Skip to main content

Advertisement

SpringerLink
Log in

Individual and group mathematical creativity among post–high school students

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

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.

    Google Scholar 

  • Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Haylock, D. (1997). Recognizing mathematical creativity in schoolchildren. ZDM Mathematics Education, 27(2), 68–74.

    Google Scholar 

  • Hershkowitz, R., Tabach, M., & Dreyfus, T. (2017). Creative reasoning and shifts of knowledge in the mathematics classroom. ZDM Mathematics Education, 49(1), 25–36.

    Google Scholar 

  • Jung, D. I. (2001). Transformational and transactional leadership and their effects on creativity in groups. Creativity Research Journal, 13(2), 185–195.

    Google Scholar 

  • Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM Mathematics Education, 45(2), 167–181.

    Google Scholar 

  • Kaufman, J., & Beghetto, R. (2009). Beyond big and little: The four C model of creativity. Review of General Psychology, 13(1), 1–12.

    Google Scholar 

  • 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.

    Google Scholar 

  • Klavir, R., & Hershkovitz, S. (2008). Teaching and evaluating ‘open-ended’ problems. International Journal for Mathematics Teaching and Learning, 20(5), 23.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Levenson, E. (2011). Exploring collective mathematical creativity in elementary school. Journal of Creative Behavior, 45(3), 215–234.

    Google Scholar 

  • Levenson, E. (2013). Tasks that may occasion mathematical creativity: Teachers’ choices. Journal of Mathematics Teacher Education, 16(4), 269–291.

    Google Scholar 

  • 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.

    Google Scholar 

  • Liljedahl, P. (2013). Illumination: An affective experience? ZDM Mathematics Education, 45(2), 253–265.

    Google Scholar 

  • Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26(1), 17–19.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Martin, L., Towers, J., & Pirie, S. (2006). Collective mathematical understanding as improvisation. Mathematical Thinking and Learning, 8(2), 149–183.

    Google Scholar 

  • Osborn, A. F. (1957). Applied imagination. New York, NY: Scribner’s.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Presmeg, N. (2003). Creativity, mathematizing, and didactizing: Leen Streefland's work continues. Educational Studies in Mathematics, 54(1), 127–137.

    Google Scholar 

  • 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.

    Google Scholar 

  • Sawyer, R. K. (2004). Creative teaching: Collaborative discussion as disciplined improvisation. Educational Researcher, 33(2), 12–20.

    Google Scholar 

  • Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM Mathematics Education, 3, 75–80.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 22, 390–408.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tel Aviv University, Haim Levanon 30, 6997801, Tel Aviv, Israel

    Osnat Molad & Esther S. Levenson

  2. The Academic College of Tel Aviv Yaffo, Khever ha-Le’umim St 2, Tel Aviv-Yafo, Israel

    Sigal Levy

Authors
  1. Osnat Molad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Esther S. Levenson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sigal Levy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Esther S. Levenson.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-020-09952-5

Keywords

Search

Navigation