Illumination: an affective experience?
 Peter Liljedahl
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
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. Open University Press, Milton Keynes
 Ashcraft, M (1989) Human memory and cognition. Scott, Foresman and Company, Glenview
 Bailin, S (1994) Achieving extraordinary ends: An essay on creativity. Ablex Publishing Corporation, Norwood
 Barnes, M (2000) ‘Magical’ moments in mathematics: Insights into the process of coming to know. For the Learning of Mathematics 20: pp. 3343
 Bruner, J (1964) Bruner on knowing. Harvard University Press, Cambridge
 Burton, L (1999) The practices of mathematicians: What do they tell us about coming to know mathematics?. Educational Studies in Mathematics 37: pp. 121143 CrossRef
 Csikszentmihalyi, C (1996) Creativity: Flow and the psychology of discovery and invention. HarperCollins Publishers, New York
 Davis, P, Hersch, R (1980) The mathematical experience. Birkhauser, Boston
 DeBellis, V, Goldin, G (2006) Affect and metaaffect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics 63: pp. 131147 CrossRef
 Dewey, J (1933) How we think. D.C. Heath and Company, Boston
 Feynman, R (1999) The pleasure of finding things out. Perseus Publishing, Cambridge
 Fischbein, E (1987) Intuition in science and mathematics: An educational approach. Kluwer Academic Publishers Group, Dordrecht
 Ghiselin, B (1952) The creative process: Reflections on invention in the arts and sciences. University of California Press, Berkeley
 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. Dover Publications, New York
 Kneller, G (1965) The art and science of creativity. Holt, Reinhart, and Winstone, Inc., New York
 Koestler, A (1964) The act of creation. The Macmillan Company, New York
 Liljedahl, P In the words of the creators. In: Leikin, R, Berman, A, Koichu, B eds. (2009) Mathematical creativity and the education of gifted children. Sense Publishers, Rotterdam, pp. 5170
 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: pp. 2023
 McLeod, D Research on the affect in mathematics education: A reconceptualization. In: Grouws, DA eds. (1992) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp. 575596
 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, Corte, E, Verschaffel, L (2001) Problem solving in the mathematics classroom: A socioconstructivist account of the role of students’ emotions.. Proceedings of 25th Annual Conference for the Psychology of Mathematics Education 4: pp. 2532
 Patton, MQ (2002) Qualitative research and evaluation methods. Sage, Thousand Oaks
 Perkins, D (2000) Archimedes’ bathtub: The art of breakthrough thinking. W.W. Norton & Company, New York
 Poincaré, H (1952) Science and method. Dover Publications, Inc., New York
 Pólya, G. (1965/1981). Mathematical discovery: On understanding, learning and teaching problem solving (vol. 2). New York: Wiley.
 Rota, G (1997) Indiscrete thoughts. Birkhauser, Boston
 Sfard, A. (2004). Personal Communication.
 Sinclair, N (2002) The kissing triangles: The aesthetics of mathematical discovery. International Journal of Computers for Mathematics Learning 7: pp. 4563 CrossRef
 Wallas, G (1926) The art of thought. Harcourt Brace, New York
 Whittlesea, B (1993) Illusions of familiarity. Journal of Experimental Psychology: Learning, Memory, and Cognition 19: pp. 12351253 CrossRef
 Whittlesea, B, Williams, L (2001) The discrepancyattribution hypothesis: The heuristic basis of feelings of familiarity. Journal for Experimental Psychology: Learning, Memory, and Cognition 27: pp. 313 CrossRef
 Title
 Illumination: an affective experience?
 Journal

ZDM
Volume 45, Issue 2 , pp 253265
 Cover Date
 20130401
 DOI
 10.1007/s1185801204733
 Print ISSN
 18639690
 Online ISSN
 18639704
 Publisher
 SpringerVerlag
 Additional Links
 Authors

 Peter Liljedahl ^{(1)}
 Author Affiliations

 1. Simon Fraser University, Burnaby, BC, Canada