Feeling of innovation in expert problem posing

Authors

  • Igor’ Kontorovich
  • Boris Koichu

DOI:

https://doi.org/10.7146/nomad.v17i3-4.148493

Abstract

This paper is one of the reports on a multiple-case study concerned with the intertwining between affect and cognition in the mechanisms governing experts when posing new mathematical problems. Based on inductive analysis of a single case of an expert poser for mathematics competitions, we suggest that the desire to experience the feeling of innovation may be one of such mechanisms. In the case of interest, the feeling was realized through expert’s reflections on the problems he created in the past, by systematically emphasizing how a new problem was innovative in comparison with other familiar problems based on the same nesting idea. The findings are discussed in light of past research on expert problem posers and expert problem solvers.

References

Carlson, M. & Bloom, I. (2005). The cyclic nature of problem solving: an emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45-75. https://doi.org/10.1007/s10649-005-0808-x

Chi, M. T. H., Feltovich, P. J. & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152. https://doi.org/10.1207/s15516709cog0502_2

Doboli, S., Tang, W., Ramnath, R., Impagliazzo, J., VanEpps, T., et al. (2010). Panel - models of entrepreneurship education and its role in increasing creativity, innovation and leadership in computer science and engineering students. In Proceedings of the 40th ASEE/IEEE Frontiers in Education Conference. Retrieved May 7, 2013 from http://ieeexplore.ieee.org/stamp/ stamp.jsp?tp=&arnumber=5673380 https://doi.org/10.1109/FIE.2010.5673380

Ericsson, K. A. (2006). The influence of experience and deliberate practice on the development of superior expert performance. In K. A. Ericsson, N. Charness, P. Feltovich & R. R. Hoffman (Eds.), Cambridge handbook of expertise and expert performance (pp. 685-706). Cambridge University Press. https://doi.org/10.1017/CBO9780511816796.038

Furinghetti, F. & Morselli, F. (2009). Every unsuccessful problem solver is unsuccessful in his or her own way: affective and cognitive factors in proving. Educational Studies in Mathematics, 70, 71-90. https://doi.org/10.1007/s10649-008-9134-4

Grugnetti, L. & Jaquet, F. (2005). A mathematical competition as a problem solving and a mathematical education experience. Journal of Mathematical Behavior, 24, 373-384. https://doi.org/10.1016/j.jmathb.2005.09.012

Hochschild, A. R. (1983). The managed heart: commercialization of human feeling. Berkeley: University of California Press.

Knight, K. E. (1967). A descriptive model of the intra-firm innovation process. The Journal of Business, 40 (4), 478-496. https://doi.org/10.1086/295013

Koichu, B. & Andžāns, A. (2009). Mathematical creativity and giftedness in out-of-school activities. In R. Leikin, A. Berman & B. Koichu (Eds.), Creativity in mathematics and education of gifted students (pp. 285-308). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789087909352_019

Konstantinov, N. N. (1997). Tournir Gorodov i matematicheskaya olympiada [Tournament of the Towns and mathematical Olympiad]. Matematicheskoe Prosveschenie, 3 (1), 164-174. (in Russian).

Kontorovich, I. (2012). What makes an interesting mathematical problem? A perception analysis of 22 adult participants of the competition movement. In B. Roesken & M. Casper (Eds.), Current state of research on mathemat- ical beliefs XVII (Proceedings of the MAVI-17 conference). University of Bochum.

Kontorovich, I., Koichu, B., Leikin, R. & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. Journal of Mathematical Behaviour, 31 (1), 149-161. https://doi.org/10.1016/j.jmathb.2011.11.002

Liljedahl, P. (2009). In the words of the creators. In R. Leikin, A. Berman & B. Koichu (Eds.), Creativity in mathematics and education of gifted students (pp. 51-70). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789087909352_005

Maslow, A. (1943). A theory of human needs. Psychological Review, 50, 370-396. https://doi.org/10.1037/h0054346

Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. The Psychological Review, 63, 81-97. https://doi.org/10.1037/h0043158

Pelczer, I. & Gamboa, F. (2009). Problem posing: comparison between experts and novices. In M. Tzekaki, M. Kaldrimidou & C. Sakonidis (Eds.), Proceedings of the 33th conference of the International Group for the Psychology of Mathematics Education (vol. 4, pp. 353-360). Thessaloniki: PME.

Schoenfeld, A. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. A. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York: Macmillan.

Sharigin, I. F. (1991). Otkuda berutsia zadachi? [Where do problems come from?] Part I, Kvant, 8, 42-48; part II, Kvant, 9, 42-49. (in Russian).

Silver, E.A., Mamona-Downs, J., Leung, S. & Kenney, P. A. (1996). Posing mathematical problems: an exploratory study. Journal for Research in Mathematics Education, 27 (3), 293-309. https://doi.org/10.2307/749366

Thomas, D. T. (2006). A general inductive approach for analyzing qualitative evaluation data. American Journal of Evaluation, 27 (2), 237-246. https://doi.org/10.1177/1098214005283748

Thrasher, T. N. (2008). The benefits of mathematics competitions. Alabama Journal of Mathematics, Spring-Fall, 59-63.

Walter, M. (1978). Generating problems almost from anything, part I. Mathematics Teaching, 120, 3-7; part II, Mathematics Teaching, 121, 2-6.

Wilkerson-Jerde, M. H. & Wilensky, U. J. (2011). How do mathematicians learn math?: resources and acts for constructing and understanding mathematics. Educational Studies in Mathematics, 78, 21-43. https://doi.org/10.1007/s10649-011-9306-5

Downloads

Published

2012-11-19

How to Cite

Kontorovich, I., & Koichu, B. (2012). Feeling of innovation in expert problem posing. NOMAD Nordic Studies in Mathematics Education, 17(3-4), 199–211. https://doi.org/10.7146/nomad.v17i3-4.148493

Issue

Section

Articles