Abstract
The investigations described in the ten fascinating research studies contained in the current volume of ZDM Mathematics Education evoke some perspectives in response. I consider the articles thematically in relation to a suggested set of important or pressing questions about creativity and giftedness in mathematics education, grouped into four areas: (1) definitions and meanings, (2) learning environments, (3) teacher preparation, (4) educational policies and societal trends. The first three of these areas are addressed most specifically; the latter is given less attention, with much remaining to be researched. In the context of the topics most addressed, possible emphases in studying mathematical creativity and giftedness include cognitive, affective, conative (motivational), social, and behavioral aspects. The studies here focus mostly on the cognitive, social, and behavioral dimensions. I highlight some specific findings, offer comments, and suggest the need for greater future emphasis on affective and motivational variables. My response concludes with consideration of the value of prioritizing mathematical creativity and giftedness (or high ability), noting some troubling policy directions and societal trends that should be taken into serious account and studied.
Keywords
Prospective Teacher Pedagogical Content Knowledge Creative Activity Mathematical Ability Gifted StudentReferences
- Cramond, B., Matthews-Morgan, J., Bandalos, D., & Zuo, L. (2005). A report on the 40-year follow-up of the Torrance tests of creative thinking: Alive and well in the new millennium. Gifted Child Quarterly, 49(4), 283–291.CrossRefGoogle Scholar
- DeBellis, V. A., & Goldin, G. A. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63, 131–147.CrossRefGoogle Scholar
- DeBellis, V. A., & Rosenstein, J. G. (2004). Discrete mathematics in primary and secondary schools in the United States. ZDM, 36(2), 46–55.CrossRefGoogle Scholar
- Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2015). The nested epistemic actions model for abstraction in context—theory as methodological tool and methodological tool as theory. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 185–217). Dordrecht: Springer, Advances in Mathematics Education series.Google Scholar
- Friedman, H. S., & Martin, L. R. (2011). The longevity project: Surprising discoveries for health and long life from the landmark eight-decade study. New York: Hudson Street Press.Google Scholar
- Gagné, F. (2015). From genes to talent: The DMGT/CMTD perspective. Revista de Educacion, 368, 12–39.Google Scholar
- Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. New York: Basic Books.Google Scholar
- Goldin, G. A. (2009). The affective domain and students’ mathematical inventiveness. In R. Leikin, A. Berman & B. Koichu (Eds.), Creativity in Mathematics and the Education of Gifted Students (pp. 181–194). Rotterdam: Sense Publishers.Google Scholar
- Goldin, G. A. (2014). Perspectives on emotion in mathematical engagement, learning, and problem solving. In R. Pekrun & L. Linnenbrink-Garcia (Eds.), International handbook of emotions in education (pp. 391–414). New York: Routledge.Google Scholar
- Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. Journal of Mathematical Behavior, 37, 48–62.CrossRefGoogle Scholar
- Hadamard, J. (1945). The psychology of invention in the mathematical field. Princeton: Princeton University Press.Google Scholar
- Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32, 195–222.CrossRefGoogle Scholar
- Hershkowitz, R., Tabach, M., & Dreyfus, T. (2017). Creative reasoning and shifts of knowledge in the mathematics classroom. ZDM Mathematics Education. doi: 10.1007/s11858-016-0816-6.Google Scholar
- Hoth, J., Kaiser, G., Busse, A., Döhrmann, M., König, J., & Blömeke, S. (2017). Professional competences of teachers for fostering creativity and supporting high-achieving students. ZDM Mathematics Education. doi: 10.1007/s11858-016-0817-5.Google Scholar
- Johnsen, S., & Sheffield, L. J. (Eds.). (2012). Using the common core state standards for mathematics with gifted and advanced learners. Washington, DC: National Association for Gifted Children (quoted in Sheffield (2017)).Google Scholar
- Kaufman, J. C., & Beghetto, R. A. (2009). Beyond big and little: The four C model of creativity. Review of General Psychology, 13, 1–12.CrossRefGoogle Scholar
- Leikin, R. (2014). Giftedness and high ability in mathematics. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 247–251). Dordrecht: Springer.Google Scholar
- Leikin, R., Koichu, B., Berman, A., & Dinur, S. (2017). How are questions that students ask in high level mathematics classes linked to general giftedness? ZDM Mathematics Education. doi: 10.1007/s11858-016-0815-7.CrossRefGoogle Scholar
- Leikin, R., & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In J. H. Woo, H. C. Lew, K. S. Park & D. Y. Seo (Eds.), Proceedings of the 31st International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 161–168). Seoul: The Korea Society of Educational Studies in Mathematics.Google Scholar
- Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM, 45, 159–166.CrossRefGoogle Scholar
- Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67, 255–276.CrossRefGoogle Scholar
- Lubinski, D., Benbow, C. P., & Kell, H. J. (2014). Life paths and accomplishments of mathematically precocious males and females four decades later. Psychological Science, 25(12), 2217–2232.CrossRefGoogle Scholar
- Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236–260.Google Scholar
- Mhlolo, M. K. (2017). Regular classroom teachers’ recognition and support of the creative potential of mildly gifted mathematics learners. ZDM Mathematics Education. doi: 10.1007/s11858-016-0824-6.Google Scholar
- Middleton, J. A., & Jansen, A. (2011). Motivation matters and interest counts: Fostering engagement in mathematics. Reston: National Council of Teachers of Mathematics.Google Scholar
- Nolte, M., & Pamperien, K. (2017). Challenging problems in a regular classroom setting and in a special foster programme. ZDM Mathematics Education. doi: 10.1007/s11858-016-0825-5.Google Scholar
- Polya, G. (1954). Mathematics and plausible reasoning, Vols. I, Vol. II. Princeton: Princeton University Press.Google Scholar
- Polya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving, Vol. I. New York: Wiley.Google Scholar
- Polya, G. (1965). Mathematical discovery: On understanding, learning, and teaching problem solving, Vol. II. New York: Wiley.Google Scholar
- Rasmussen, C., & Stephan, M. (2008). A methodology for documenting collective activity. In A. E. Kelly, R. A. Lesh & J. Y. Baek (Eds.), Handbook of design research methods in education (pp. 195–215). London: Taylor & Francis.Google Scholar
- Sheffield, L. J. (2017). Dangerous myths about “gifted” mathematics students. ZDM Mathematics Education. doi: 10.1007/s11858-016-0814-8.Google Scholar
- Singer, F. M., Voica, C., & Pelczer, I. (2017). Cognitive styles in posing geometry problems: implications for assessment of mathematical creativity. ZDM Mathematics Education. doi: 10.1007/s11858-016-0820-x.Google Scholar
- Sriraman, B., & Dickman, B. (2017). Mathematical pathologies as pathways into creativity. ZDM Mathematics Education. doi: 10.1007/s11858-016-0822-8.Google Scholar
- Sternberg, R. J., & Lubart, T. I. (1996). Investing in creativity. American Psychologist, 51, 677–688.CrossRefGoogle Scholar
- Tabach, M., & Friedlander, A. (2017). Algebraic procedures and creative thinking. ZDM Mathematics Education. doi: 10.1007/s11858-016-0803-y.Google Scholar
- Torrance, E. P. (1974). Torrance tests of creative thinking. Lexington: Ginn & Co.Google Scholar
- Zazkis, R. (2017). Lesson Play tasks as a creative venture for teachers and teacher educators. ZDM Mathematics Education. doi: 10.1007/s11858-016-0808-6.Google Scholar