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Students’ Creative Process in Mathematics: Insights from Eye-Tracking-Stimulated Recall Interview on Students’ Work on Multiple Solution Tasks

Schindler, Maike, Lilienthal, Achim J.·2020·International Journal of Science and Mathematics Education

Abstract

Students’ creative process in mathematics is increasingly gaining significance in mathematics education research. Researchers often use Multiple Solution Tasks (MSTs) to foster and evaluate students’ mathematical creativity. Yet, research so far predominantly had a product-view and focused on solutions rather than the process leading to creative insights. The question remains unclear how students’ process solving MSTs looks like—and if existing models to describe (creative) problem solving can capture this process adequately. This article presents an explorative, qualitative case study, which investigates the creative process of a school student, David. Using eye-tracking technology and a stimulated recall interview, we trace David’s creative process. Our findings indicate what phases his creative process in the MST involves, how new ideas emerge, and in particular where illumination is situated in this process. Our case study illustrates that neither existing models on the creative process, nor on problem solving capture David’s creative process fully, indicating the need to partially rethink students’ creative process in MSTs.

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Research works printed but not linked: 50

  1. Czarnocha, B., & Baker, W. (2015). Creativity and bisociation. Mathematics Teaching-Research Journal Online, 7(3), 1–7.
  2. Dewey, J. (1910). How we think. Boston, MA: Heath. · DOI · Paper page
  3. Epelboim, J., & Suppes, P. (2001). A model of eye movements and visual working memory during problem solving in geometry. Vision Research, 41(12), 1561–1574. · DOI
  4. Ericsson, K. A., & Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87(3), 215–251. · DOI
  5. Gass, S. M., & Mackey, A. (2000). Stimulated recall methodology in second language research. Mahwah, NJ: Lawrence Erlbaum.
  6. Guilford, J. P. (1967). The nature of human intelligence. New York: McGraw-Hill.
  7. Haavold, P. O., & Birkeland, A. (2017). Contradictory concepts of creativity in mathematics teacher education. In R. A. Beghetto & B. Sriraman (Eds.), Creative contradictions in education. Cross disciplinary paradoxes and perspectives (pp. 181–200). Cham, SL: Springer. · DOI
  8. Hadamard, J. (1954). An essay on the psychology of invention in the mathematical field. New York: Dover.
  9. Hansen, J. P. (1991). The use of eye mark recordings to support verbal retrospection in software testing. Acta Psychologica, 76(1), 31–49. · DOI · Paper page
  10. Haylock, D. W. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18, 59–74. · DOI
  11. Holmqvist, K., Nyström, M., Andersson, R., Dewhurst, R., Jarodzka, H., & Van de Weijer, J. (2011). Eye tracking: A comprehensive guide to methods and measures. Oxford: OUP.
  12. Just, M. A., & Carpenter, P. A. (1976). Eye fixations and cognitive processes. Cognitive Psychology, 8(4), 441–480. · DOI · Paper page
  13. Kassner, M., Patera, W., & Bulling, A. (2014). Pupil: An open source platform for pervasive eye tracking and mobile gaze-based interaction. arXiv:1405.0006. · arXiv
  14. Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–145). Rotterdam, NL: Sense. · doi:10.1163/9789087909352_010
  15. Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM, 45(2), 183–197. · DOI
  16. Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: the state of the art. ZDM, 45, 159–166. · DOI · Paper page
  17. Levav-Waynberg, A., & Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. Journal of Mathematical Behavior, 31(1), 73–90. · DOI
  18. Liljedahl, P. (2013). Illumination: An affective experience? ZDM, 45, 253–265. · DOI
  19. Lyle, J. (2003). Stimulated recall: A report on its use in naturalistic research. British Educational Research Journal, 29(6), 861–878. · DOI · Paper page
  20. Mann, E. L. (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students (Doctoral dissertation). University of Connecticut, USA. Retrieved Nov. 26, 2019 from http://www.fisme.science.uu.nl/publicaties/literatuur/2005_mann_creativity.pdf.
  21. Mousoulides, N., & Sriraman, B. (2014). Heuristics in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 253–255). Dordrecht, NL: Springer. · doi:10.1007/978-94-007-4978-8_172
  22. Muldner, K., & Burleston, W. (2015). Utilizing sensor data to model students’ creativity in a digital environment. Computers in Human Behavior, 42, 127–137. · DOI
  23. Novotná, J. (2017). Problem solving through heuristic strategies as a way to make all pupils engaged. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of the 41st conference of the IGPME (Vol. 1, pp. 29–44). Singapore: PME.
  24. Obersteiner, A., & Tumpek, C. (2016). Measuring fraction comparison strategies with eye-tracking. ZDM—Mathematics Education, 48(3), 255–266. · DOI · Paper page
  25. Pitta-Pantazi, D., Kattou, M., & Christou, C. (2018). Mathematical creativity: Product, person, process and press. In M. F. Singer (Ed.), Mathematical creativity and mathematical giftedness. Enhancing creative capacities in mathematically promising students (pp. 27–54). New York: Springer. · DOI
  26. Poincaré, H. (1948). Science and method. New York: Dover.
  27. Pólya, G. (1945). How to solve it. Princeton, NJ: University Press. · DOI · Paper page
  28. Prabhu, V., & Czarnocha, B. (2014). Democratizing mathematical creativity through Koestler’s bisociation theory. Mathematics Teaching-Research Journal Online, 6(4), 33–46.
  29. Rhodes, M. (1961). An analysis of creativity. The Phi Delta Kappan, 42(7), 305–310.
  30. Rott, B. (2014). Mathematische Problembearbeitungsprozesse von Fünftklässlern–Entwicklung eines deskriptiven Phasenmodells [Mathematical problem-solving processes of fifth-grader development of a descriptive phase model]. JMD, 35(2), 251–282. · doi:10.1007/s13138-014-0069-2
  31. Schindler, M., Joklitschke, J., & Rott, B. (2018). Mathematical creativity and its subdomain-specificity. Investigating the appropriateness of solutions in multiple solution tasks. In M.F. Singer (Ed.), Mathematical creativity and mathematical giftedness. Enhancing creative capacities in mathematically promising students (pp. 115–142). New York: Springer.
  32. Schindler, M., Lilienthal, A.J., Chadalavada, R., & Ögren, M. (2016). Creativity in the eye of the student. Refining investigations of mathematical creativity using eye-tracking goggles. In C. Csíkos, A. Rausch, & J. Szitányi (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (PME), 4, 163–170. Szeged, Hungary: PME.
  33. Schindler, M., & Lilienthal, A.J. (2017a). Eye-tracking and its domain-specific interpretation. A stimulated recall study on eye movements in geometrical tasks. In B. Kaur, W.K. Ho, T.L. Toh, & B.H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (PME), 4, 153–160. Singapore: PME.
  34. Schindler, M., & Lilienthal, A.J. (2017b). Eye-tracking as a tool for investigating mathematical creativity from a process-view. In D. Pitta-Pantazi (Ed.), Proceedings of the 10th International Conference on Mathematical Creativity and Giftedness (MCG 10) (pp. 45–50). Nicosia, Cyprus: Department of Education, University of Cyprus.
  35. Schindler, M., & Lilienthal, A.J. (2018). Eye-tracking for studying mathematical difficulties—also in inclusive settings. In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.), Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (PME), 4, 115–122. Umeå, Sweden: PME.
  36. Schindler, M., & Lilienthal, A.J. (2019). Domain-specific interpretation of eye tracking data: Towards a refined use of the eye-mind hypothesis for the field of geometry. Educational Studies in Mathematics, 101(1), 123–139. · DOI · Paper page
  37. Sheffield, L. J. (2009). Developing mathematical creativity—questions may be the answer. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 87–100). Rotterdam, NL: Sense Publishers. · doi:10.1163/9789087909352_007
  38. Sheffield, L. J. (2013). Creativity and school mathematics: Some modest observations. ZDM— Mathematics Education, 45, 325–332. · doi:10.1007/s11858-013-0484-8
  39. Sheffield, L. J. (2018). Commentary paper: A reflection on mathematical creativity and giftedness. In M. F. Singer (Ed.), Mathematical creativity and mathematical giftedness. Enhancing creative capacities in mathematically promising students (pp. 405–423). Nk: Springer.
  40. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 29(3), 75–80.
  41. Sinclair, N., Bartolini Bussi, M. G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM, 48(5), 691–719. · DOI
  42. Singer, M. F. (2018). Enhancing creative capacities in mathematically-promising students. Challenges and limits. In M. F. Singer (Ed.), Mathematical creativity and mathematical giftedness. Enhancing creative capacities in mathematically promising students (pp. 1–23). New York: Springer. · doi:10.1007/978-3-319-73156-8
  43. Sitorus, J., & Masrayati. (2016). Students’ creative thinking process stages: Implementation of realistic mathematics education. Thinking Skills and Creativity, 22, 111–120. · DOI
  44. Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34.
  45. Sriraman, B. (2005). Are giftedness & creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17, 20–36. · DOI · Paper page
  46. Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM, 41(1–2), 13–27. · DOI · Paper page
  47. Sriraman, B., Haavold, P., & Lee, K. (2014). Creativity in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 109–115). Dordrecht, NL: Springer. · DOI
  48. Stickler, U., & Shi, L. (2017). Eye tracking methodology in SCMC: A tool for empowering learning and teaching. ReCALL, 29(2), 160–177. · DOI
  49. Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville, IL: STS.
  50. Wallas, G. (1926). The art of thought. London: C.A. Watts & Co.

Cited by

Metadata

Authors
Schindler, M., & Lilienthal, A. J.
Venue
International Journal of Science and Mathematics Education
Published
2019-12-02
Volume
18
Issue
8
Pages
1565-1586
ISSN
  • 1571-0068
  • 1573-1774
Cited by
45
References
0
Language
en
Licence
Funders
Örebro University

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