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Creativity, Imagination, and Early Mathematics Education

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Creativity and Giftedness

Abstract

In this chapter, we draw heavily on a new typological model of creativity and show its consequences for early maths education. According to this model, creativity is made up of three interrelated components: creative abilities (mainly creative imagination and divergent thinking), openness to experiences, and independence. This model is our starting point for the description of the importance and organization of the Mathematical Creative Problem Solving Model. We describe the assumptions, aims, and elements of this model, as well as demonstrate the practical and methodological aspects of supporting the development of mathematics. We also focus on the role played by visual and creative imagination and on new ways of enhancing mathematical creativity using heuristic rhymes.

The preparation of this chapter was supported by grants from the National Science Centre, Poland (UMO-2011/03/N/HS6/05153) and the Polish Ministry of Science and Higher Education (Iuventus Plus Program, 0193/IP3/2015/73).

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References

  • Amabile, T. M. (1983). The social psychology of creativity: A componential conceptualization. Journal of Personality and Social Psychology, 45, 357–377.

    Article  Google Scholar 

  • Baer, J. (1998). The case for domain specificity in creativity. Creativity Research Journal, 11, 173–177.

    Article  Google Scholar 

  • Batey, M., & Furnham, A. (2006). Creativity, intelligence, and personality: A critical review of the scattered literature. Genetic, Social, and General Psychology Monographs, 132, 355–429.

    Article  Google Scholar 

  • Beghetto, R. A. (2014). Is the sky falling or expanding? A promising turning point in the psychology of creativity. Creativity: Theories – Research – Applications, 1, 206–212.

    Article  Google Scholar 

  • Bellos, A. (2010). Alex’s adventures in Numberland: Dispatches from wonderful world of mathematics. London: Bloomsbury Publishing Plc.

    Google Scholar 

  • Boden, M. A. (2004). The creative mind: Myths and mechanisms. London: Routledge.

    Google Scholar 

  • Chen, C., Himsel, A., Kasof, J., Greenberger, E., & Dmitrieva, J. (2006). Boundless creativity: Evidence for the domain-generality of individual differences in creativity. Journal of Creative Behavior, 40, 179–199.

    Article  Google Scholar 

  • Cropley, A. J. (1999). Definitions of creativity. In M. A. Runco & S. R. Pritzker (Eds.), Encyclopedia of creativity (pp. 511–522). San Diego: Academic.

    Google Scholar 

  • Cropley, A. J. (2001). Creativity in education and learning. A guide for teachers and educators. London: Kogan, Page.

    Google Scholar 

  • Dollinger, S. J., & Clancy, S. M. (1993). Identity, self, and personality: II. Glimpses through the autophotographic eye. Journal of Personality and Social Psychology, 64, 1064–1071.

    Article  Google Scholar 

  • Dziedziewicz, D., & Karwowski, M. (2015). Development of children’s creative visual imagination: A theoretical model, measure and stimulation program. Education, 3–13, 1–3.

    Google Scholar 

  • Dziedziewicz, D., OlÄ™dzka, D., & Karwowski, M. (2013). Developing 4- to 6-year-old children’s figural creativity using a doodle-book program. Thinking Skills and Creativity, 9, 85–95.

    Article  Google Scholar 

  • Eysenck, H. J. (1994). Personality: Biological foundations. In P. A. Vernon (Ed.), The neuropsychology of individual differences (pp. 151–207). San Diego: Academic.

    Chapter  Google Scholar 

  • Feist, G. J. (1998). A meta-analysis of personality in scientific and artistic creativity. Personality and Social Psychology Review, 2, 290–309.

    Article  Google Scholar 

  • Finke, R. A., Pinker, S., & Farah, M. J. (1989). Reinterpreting visual patterns in mental imagery. Cognitive Science, 13, 51–78.

    Article  Google Scholar 

  • Fromm, E. (1959). The creative attitude. In H. H. Anderson (Ed.), Creativity and its cultivation (pp. 44–54). New York: Harper & Brothers.

    Google Scholar 

  • Galton, F. (1880). Statistics of mental imagery. Mind, 5, 301–318.

    Article  Google Scholar 

  • Galton, F. (1883). Inquiries into human faculty and its developmental. London: Macmillan.

    Book  Google Scholar 

  • Gilson, L. L., & Shalley, C. E. (2004). A little creativity goes a long way: An examination of teams’ engagement in creative processes. Journal of Management, 30, 453–470.

    Article  Google Scholar 

  • Glăveanu, V. P. (2010). Principles for a cultural psychology of creativity. Culture & Psychology, 16, 147–163.

    Article  Google Scholar 

  • Gonzales, M. A., Campos, A., Perez, M. J. (1997). Mental imagery and creative thinking. The Journal of Psychology, 131, 357–364.

    Google Scholar 

  • Guilford, J. P. (1950). Creativity. American Psychologist, 5, 444–454.

    Article  Google Scholar 

  • Guilford, J. P. (1967). The nature of human intelligence. New York: McGraw-Hill.

    Google Scholar 

  • Harskamp, E. (2014). The effects of computer technology on primary school students’ mathematics achievement: A meta-anylysis. In S. Chinn (Ed.), The Routledge international handbook of dyscalculia and mathematical learning difficulties (pp. 383–399). London: Routledge.

    Google Scholar 

  • Holt, R. R. (1964). Imagery: The return of the ostracized. American Psychologist, 19, 254–264.

    Article  Google Scholar 

  • Jensen. A. R. (1998). The g Factor: The Science of Mental Ability. Westport, CN: Praeger.

    Google Scholar 

  • Karwowski, M. (2010). Kreatywność – feeria rozumieÅ„, uwikÅ‚aÅ„, powodów. Teoretyczno-empiryczna prolegomena. [Creativity: a feeria of understandings, entanglements, conditions]. In M. Karwowski & A. Gajda (Eds.), Kreatywność (nie tylko) w klasie szkolnej [Creativity not only in the classroom] (pp. 12–45). Warszawa: Wydawnictwo Akademii Pedagogiki Specjalnej.

    Google Scholar 

  • Karwowski, M., & Lebuda, I. (2013). Types and profiles of creativity toward theoretical integration. The 32nd international human science research conference.

    Google Scholar 

  • Kaufman, J. C. (2009). Creativity 101. New York: Springer.

    Google Scholar 

  • Kaufman, J. C., & Baer, J. (2004). Sure, I’m creative – but not in math!: Self-reported creativity in diverse domains. Empirical Studies of the Arts, 22, 143–155.

    Article  Google Scholar 

  • Kaufman, J. C., & Baer, J. (Eds.). (2005). Creativity across domains: Faces of the muse. Mahwah: Lawrence Erlbaum Associates, Inc.

    Google Scholar 

  • Khatena, J. (1975). Vivdness of imagery and creative self-perceptions. Gifted Child Quarterly, 19, 33–37.

    Google Scholar 

  • LeBoutillier, N., & Marks, D. F. (2003). Mental imagery and creativity: A meta-analytic review study. British Journal of Psychology, 94, 29–44.

    Article  Google Scholar 

  • Maslow, A. (1959). Creativity in self-actualizing people. In H. H. Anderson (Ed.), Creativity and its cultivation (pp. 83–95). New York: Harper & Brothers.

    Google Scholar 

  • Montgomery, D., Bull, K. S., & Baloche, L. (1993). Characteristics of the creative person: Perceptions of university teachers in relation to the professional literature. American Behavioral Scientist, 37, 68–78.

    Article  Google Scholar 

  • Nickerson, R. S. (1999). Enhancing creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 392–430). Cambridge: Cambridge University Press.

    Google Scholar 

  • Patel, A. D., & Daniele, J. R. (2003). An empirical comparison of rhythm in language and music. Cognition, 87, B35–B45.

    Article  Google Scholar 

  • Perrine, N. E., & Brodersen, M. R. (2005). Artistic and scientific creative behavior: Openness and mediating role of interests. Creativity Research Journal, 39, 217–236.

    Google Scholar 

  • Plucker, J. A. (1998). Beware of simple conclusions: The case for the content generality of creativity. Creativity Research Journal, 11, 179–182.

    Article  Google Scholar 

  • Plucker, J. A. (2004). Generalization of creativity across domains: Examination of the method effect hypothesis. Journal of Creative Behavior, 38, 1–12

    Google Scholar 

  • Ribot, T. (1906). Essay on the Creative Imagination. Chicago: The Open Court Publishing CO.

    Google Scholar 

  • Rozet, I. M. (1977/1982). Psychologia fantazji. Badania twórczej aktywnoÅ›ci umysÅ‚owej. Warszawa: PaÅ„stwowe Wydawnictwo Naukowe.

    Google Scholar 

  • Rogers, C. R. (1970). Towards a theory of creativity. In P. E. Vernon (Ed.), Creativity (pp. 137–152). Middlesex: Penguin.

    Google Scholar 

  • Runco, M. A. (2009). Creativity definition. In B. Kerr (Ed.), Encyclopedia of giftedness, creativity, and talent (pp. 200–202). Newbury Park: Sage Publications.

    Google Scholar 

  • Sawyer, R. K. (2006). Educating for innovation. Thinking Skills and Creativity, 1, 41–48.

    Article  Google Scholar 

  • Schmeidler, G. (1965). Visual imagery correlated to a measure creativity. Journal of Consulting Psychology, 29, 78–80.

    Article  Google Scholar 

  • Silver, E. A. (1994). On mathematical problem posing. For the learning of mathematics, 14, 19–28.

    Google Scholar 

  • Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14, 19–34.

    Google Scholar 

  • Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics. Journal of Secondary Gifted Education, 17, 20–36.

    Google Scholar 

  • Stavridou, A., & Furnham, A. (1996). The relationship between psychoticism, trait-creativity and the attentional mechanism of cognitive inhibition. Personality and Individual Differences, 21, 143–153.

    Article  Google Scholar 

  • Szwajkowski, W. (2011). Uwaga! Rymowanki. Magazyn ZdolnoÅ›ci, 1, 14–24.

    Google Scholar 

  • Vygotsky, L. S. (1930/2004). Imagination and creativity in childhood. Journal of Russian and East European Psychology, 1, 7–97.

    Google Scholar 

  • Ward, T. B. (1994). Structured imagination: The role of category structure in exemplar generation. Cognitive Psychology, 27, 1–40.

    Article  Google Scholar 

  • Wang, Y., & Shang, Q. (2014). Developing mathematical thinking and innovation capability of students in engineering mechanics teaching. 3rd International Conference on Science and Social Research (ICSSR).

    Google Scholar 

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Correspondence to Maciej Karwowski .

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Karwowski, M., Jankowska, D.M., Szwajkowski, W. (2017). Creativity, Imagination, and Early Mathematics Education. In: Leikin, R., Sriraman, B. (eds) Creativity and Giftedness. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-38840-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-38840-3_2

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