The Korea Society Of Educational Studies In Mathematics

Current Issue

Journal of Educational Research in Mathematics - Vol. 29 , No. 4

[ Article ]
Journal of Educational Research in Mathematics - Vol. 29, No. 2, pp.251-282
Abbreviation: JERM
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 31 May 2019
Received 08 Apr 2019 Reviewed 07 May 2019 Accepted 07 May 2019
DOI: https://doi.org/10.29275/jerm.2019.5.29.2.251

A Case Study of Group Creativity in Mathematical Modeling Activities: Focusing on Mathematical Representation and Model Derivation Activities
Jung, Hye-Yun* ; Lee, Kyeong-Hwa**,
*Teacher, Sejong Science High School, South Korea (hy0501@snu.ac.kr)
**Professor, Center of Education Research, Seoul National University, South Korea (khmath@snu.ac.kr)

Correspondence to : Professor, Center of Education Research, Seoul National University, South Korea, khmath@snu.ac.kr


Abstract

In this study, we analyzed the developed group creativity in mathematical modeling activities of 9th students. We especially focused on mathematically various representation and model derivation stages. We then identified features of group creativity and their effects on each stage. The details were as follows: First, through theoretical review, we identified the possibility of group creativity in the above two stages. Second, after identifying the factors that influence the development of group creativity, we designed the instructions. The results of this study were as follows: First, at the mathematically various representation stage, different types of interactions were observed depending on the group. Moreover there were also differences in the creative synergy according to the type of interactions. Second, at the mathematical model accumulation stage, metacognitive interaction was observed in some groups. It was then confirmed that there were differences in creative synergies. Third, at the mathematical model selection stage, metacognitive interaction and its creative synergies were observed in all groups.


Keywords: mathematical modeling, group creativity, interaction, creative synergy, instructional design

References
1. Amabile, T. M., & Pillemer, J. (2012). Perspectives on the social psychology of creativity. Journal of Creative Behavior, 46(1), 3-15.
2. Beghetto, R. A., & Kaufman, J. C. (2007). Toward a broader conception of creativity: A case for “mini-c” creativity. Psychology of Aesthetics, Creativity, and the Arts, 1(2), 73-79.
3. Beghetto, R. A., & Kaufman, J. C. (2010). Nurturing creativity in the classroom. Cambridge: Cambridge University Press.
4. Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool develop and identify creatively gifted mathematicians. The Journal of Gifted Education, 17(1), 37-47.
5. Cho, M. J., & Jin, S. U. (2016). A phenomenological study on group creativity emerging precess experiences of gifted students in elementary schools. The Journal of Creativity Education, 16(2), 35-59.
6. Choi, H. S., & Thompson, L. (2005). Old wine in a new bottle: Impact of membership change on group creativity. Organizational Behavior and human decision processes, 98(2), 121-132.
7. Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Research, 23(7), 13-20.
8. Cobb, P. (2002). Modeling, symbolizing, and tool use in statistical data analysis. In K. Gravemeijer, R. Lehrer, B. Oers, & L. Verschaffel (Eds.), Symbolizing, modeling, and tool use in mathematics education (pp. 171-195). Netherlands: Kluwer Academic Publishers.
9. Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23, 2-33.
10. Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods. Sage Publications.
11. Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110-136.
12. English, L. D. & Sriraman, B. (2009). Problem solving for the 21st century. In B. Sriraman, & L. English (Eds.), Theories of mathematics education (pp. 263-301). Berlin: Springer.
13. Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143-162.
14. Gravemeijer, K., Cobb, P., Bowers, J., & Whitenack, J. (2012). Symbolizing, modeling, and instructional design. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instruction design (pp. 225-273). Mahwah: Lawrence Erlbaum Associates.
15. Jung, H. Y., & Lee, K. H. (2018). Manifestation examples of group creativity in mathematical modeling. The Mathematical Education, 57(4), 371-391.
16. Jung, H. Y., & Lee, K. H. (2019). Instructional design of mathematical modeling for group creativity. Journal of Educational Research in Mathematics, 29(1), 157-188.
17. Jung, H. Y., Lee, K. H., Baek, D. H., Jung, J. H., & Lim, K. S. (2018). Design for <Mathematical Task Inquiry> subject’s task based on the mathematical modeling perspective. School Mathematics, 20(1), 149-169.
18. Kaiser, G., & Stender, P. (2013). Complex modelling problems in co-operative, self-directed learning environments. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 277-293). Dordrecht: Springer.
19. Kaufman, J. C., & Beghetto, R. A. (2009). Beyond big and little: The four C model of creativity. Review of General Psychology, 13, 1-12.
20. Kim, S. Y. (2017). An in-depth conceptual analysis of synergy in group collaborative learning. Journal of Educational Technology, 33(1), 75-104.
21. Lee, K. H. (2015). Mathematical creativity. Seoul: Kyungmunsa.
22. Lee, K. H. (2016). Reanalysis of realistic mathematics education perspective in relation to cultivation of mathematical creativity. Journal of Educational Research in Mathematics, 26(1), 47-62.
23. 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: Sense Publisher.
24. Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 35-58). Mahwah: Lawrence Erlbaum Associates.
25. Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Mahwah: Lawrence Erlbaum Associates.
26. Lesh, R., & Doerr, H. M. (2012). Symbolizing, communicating, and mathematizing: Key components of models and modeling. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instruction design (pp. 361-384). Mahwah: Lawrence Erlbaum Associates.
27. Luria, S. R., Sriraman, B., & Kaufman, J. C. (2017). Enhancing equity in the classroom by teaching for mathematical creativity. ZDM, 49(7), 1033-1039.
28. Mann, E. L., Chamberlin, S. A., & Graefe, A. K. (2017). The prominence of affect in creativity: Expanding the conception of creativity in mathematical problem solving. In R. Leikin, & B. Sriraman (Eds.), Creativity and giftedness: Interdisciplinary perspectives from mathematics beyond (pp. 57-73). Switzerland: Springer.
29. Ministry of Education. (2015). Mathematical curriculum. Notification of the Ministry of Education No. 2015-74. [Vol. 8]. Seoul: Author.
30. Nemeth, C. J., Brown, K. S., & Rogers, J. (2001). Devil’s advocate versus authentic dissent: stimulating quantity and quality. European Journal of Social Psychology, 31, 707-720.
31. Núñez-Oveido, M. C., Clement, J., & Rea-Ramirez, M. A. (2008). Developing complex mental modes in biology through model evolution. In J. J. Clement, & M. A. Rea-Ramirez (Eds.), Model based learning and instruction in science (pp. 173-193). Netherlands: Springer.
32. Pakeltienė, R., & Ragauskaitė, A. (2017). Creative synergy as a potential factor for the development of social innovations. Research for Rural Development, 2, 174-181.
33. Palsdottir, G., & Sriraman, B. (2017). Teacher’s views on modeling as a creative mathematical activity. In R. Leikin, & B. Sriraman (Eds.), Creativity and giftedness (pp. 47-55). Switzerland: Springer.
34. Paulus, P. B. (2000). Groups, teams, and creativity: The creative potential of idea-generating groups. Applied Psychology: An International Review, 49(2), 237-262.
35. Paulus, P. B., & Nijstad, B. A. (2003). Group creativity. In P. B. Paulus, & B. A. Nijstad (Eds.), Group creativity: Innovation through collaboration (pp. 3-11). Oxford University Press.
36. Paulus, P. B., & Yang, H. (2000). Idea generation in groups: A basis for creativity in organizations. Organizational Behavior and Human Decision Processes, 82(1), 76-87.
37. Redmond, T., Brown, R., & Sheehy, J. (2013). Exploring the relationship between mathematical modelling and classroom discourse. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 349-360). Dordrecht: Springer.
38. Sawyer, R. K. (2007). Group genius: The creative power of collaboration. Basic Books.
39. Sawyer, R. K. (2012). Explaining creativity: The science of human innovation account. Oxford University Press.
40. Siau, K. L. (1995). Group creativity and technology. Journal of Creative Behavior, 29(3), 201-216.
41. Starko, A. J. (1995). Creativity in the classroom. New York: Longman.
42. Verschaffel, L., Greer, B., & De Corte, E. (2002). Everyday knowledge and mathematical modeling of school word problems. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 257-276). Dordrecht: Springer.
43. Vorhölter, K. (2018). Conceptualization and measuring of metacognitive modelling competencies: Empirical verification of theoretical assumption. ZDM, 50(1-2), 343-354.
44. Vorhölter, K., Krüger, A., & Wendt, L. (2017). Metacognitive modelling competencies in small groups. In Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education. Dublin, Ireland: DCU Institute of Education and ERME.
45. Woo, J. H. et al., (2014). Research methodology in mathematics education. Seoul: Kyungmunsa.
46. Woodman, R. W., Sawyer, J. E., & Griffin, R. W. (1993). Toward a theory of organizational creativity. The Academy of Management Review, 18(2), 293-321.
47. Zhou, C., & Luo, L. (2012). Group creativity in learning context: Understanding in a social-cultural framework and methodology. Creative Education, 3(4), 392-399.