Abstract
Conceptions of mathematical creativity and their implicit and explicit value in society are discussed. In this chapter, the construct of mathematical creativity is discussed in relation to its value to greater society through the lens of national standards documents, as well as mathematics educators and policymakers. In specific, the chasm between how society views mathematical creativity (i.e., as quite important), the manner in which it is emphasized in mathematics standards documents (again, as quite important), and lack of resources invested in it from educational administrators, enjoys a rather large disparity. In practicality, policymakers and academicians assert the relative importance of mathematical creativity, but scant resources in the form of time and money are invested when it comes to engendering it in the mathematics classroom. In this chapter, this chasm is explored. In addition, the organizational framework for the book is outlined and readers will gain a deepened conception of mathematical creativity through the lens of development. Creativity in mathematics is not as homogeneous as perhaps thought when one analyzes the processes, as well as accompanying products, involved in ages 5–12, 13–18, and 19–23. This is because mathematics becomes increasingly sophisticated as learners age and the domains of mathematics are subtly altered from predominately number sense and operations to more complex domains such as algebra, geometry, and calculus, in addition to requiring myriad types of reasoning and processes, such as mathematical modeling.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aiken, L. R., Jr. (1973). Ability and creativity in mathematics. Review of Educational Research, 43, 405–432. https://doi.org/10.2307/1170074
Akgul, S., & Kahveci, N. G. (2016). A study on the development of a mathematics creativity scale. Eurasian Journal of Educational Research, 62, 57–76. https://doi.org/10.14689/ejer.2016.62.5
Albert, R. S., & Runco, M. A. (1999). A history of research on creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 16–31). Cambridge University Press.
Amabile, T. M. (1983). Social psychology of creativity: A componential conceptualization. Journal of Personality and Social Psychology, 45, 997–1013.
Amabile, T., Barsade, S., Mueller, J., & Staw, B. (2005). Affect and creativity at work. Administrative Science Quarterly., 50, 367–403. https://doi.org/10.2189/asqu.2005.50.3.367
Balka, D. S. (1974). Creative ability in mathematics. Arithmetic Teacher, 21, 633–363.
Browder, F. E. (1983). Proceedings of symposia in pure mathematics of the American Mathematical Society (volume 39). American Mathematical Society. Retrieved from: http://www.ams.org/books/pspum/039.1/pspum039.1-endmatter.pdf
Brownell, W. A. (1947). The place of meaning in the teaching of arithmetic. The Elementary School Journal, 47, 256–265.
Buckeye, D. A. (1970). The mathematics laboratory: Its effects on achievement, attitude, and creativity. Unpublished manuscript. Eastern Michigan University.
Carlton, V. L. (1959). An analysis of the educational concepts of fourteen outstanding mathematicians, 1790–1940, in the areas of mental growth and development, creative thinking, and symbolism and meaning. Dissertation Abstracts, 20(06), 2131. (UMI No. AAT 5904782).
Chamberlin, S. A., & Moon, S. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Journal of Secondary Gifted Education, 17, 37–47.
Chamberlin, S. A., & Mann, E. L. (2021). The relationship of affect and creativity in mathematics. Prufrock Academic Press.
Chassell, L. M. (1916). Tests for originality. Journal of Educational Psychology, 7, 317–328. https://doi.org/10.1037/h0070310
Chen, R.-J. (2017). Prospective elementary teachers’ aesthetic experience and relationships to mathematics. Journal of Mathematics Teacher Education, 20, 207–230. https://doi.org/10.1007/s10857-015-9329-4
Ellis, J. J., & Reingold, E. M. (2014). The Einstellung effect in anagram problem solving: Evidence from eye movements. Frontiers in Psychology, 5, Article 679. https://doi.org/10.3389/fpsyg.2014.00679
Evans, E. W. (1965). Measuring the ability of students to respond in creative mathematical situations at the late elementary and early junior high school level. (Doctoral dissertation), University of Michigan. Dissertation Abstracts, 25, 7108–7109.
Foster, J. (1970). An exploratory attempt to assess creative ability in mathematics. Primary Mathematics, 8, 2–7.
Goldin, G. A. (2017). Mathematical creativity and giftedness: Perspectives in response. ZDM: The International Journal on Mathematics Education, 49, 147–157. https://doi.org/10.1007/s11858-017-0837-9
Gravemeijer, K., Stephan, M., Julie, C., Lin, F.-L., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15, 105–123. https://doi.org/10.1007/s10763-017-9814-6
Guilford, J. P. (1950). Creativity. American Psychologist, 5, 444–454.
Haavold, P. O. (2018). An empirical investigation into a theoretical model for mathematical creativity. Journal of Creative Behavior, 52, 226–239. https://doi.org/10.1002/jocb.145
Hadamard, J. (1945). The psychology of invention in the mathematical field. Princeton University Press.
Hollands, R. (1972). Math School. 1, 22–23.
Imai, T. (2000). The influence of overcoming fixation in mathematics towards divergent thinking in open-ended mathematics problems on Japanese junior high school students. International Journal of Mathematical Education in Science and Technology, 31, 187–193. https://doi.org/10.1080/002073900287246
Jung, R. E., Gasparovic, C., Chavez, R. S., Flores, R. A., Smith, S. M., Caprihan, A., & Yeo, R. A. (2009). Biochemical support for the “Threshold” theory of creativity: A magnetic resonance spectroscopy study. The Journal of Neuroscience, 29, 5319–5325. https://doi.org/10.1523/JNEUROSCI.0588-09.2009
Kainulainen, M., McMullen, J., & Lehtinen, E. (2017). Early developmental trajectories toward concepts of rational numbers. Cognition and Instruction, 35, 4–19. https://doi.org/10.1080/07370008.2016.1251287
Kattou, M., Christou, C., & Pitta-Pantazi, D. (2016). Characteristics of the creative person in mathematics. In G. B. Moneta & J. Rogaten (Eds.), Psychology of creativity: Cognitive, emotional, and social processes (pp. 99–123). Nova Science Publishers.
Kaufman, J. C., & Beghetto, R. (2009). Beyond big and little: The four C model of creativity. Review of General Psychology, 13, 1–12. https://doi.org/10.1037/a0013688
Kozlowski, J., Chamberlin, S. A., & Mann, E. L. (2019). Factors that Influence Mathematical Creativity. The Mathematics Enthusiast, 16, Article 26. Retrieved at: https://scholarworks.umt.edu/tme/vol16/iss1/26/
Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. University of Chicago Press.
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For The Learning of Mathematics, 26, 17–19.
Lingefjärd, T., & Hatami, R. (2020). The beauty of abstraction in mathematics. Policy Futures in Education, 18, 467–482. https://doi.org/10.1177/1478210319895104
Lykken, D. (2005). Mental energy. Intelligence, 33, 331–335. https://doi.org/10.1016/j.intell.2005.03.005
Manville, W. E. (1972). A study of the effect of mathematics activity materials upon certain aspects of creative thinking ability of prospective elementary school teachers. (Doctoral dissertation), University of Maine. No 72–29,994
Maslow, A. H. (1943). A theory of human motivation. Psychological Review, 50, 370–396.
Meyer, R. W. (1970). The identification and encouragement of mathematical creativity in first grade students. (Doctoral dissertation), University of Wisconsin. No. 70-3627.
Nadjafikhah, M., Yaftian, N., & Bakhshalizadeh, S. (2012). Mathematical creativity: Some definitions and characteristics. Procedia – Social and Behavioral Sciences, 31, 285–291. https://doi.org/10.1016/j.sbspro.2011.12.056
Olson, J., Colasanti, M., & Trujillo, K. (2006). Prompting growth for prospective teachers using cognitive dissonance. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (p. 4–281–288), Czech Republic, 16–21 July 2006. International Group for the Psychology of Mathematics Education.
Plucker, J., Beghetto, R. A., & Dow, G. (2004). Why isn’t creativity more important to educational psychologists? Potential pitfalls and future directions in creativity research. Educational Psychologist, 39, 83–96. https://doi.org/10.1207/s15326985ep3902_1
Poincaré, H. (1908). Science et méthode. E. Flammarion.
Poincaré, H. (1956). Mathematical creation. In J. R. Newman (Ed.), The world of mathematics (Vol. 4, pp. 2041–2050). Simon and Schuster.
Prouse, H. L. (1967). Creativity in school mathematics. Mathematics Teacher, 60, 876–879.
Rhodes, M. (1961). An analysis of creativity. Phi Delta Kappan, 42, 305–310.
Scherer, R., Siddiq, F., & Sánchez Viveros, B. (2019). The cognitive benefits of learning computer programming: A meta-analysis of transfer effects. Journal of Educational Psychology, 111, 764–792. https://doi.org/10.1037/edu0000314
Seeley, C. (2004). Twenty-first century mathematics. Principal Leadership, 5, 22–26.
Silver, E. A. (1994a). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM: The International Journal on Mathematics Education, 29, 75–80. https://doi.org/10.1007/s11858-997-0003-x
Silver, E. A. (1994b). On mathematical problem posing. For the Learning of Mathematics, 14, 19–28.
Silver, E. A. (1997). Fostering creativity through instruction rich in problem solving and problem posing. Zentrallblat für Didaktik der Mathematik, 29, 75–80. https://doi.org/10.1007/s11858-997-0003-x
Simonton, D. K. (1988). Scientific genius: A psychology of science. Cambridge University Press.
Simonton, D. K. (1999). Creativity as blind variation and selective retention: Is the creative process Darwinian? Psychological Inquiry, 10, 309–328.
Singer, F. M. (2018). Mathematical creativity and mathematical giftedness: Enhancing creative capacities in mathematically promising students. Springer International Publishing.
Spraker, H. S. (1960). A study of the comparative emergence of creative behavior during the process of group and individual study. (Doctoral dissertation), University of Virginia. No. 60-4637.
Sriraman, B. (2004). The characteristics of mathematical creativity. The International Journal on Mathematics Education [ZDM], 41, 13–27.
Sternberg, R. J., & Davidson, J. E. (1995). The nature of insight. MIT Press.
Torrance, E. P. (1966). Guiding creative talent. Prentice-Hall, Incorporated.
Tubb, A. L., Cropley, D. H., Marrone, R. L., Patston, T., & Kaufman, J. C. (2020). The development of mathematics across high school: Increasing, decreasing, or both. Thinking Skills and Creativity, 35. https://doi.org/10.1016/j.tsc.2020.100634
Vorhölter, K., Kaiser, G., & Ferri, R. B. (2014). Modelling in mathematics classroom instruction: An innovative approach for transforming mathematics education. In Y. Li, E. Silver, & S. Li (Eds.), Transforming mathematics instruction (pp. 21–36). Springer.
Wagner, T. (2014). The global achievement gap. Updated edition. Perseus Books Group.
Wallas, G. (1926). The art of thought. Jonathan Cape.
Welter, M. M., Jaarsveld, S., van Leeuwen, C., & Lachmann, T. (2016). Intelligence and creativity: Over the threshold together? Creativity Research Journal, 28, 212–218. https://doi.org/10.1080/10400419.2016.1162564
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Chamberlin, S.A., Payne, A. (2022). Mathematical Creativity and Society. In: Chamberlin, S.A., Liljedahl, P., Savić, M. (eds) Mathematical Creativity . Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-14474-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-031-14474-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-14473-8
Online ISBN: 978-3-031-14474-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)