Riv. Mat. Univ. Parma, Vol. 14, No. 2, 2023

Johanna Schoenherr [a] and Stanislaw Schukajlow [b]

Does drawing help or hinder creativity when solving a modelling problem? Findings from an eye-tracking study

Pages: 233-248
Received: 19 April 2022
Accepted in revised form: 21 March 2023
Mathematics Subject Classification: 97C30, 97M99.
Keywords: Creativity, mathematical modelling, drawing, eye tracking.
Authors address:
[a],[b]: University of Muenster, Muenster, Germany

Full Text (PDF)

Abstract: Solving a mathematical modelling problem is an activity that allows students to be creative. In the current study, we recorded the eye movements of two students while they solved a geometry modelling problem with instructions to make a drawing, and we conducted a stimulated recall interview (SRI). Using qualitative content analysis, we coded the gaze-overlaid videos and SRI with respect to students' modelling processes and their levels of usefulness, fluency, and originality. We found that the levels of originality and fluency varied during the modelling process, indicating that modelling processes involve creativity and that the final solution might not fully reflect students' creative processes as they work through a problem. In addition, we describe how constructing and using a drawing helped or hindered students being creative. Findings are discussed regarding future studies on creativity in mathematical modelling and implications for classroom practice.

References
[1]
M. Cevikbas, G. Kaiser and S. Schukajlow, A systematic literature review of the current discussion on mathematical modelling competencies: state-of-the-art developments in conceptualizing, measuring, and fostering, Educ. Stud. Math. 109 (2022), no. 2, 205-236. DOI
[2]
R. Cox, Representation construction, externalised cognition and individual differences, Learning and Instruction 9 (1999), no. 4, 343-363. DOI
[3]
P. L. Galbraith and G. Stillman, A framework for identifying student blockages during transitions in the modelling process, ZDM Mathematics Education 38 (2006), no. 2, 143-162. DOI
[4]
J. Joklitschke, B. Rott and M. Schindler, Notions of creativity in mathematics education research: a systematic literature review, Int. J. of Sci. and Math. Educ. 20 (2022), 1161-1181. DOI
[5]
M. Kattou, K. Kontoyianni, D. Pitta-Pantazi and C. Christou, Connecting mathematical creativity to mathematical ability, ZDM Mathematics Education 45 (2013), no. 2, 167-181. DOI
[6]
R. Leikin and M. Lev, Mathematical creativity in generally gifted and mathematically excelling adolescents: what makes the difference?, ZDM Mathematics Education 45 (2013), no. 2, 183-197. DOI
[7]
X. Lu and G. Kaiser, Can mathematical modelling work as a creativity-demanding activity? An empirical study in China, ZDM Mathematics Education 54 (2022), no. 1, 67-81. DOI
[8]
M. Q. Patton, Qualitative research and evaluation methods. Integrating theory and practice, Sage Publications, Los Angeles, 2015.
[9]
D. Pitta-Pantazi, M. Kattou and C. Christou, Mathematical creativity: product, person, process and press, in: F. Singer, ed., ''Mathematical creativity and mathematical giftedness'', ICME-13 Monographs, Springer, Cham, 2018, 27-53. DOI
[10]
J. Rellensmann, S. Schukajlow, J. Blomberg and C. Leopold, Does strategic knowledge matter? Effects of strategic knowledge about drawing on students' modeling competencies in the domain of geometry, Mathematical Thinking and Learning 25 (2023), no. 3, 296-316. DOI
[11]
J. Rellensmann, S. Schukajlow, J. Blomberg and C. Leopold, Effects of drawing instructions and strategic knowledge on mathematical modelling performance: mediated by the use of the drawing strategy, Appl. Cognit. Psychol. 36 (2022), no. 2, 402-417. DOI
[12]
S. Schukajlow, A. Krug and K. Rakoczy, Effects of prompting multiple solutions for modelling problems on students' performance, Educ. Stud. Math. 89 (2015), no. 3, 393-417. DOI
[13]
S. Sydow, LordSydow/AOIanalyseR, Release v1.0.0, Software, Zenodo, 2020, DOI 10.5281/ZENODO.3635895. DOI
[14]
A. Thomaneck, M. Vollstedt and M. Schindler, What can eye movements tell about students' interpretations of contextual graphs? A methodological study on the use of the eye-mind hypothesis in the domain of functions, Front. Educ. 7 (2022), 1-19. DOI
[15]
P. Van Meter and C. M. Firetto, Cognitive model of drawing construction: Learning through the construction of drawings, In: G. Schraw, M. T. McCrudden and D. Robinson, eds, ''Learning through visual displays'', IAP Information Age Publishing, Charlotte, 2013, 247-280. Article
[16]
H. M. Wessels, Exploring aspects of creativity in mathematical modelling, In: G. Stillman, W. Blum and G. Kaiser, eds, ''Mathematical Modelling and Applications'', Springer, Cham, 2017, 491-501. DOI


Home Riv.Mat.Univ.Parma