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Mathematical creativity: psychology, progress and caveats

Abstract

The aim of this paper is to provide a concise survey of advances in the study of the psychology of creativity, with an emphasis on literature that is typically not cited in mathematics education. In spite of claims that mathematical creativity is an ill-defined area of inquiry in mathematics education, the literature from psychology can serve as an illustration for steady progress on numerous fronts including well defined terminology, established links between constructs (e.g., creativity and intelligence; creativity and motivation), integrated perspectives that resolve dichotomies (e.g., process vs product), and theories that are verifiable through empirical research. Psychology can provide us with prospects to pursue well defined lines of inquiry, and absolve us from the pressure of re-inventing well known findings. Three postulates and corollaries are provided with caveats to provoke readers and to stimulate future progress.

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Notes

  1. 1.

    Active Concerned Citizenship and Ethical Leadership.

  2. 2.

    Caveat 0: There is ongoing debate about the notion of intelligence in the field of psychology. Even though I mention more holistic conceptions of intelligence such as Howard Gardner’s multiple intelligences and Sternberg’s ACCEL model, one has to keep in mind that there now seems to be a trend in psychology and education rejecting or at least marginalizing the multiple intelligence construct and the notion of learning styles. I think these rejections are overblown because they come from within psychology and education and ignore insights from other fields such as neuroscience and the history/philosophy of science. These latter fields strongly illustrate the importance of visual-spatial thinking (for example) in intelligence and creativity. That said, the astute reader might want to contemplate reactions from the more insular psychologists and educators who make up the majority in their fields (as insular thinkers make up the majority in most fields!).

  3. 3.

    Those who promote the notion of “domain-specific” creativity strive to debunk divergent thinking, especially as it comes through in Torrance’s creativity tests. Again here, my opinion is that they go too far with these kinds of rejections but I leave my assertions with the hope that some readers might raise an eyebrow over this.

  4. 4.

    Caveat1: While there is evidence that incubation facilitates creativity—there is still much work to be done in understanding how exactly this process works and under what conditions? (see Sawyer 2012).

  5. 5.

    This famous conjecture, and its generalization known as Thurston’s Geometrization Conjecture, were finally proved by Grigori Perelman in a trio of papers posted to the arXiv in 2002 and 2003 (arXiv:math.DG/0211159; arXiv:math.DG/0303109; arXiv:math.DG/0307245).

  6. 6.

    Caveat 2: Although intrinsic motivation has been associated with creativity it is more the case that it “tends” to foster creativity (there are also cases where extrinsic motivators, like rewards, can facilitate creativity for certain people under certain conditions). Arguably this corollary is “a bit of a stretch” as no detailed argument has been made on why in creative math teaching, process/product and design/implementing tasks need not be as clearly demarcated in practice as they may seem in theory. The reader may simply view this as a recommendation to move between these categories in teaching practice.

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Correspondence to Bharath Sriraman.

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Sriraman, B. Mathematical creativity: psychology, progress and caveats. ZDM Mathematics Education 49, 971–975 (2017). https://doi.org/10.1007/s11858-017-0886-0

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Keywords

  • Psychology of creativity
  • Mathematical creativity
  • Creativity and equity
  • Task design
  • Teaching for creativity