Illumination: an affective experience?
- Peter Liljedahl
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What is the nature of illumination in mathematics? That is, what is it that sets illumination apart from other mathematical experiences? In this article the answer to this question is pursued through a qualitative study that seeks to compare and contrast the AHA! experiences of preservice teachers with those of prominent research mathematicians. Using a methodology of analytic induction in conjunction with historical and contemporary theories of discovery, creativity, and invention along with theories of affect the anecdotal reflections of participants from these two populations are analysed. Results indicate that, although manifested differently in the two populations, what sets illumination apart from other mathematical experiences are the affective aspects of the experience.
- Ajzen, I. (1988). Attitudes, personality, and behaviour. Milton Keynes: Open University Press.
- Ashcraft, M. (1989). Human memory and cognition. Glenview: Scott, Foresman and Company.
- Bailin, S. (1994). Achieving extraordinary ends: An essay on creativity. Norwood: Ablex Publishing Corporation.
- Barnes, M. (2000). ‘Magical’ moments in mathematics: Insights into the process of coming to know. For the Learning of Mathematics, 20(1), 33–43.
- Bruner, J. (1964). Bruner on knowing. Cambridge: Harvard University Press.
- Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37(2), 121–143. CrossRef
- Csikszentmihalyi, C. (1996). Creativity: Flow and the psychology of discovery and invention. New York: HarperCollins Publishers.
- Davis, P., & Hersch, R. (1980). The mathematical experience. Boston: Birkhauser.
- DeBellis, V., & Goldin, G. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63(2), 131–147. CrossRef
- Dewey, J. (1933). How we think. Boston: D.C. Heath and Company.
- Feynman, R. (1999). The pleasure of finding things out. Cambridge: Perseus Publishing.
- Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht: Kluwer Academic Publishers Group.
- Ghiselin, B. (1952). The creative process: Reflections on invention in the arts and sciences. Berkeley: University of California Press.
- Glaser, B. & Strauss, A. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine Publishing Co.
- Hadamard, J. (1945). The psychology of invention in the mathematical field. New York: Dover Publications.
- Kneller, G. (1965). The art and science of creativity. New York: Holt, Reinhart, and Winstone, Inc.
- Koestler, A. (1964). The act of creation. New York: The Macmillan Company.
- Liljedahl, P. (2009). In the words of the creators. In R. Leikin, A. Berman, & B. Koichu (Eds.), Mathematical creativity and the education of gifted children (pp. 51–70). Rotterdam: Sense Publishers.
- Liljedahl, P., & Allen, D. (in press). Mathematical discovery. In E. G. Carayannis (Ed.), Encyclopedia of creativity, invention, innovation, and entrepreneurship. New York: Springer.
- Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For The Learning of Mathematics, 26(1), 20–23.
- McLeod, D. (1992). Research on the affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: Macmillan.
- Nova (1993). The proof. Aired on PBS on October 28, 1997. http://www.pbs.org/wgbh/nova/transcripts/2414proof.html. Accessed 11 December 2003.
- O’pt Eynde, P., De Corte, E., & Verschaffel, L. (2001). Problem solving in the mathematics classroom: A socio-constructivist account of the role of students’ emotions. Proceedings of 25th Annual Conference for the Psychology of Mathematics Education, 4, 25–32.
- Patton, M. Q. (2002). Qualitative research and evaluation methods. Thousand Oaks: Sage.
- Perkins, D. (2000). Archimedes’ bathtub: The art of breakthrough thinking. New York: W.W. Norton & Company.
- Poincaré, H. (1952). Science and method. New York: Dover Publications, Inc.
- Pólya, G. (1965/1981). Mathematical discovery: On understanding, learning and teaching problem solving (vol. 2). New York: Wiley.
- Rota, G. (1997). Indiscrete thoughts. Boston: Birkhauser.
- Sfard, A. (2004). Personal Communication.
- Sinclair, N. (2002). The kissing triangles: The aesthetics of mathematical discovery. International Journal of Computers for Mathematics Learning, 7(1), 45–63. CrossRef
- Wallas, G. (1926). The art of thought. New York: Harcourt Brace.
- Whittlesea, B. (1993). Illusions of familiarity. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19(7), 1235–1253. CrossRef
- Whittlesea, B., & Williams, L. (2001). The discrepancy-attribution hypothesis: The heuristic basis of feelings of familiarity. Journal for Experimental Psychology: Learning, Memory, and Cognition, 27(1), 3–13. CrossRef
- Illumination: an affective experience?
Volume 45, Issue 2 , pp 253-265
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- Peter Liljedahl (1)
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- 1. Simon Fraser University, Burnaby, BC, Canada