedness and creativity using the PASS theory. Roeper Review, 23(3), 151–156.

    Article  Google Scholar 

  • Neubauer, A. C., & Fink, A. (2009). Intelligence and neural efficiency. Neuroscience & Biobehavioral Reviews, 33(7), 1004–1023.

    Article  Google Scholar 

  • Paulus, P. B., & Brown, V. R. (2007). Toward more creative and innovative group idea generation: A cognitive‐social‐motivational perspective of brainstorming. Social and Personality Psychology Compass, 1(1), 248–265.

    Article  Google Scholar 

  • Paunesku, D., Walton, G. M., Romero, C., Smith, E. N., Yeager, D. S., & Dweck, C. S. (2015). Mind-set interventions are a scalable treatment for academic underachievement. Psychological Science, 26(6), 784–793.

    Article  Google Scholar 

  • Plucker, J. A. (1998). Beware of simple conclusions: The case for content generality of creativity. Creativity Research Journal, 11, 179–182.

    Article  Google Scholar 

  • Preckel, F., Holling, H., & Wiese, M. (2006). Relationship of intelligence and creativity in gifted and non-gifted students: An investigation of threshold theory. Personality and Individual Differences, 40(1), 159–170.

    Article  Google Scholar 

  • Reis, S. M., & Renzulli, J. S. (1991). The assessment of creative products in programs for gifted and talented students. Gifted Child Quarterly, 35(3), 128–134.

    Article  Google Scholar 

  • Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60(3), 180–184.

    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. 53–92). Cambridge: Cambridge University Press.

    Google Scholar 

  • Renzulli, J. S. (2011). What makes giftedness? Reexamining a definition: Giftedness needs to be redefined to include three elements: Above-average intelligence, high levels of task commitment, and high levels of creativity. Phi Delta Kappan, 92(8), 81.

    Article  Google Scholar 

  • Rhodes, M. (1961). An analysis of creativity. The Phi Delta Kappan, 42(7), 305–310.

    Google Scholar 

  • Runco, M. A. (1993). Divergent thinking, creativity, and giftedness. Gifted Child Quarterly, 37(1), 16–22.

    Article  Google Scholar 

  • Sawyer, K. (2011). The cognitive neuroscience of creativity: A critical review. Creativity Research Journal, 23(2), 137–154.

    Article  Google Scholar 

  • Scott, G., Leritz, L. E., & Mumford, M. D. (2004a). The effectiveness of creativity training: A quantitative review. Creativity Research Journal, 16(4), 361–388.

    Article  Google Scholar 

  • Scott, G., Leritz, L. E., & Mumford, M. D. (2004b). Types of creativity training: Approaches and their effectiveness. The Journal of Creative Behavior, 38(3), 149–179.

    Article  Google Scholar 

  • Sriraman, B. (Ed.). (2008). Creativity, giftedness, and talent development in mathematics. Charlotte: IAP.

    Google Scholar 

  • Sternberg, R. J. (2007). Creativity as a habit. In A.-G. Tan (Ed.), Creativity: A handbook for teachers (pp. 3–25). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Sternberg, R. J., & Lubart, T. I. (1993). Creative giftedness: A multivariate investment approach. Gifted Child Quarterly, 37(1), 7–15.

    Article  Google Scholar 

  • Sternberg, R. J., & Lubart, T. I. (1999). The concept of creativity: Prospects and paradigms. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 3–15). Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Treffinger, D. J. (2004). Introduction to creativity and giftedness: Three decades of inquiry and development. In D. J. Treffinger (Ed.), Creativity and giftedness. Thousand Oaks: Corwin Press and the National Association for Gifted Children.

    Google Scholar 

  • Treffinger, D. J., & Reis, S. M. (2004). Creativity and giftedness. Thousand Oaks, CA: Corwin Press.

    Google Scholar 

  • Treffinger, D. J., Sortore, M. R., & Cross, J. A. (1993). Programs and strategies for nurturing creativity. In K. Heller, F. J. Monks, & A. H. Passow (Eds.), International handbook for research on giftedness and talent (pp. 555–567). Oxford: Pergamon.

    Google Scholar 

  • Wallach, M. A. (1985). Creativity testing and giftedness. In F. D. Horowitz & M. O’Brien (Eds.), The gifted and talented: Developmental perspectives (pp. 99–123). Washington, DC: American Psychological Association.

    Chapter  Google Scholar 

  • Yoruk, S., & Runco, M. (2014). The neuroscience of divergent thinking. ANS: The Journal for Neurocognitive Research, 56(1–2), 1–16.

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of South Australia, Adelaide, Australia

    David H. Cropley

  2. Flinders University, Bedford Park, Australia

    Martin Westwell & Florence Gabriel

Authors
  1. David H. Cropley
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  2. Martin Westwell
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  3. Florence Gabriel
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Correspondence to David H. Cropley .

Editor information

Editors and Affiliations

  1. Faculty of Education RANGE Center, University of Haifa, Haifa, Israel

    Roza Leikin

  2. Department of Mathematical Sciences, The University of Montana, Missoula, Montana, USA

    Bharath Sriraman

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Cropley, D.H., Westwell, M., Gabriel, F. (2017). Psychological and Neuroscientific Perspectives on Mathematical Creativity and Giftedness. In: Leikin, R., Sriraman, B. (eds) Creativity and Giftedness. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-38840-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-38840-3_12

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