Abstract
Promoting mathematical creativity is an important aim of mathematics education, which may be promoted by engaging students with open-ended tasks. Most studies of students’ creativity have investigated the creativity of students working individually. This study concerns the mathematical creativity of students working as individuals as compared with those working in groups. Participants were 92 post–high school students, separated into two heterogeneous classes. Both classes engaged with the same three geometric open-ended tasks. For the first two tasks, one class worked individually, while the second worked in small groups of four to six students. For the third task, all students worked individually. Results were analyzed in terms of fluency, flexibility, and originality. No significant differences were found between classes for fluency and flexibility on the first task. However, for the second and third tasks, there were greater fluency and flexibility among those who worked or had worked in groups. For all three tasks, no significant differences between the classes were found regarding originality.
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References
Chiu, M. M. (2008). Effects of argumentation on group micro-creativity: Statistical discourse analyses of algebra students’ collaborative problem solving. Contemporary Educational Psychology, 33(3), 382–402.
Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.
Eizenberg, M. M., & Zaslavsky, O. (2003). Cooperative problem solving in combinatorics: The inter-relations between control processes and successful solutions. The Journal of Mathematical Behavior, 22(4), 389–403.
Francisco, J. M. (2013). Learning in collaborative settings: Students building on each other’s ideas to promote their mathematical understanding. Educational Studies in Mathematics, 82(3), 417–438.
Gómez-Chacón, I. M., & de la Fuente, C. (2018). Problem-solving and mathematical research projects: Creative processes, actions, and mediations. In N. Amado, S. Carreira, & K. Jones (Eds.), Broadening the scope of research on mathematical problem solving (pp. 347–373). Cham, Switzerland: Springer.
Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving. Educational Studies in Mathematics, 49(2), 193–223.
Haylock, D. (1997). Recognizing mathematical creativity in schoolchildren. ZDM Mathematics Education, 27(2), 68–74.
Hershkowitz, R., Tabach, M., & Dreyfus, T. (2017). Creative reasoning and shifts of knowledge in the mathematics classroom. ZDM Mathematics Education, 49(1), 25–36.
Jung, D. I. (2001). Transformational and transactional leadership and their effects on creativity in groups. Creativity Research Journal, 13(2), 185–195.
Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM Mathematics Education, 45(2), 167–181.
Kaufman, J., & Beghetto, R. (2009). Beyond big and little: The four C model of creativity. Review of General Psychology, 13(1), 1–12.
Kim, M. K., Roh, I. S., & Cho, M. K. (2016). Creativity of gifted students in an integrated math-science instruction. Thinking Skills and Creativity, 19, 38–48.
Klavir, R., & Hershkovitz, S. (2008). Teaching and evaluating ‘open-ended’ problems. International Journal for Mathematics Teaching and Learning, 20(5), 23.
Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281–310.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. J. Teller, J. Kilpatrick, & I. Wirszup (Eds.). Chicago, IL: The University of Chicago Press.
Kurtzberg, T., & Amabile, T. (2001). From Guilford to creative synergy: Opening the black box of team-level creativity. Creativity Research Journal, 13(3 & 4), 285–294.
Kwon, O. N., Park, J. S., & Park, J. H. (2006). Cultivating divergent thinking in mathematics through an open-ended approach. Asia Pacific Education Review, 7(1), 51–61.
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman and B. Koichu (Eds.) Creativity in mathematics and the education of gifted students (pp. 129-135), Sense Publishers.
Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM Mathematics Education, 45(2), 183–197.
Levav-Waynberg, A., & Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. The Journal of Mathematical Behavior, 31(1), 73–90.
Levenson, E. (2011). Exploring collective mathematical creativity in elementary school. Journal of Creative Behavior, 45(3), 215–234.
Levenson, E. (2013). Tasks that may occasion mathematical creativity: Teachers’ choices. Journal of Mathematics Teacher Education, 16(4), 269–291.
Levenson, E. (2014). Investigating mathematical creativity in elementary school through the lens of complexity theory. In Ambrose, D., Sriraman, B. and Pierce, K. M. (Eds.), A critique of creativity and complexity- Deconstructing clichés (pp. 35-52). Rotterdam, the Netherlands: Sense Publishers.
Levenson, E., Swisa, R., & Tabach, M. (2018). Evaluating the potential of tasks to occasion mathematical creativity: Definitions and measurements. Research in Mathematics Education, 20(3), 273–294.
Liljedahl, P. (2013). Illumination: An affective experience? ZDM Mathematics Education, 45(2), 253–265.
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26(1), 17–19.
Luria, S. R., Sriraman, B., & Kaufman, J. C. (2017). Enhancing equity in the classroom by teaching for mathematical creativity. ZDM Mathematics Education, 49(7), 1033–1039.
Mann, E., 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 and beyond (pp. 57–76). Cham, Switzerland: Springer.
Martin, L., Towers, J., & Pirie, S. (2006). Collective mathematical understanding as improvisation. Mathematical Thinking and Learning, 8(2), 149–183.
Osborn, A. F. (1957). Applied imagination. New York, NY: Scribner’s.
Paulus, P. B., Larey, T. S., & Dzindolet, M. T. (2000). Creativity in groups and teams. In M. Turner (Ed.), Groups at work: Advances in theory and research (pp. 319–338). Hillsdale, NJ: Hampton.
Paulus, P. B., & Yang, H. (2000). Idea generation in groups: A basis for creativity in organizations. Organizational Behavior and Human Decision Processes, 82(1), 86–87.
Plucker, J. A., Qian, M., & Wang, S. (2011). Is originality in the eye of the beholder? Comparison of scoring techniques in the assessment of divergent thinking. The Journal of Creative Behavior, 45(1), 1–22.
Presmeg, N. (2003). Creativity, mathematizing, and didactizing: Leen Streefland's work continues. Educational Studies in Mathematics, 54(1), 127–137.
Runco, M. A., & Albert, R. S. (1985). The reliability and validity of ideational originality in the divergent thinking of academically gifted and nongifted children. Educational and Psychological Measurement, 45, 483–501.
Sawyer, R. K. (2004). Creative teaching: Collaborative discussion as disciplined improvisation. Educational Researcher, 33(2), 12–20.
Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM Mathematics Education, 3, 75–80.
Tsamir, P., Tirosh, D., Tabach, M., & Levenson, E. (2010). Multiple solution methods and multiple outcomes – Is it a task for kindergarten children? Educational Studies in Mathematics, 73(3), 217–231.
Van Harpen, X. Y., & Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics, 83(1), 117–132.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 22, 390–408.
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Molad, O., Levenson, E.S. & Levy, S. Individual and group mathematical creativity among post–high school students. Educ Stud Math 104, 201–220 (2020). https://doi.org/10.1007/s10649-020-09952-5
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DOI: https://doi.org/10.1007/s10649-020-09952-5