Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Book cover The Philosophy of Mathematics Education Today

Part of the book series: ICME-13 Monographs ((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.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • 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 

  • Bohr, N. (1935). Can quantum reality be considered complete? Physical Review, 48, 696.

    Article  Google Scholar 

  • Czarnocha, B. (2014). On the culture of creativity in mathematics education. Teaching Innovations, 27(3), 30–45.

    Google Scholar 

  • 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 

  • Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum reality be considered complete? Physical Review, 47, 777.

    Article  Google Scholar 

  • 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 

  • Gauch, H. G. (2003). Scientific method in practice. England: Cambridge University Press.

    Google Scholar 

  • Hadamard, J. (1996). The mathematician’s mind: The psychology of invention in the mathematical field. ISBN: 0-691-02931-8.

    Google Scholar 

  • Ilyenkov, E. (1974/2014). Dialectical logic. ISBN: 978-1-312-10852-3.

    Google Scholar 

  • 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 

  • Koestler, A. (1964). The act of creation. London: Hutchinson.

    Google Scholar 

  • Krathwohl, D. R. (2002). A revision of bloom taxonomy. Theory into Practice, 41(4), 212–218.

    Article  Google Scholar 

  • 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 

  • Leikin, R., Berman, A., & Koichu, B. (Eds.) (2009). Creativity in mathematics and the education of gifted students. Rotterdam, the Netherlands: Sense Publisher.

    Google Scholar 

  • 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 

  • Liljedahl, P. (2013). Illumination: An affective experience. The International Journal of Mathematics Education, 45, 253–326.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Piaget, J., & Roland, G. (1987). Psychogenesis and the history of science. New York: Columbia Press.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Sfard, A. (1995). The development of algebra: Confronting historical and psychological perspectives. Journal of Mathematic Behavior, 14, 15–39.

    Article  Google Scholar 

  • Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, 17(1), 20–36.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Stenhouse, L. (1975). An introduction to curriculum research and development. London: Heinemann.

    Google Scholar 

  • Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville, IL, USA: Scholastic Testing Service.

    Google Scholar 

  • Von Glasersfeld, E. (1989). Cognition, construction of knowledge, and teaching. Synthese, 80(1), 121–140.

    Article  Google Scholar 

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

    Google Scholar 

  • 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 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Hostos Community College, City University of New York, 500 Grand Concourse, Bronx, NY, 10451, USA

    Bronislaw Czarnocha, William Baker & Olen Dias

Authors
  1. Bronislaw Czarnocha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William Baker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Olen Dias
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bronislaw Czarnocha .

Editor information

Editors and Affiliations

  1. School of Education, University of Exeter, Exeter, United Kingdom

    Paul Ernest

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Czarnocha, B., Baker, W., Dias, O. (2018). Creativity Research in Mathematics Education Simplified: Using the Concept of Bisociation as Ockham’s Razor. In: Ernest, P. (eds) The Philosophy of Mathematics Education Today. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-77760-3_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-77760-3_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77759-7

  • Online ISBN: 978-3-319-77760-3

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation