Advertisement

Creativity Research in Mathematics Education Simplified: Using the Concept of Bisociation as Ockham’s Razor

  • Bronislaw CzarnochaEmail author
  • William Baker
  • Olen Dias
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

This chapter proposes that bisociation, the Koestler theory of the creativity of the “Aha!” Moment, is the Ockham Razor for creativity research in mathematics education. It shows the power of bisociation in simplifying unnecessary components and in the synthesis of the fragmented ones. The discussion leads through the relationship of bisociation with Piaget’s reflective abstraction, proposes cognitive/affective duality of the “Aha!” Moment and enriches Mason’s theory of attention by the new structure of simultaneous attention necessary for the Eureka experience.

Keywords

Ocham razor Bisociation Aha! Moment Restructuring Creativity 

References

  1. Baker, B. (2016). Koestler theory as a foundation for problem solving. In B. Czarnocha, W. Baker, O. Dias, & V. Prabhu (Eds.), The creative enterprise of mathematics teaching-research. The Netherlands: Sense Publishers.Google Scholar
  2. Bohr, N. (1935). Can quantum reality be considered complete? Physical Review, 48, 696.CrossRefGoogle Scholar
  3. Czarnocha, B. (2014). On the culture of creativity in mathematics education. Teaching Innovations, 27(3), 30–45.Google Scholar
  4. Czarnocha, B. (2016). Teaching-research NY City model. In B. Czarnocha, W. Baker, O. Dias, & V. Prabhu (Eds.), The creative enterprise of mathematics teaching-research. The Netherlands: Sense Publishers.Google Scholar
  5. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum reality be considered complete? Physical Review, 47, 777.CrossRefGoogle Scholar
  6. Eisenhart, M. (1991). Conceptual frameworks for research circa 1991: Ideas from a cultural anthropologist; Implications for mathematics education researchers. In R. G. Underhill (Ed.), 13th Proceedings of the Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 16–19). Blacksburg, VA: Psychology of Mathematics Education.Google Scholar
  7. Gauch, H. G. (2003). Scientific method in practice. England: Cambridge University Press.Google Scholar
  8. Hadamard, J. (1996). The mathematician’s mind: The psychology of invention in the mathematical field. ISBN: 0-691-02931-8.Google Scholar
  9. Ilyenkov, E. (1974/2014). Dialectical logic. ISBN: 978-1-312-10852-3.Google Scholar
  10. Kattou, M., Kontoyianni, K., Pantazi, D., & Christou, C. (2011). Does mathematical creativity differentiate mathematical ability? In Proceedings of the 7th Congress of European Research in Mathematics Education (p. 1056). Rzeszow, Poland: University of Rzeszów.Google Scholar
  11. Koestler, A. (1964). The act of creation. London: Hutchinson.Google Scholar
  12. Krathwohl, D. R. (2002). A revision of bloom taxonomy. Theory into Practice, 41(4), 212–218.CrossRefGoogle Scholar
  13. Lamon, S. (2003). Beyond constructivism: An improved fitness metaphor for the acquisition of mathematical knowledge. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 435–448). Mahwah, NJ, USA: Lawrence Erlbaum and Associates.Google Scholar
  14. Leikin, R., Berman, A., & Koichu, B. (Eds.) (2009). Creativity in mathematics and the education of gifted students. Rotterdam, the Netherlands: Sense Publisher.Google Scholar
  15. Lester, F. K., Jr. (2010). On the theoretical, conceptual, and philosophical foundations for mathematics education research in mathematics education. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 67–86). Berlin, Heidelberg: Spring.Google Scholar
  16. Liljedahl, P. (2013). Illumination: An affective experience. The International Journal of Mathematics Education, 45, 253–326.Google Scholar
  17. Mann, E. L. (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students. Doctoral Dissertation. Connecticut: University of Connecticut.Google Scholar
  18. Mason, J. (2008). Being mathematical with and in front of learners: Attention, awareness, and attitude as sources of differences between teacher educators, teachers and learners. In B. Jaworski & T. Wood (Eds.), The mathematics teacher educator as a developing professional (pp. 31–56). Rotterdam/Taipei: Sense Publishers.Google Scholar
  19. Naglieri, J. A., & Das, J. P. (1997). Simultaneous processing is engaged when the relationship between items and their integration into whole units of information is required. In Das-Naglieri cognitive assessment system. Itasca, IL, USA: Riverside Publishing.Google Scholar
  20. Piaget, J., & Roland, G. (1987). Psychogenesis and the history of science. New York: Columbia Press.Google Scholar
  21. Prabhu, V. (2016) Unit 2 Creative Learning Environment. In B. Czarnocha, W. Baker, O. Dias & V. Prabhu (Eds.), The Creative Enterprise of Mathematics Teachhing Research. Sense Publishers, 2016.Google Scholar
  22. Prabhu, V., & Czarnocha, B. (2014). Democratizing mathematical creativity through koestler’s bisociation theory. In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 3). Vancouver, Canada: PME.Google Scholar
  23. Riquelie, F., & de Schonen, S. (1997). Simultaneous attention in the two visual hemifields and interhemispheric integration: A developmental study on 20–26 months old infant. Neuropsycholgia, 35(2), 380–385.Google Scholar
  24. Sfard, A. (1995). The development of algebra: Confronting historical and psychological perspectives. Journal of Mathematic Behavior, 14, 15–39.CrossRefGoogle Scholar
  25. Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, 17(1), 20–36.CrossRefGoogle Scholar
  26. Sriraman, B., Yaftian, N., & Lee, K. H. (2011). Mathematical creativity and mathematics education: A derivative of existing research. In Sriraman & Lee (Eds.), The elements of creativity and giftedness in mathematics. Holland: Sense Publishers.CrossRefGoogle Scholar
  27. Stenhouse, L. (1975). An introduction to curriculum research and development. London: Heinemann.Google Scholar
  28. Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville, IL, USA: Scholastic Testing Service.Google Scholar
  29. Von Glasersfeld, E. (1989). Cognition, construction of knowledge, and teaching. Synthese, 80(1), 121–140.CrossRefGoogle Scholar
  30. Wallas, G. (1926). The art of thought. New York: Harcourt Brace.Google Scholar
  31. Weisberg, R. W. (1995). Prolegomena to theories of insight. In R. Sternberg & J. Davidson (Eds.), The nature of insight (3rd ed.). Cambridge, MA: MIT Press.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentHostos Community College, City University of New YorkBronxUSA

Personalised recommendations