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Cognitive Variety in Rich-Challenging Tasks

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Mathematical Creativity and Mathematical Giftedness

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

Cognitive flexibility—a parameter that characterizes creativity—results from the interaction of various factors, among which is cognitive variety. Based on an empirical study, we analyze students’ and experts’ cognitive variety in a problem-posing context. Groups of students of different ages and studies (from primary to university) were asked to start from an image rich in mathematical properties, and generate as many problem statements related to the given input as possible. The students’ products were compared in-between, and to the problems posed by a group of experts (teachers of mathematics and researchers) who received the same images as input. The study revolves around the question: “In what ways does cognitive variety depend on age or training in mathematically promising individuals?” We found that cognitive variety seems randomly distributed among the groups we tested, contradicting the intuitive idea that this is age (and training) related, except at the expert level. In addition, when talking about mathematical creativity, more sophisticated parameters, such as validity, complexity and topic variety, as well as the potential of respondents’ products to break a well-internalized frame have to be taken into account. All those are to be balanced against the person’s level of expertise in the specified domain.

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References

  • Abramovich, S. (2003). Cognitive heterogeneity in computer-mediated mathematical action as a vehicle for concept development. Journal of Computers in Mathematics and Science Teaching, 22(1), 19–41.

    Google Scholar 

  • Abramovich, S., & Cho, E. K. (2015). Using digital technology for mathematical problem posing. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 71–102). New York: Springer.

    Chapter  Google Scholar 

  • Amabile, T. M. (1996). Creativity in context: Update to the social psychology of creativity. Boulder, CO: West-view press.

    Google Scholar 

  • Baer, J. (2010). Is creativity domain-specific? In J. C. Kaufman & R. J. Sternberg (Eds.), Cambridge handbook of creativity (pp. 321–341). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Baer, J. (2012). Domain specificity and the limits of creativity theory. The Journal of Creative Behavior, 46(1), 16–29.

    Article  Google Scholar 

  • Bateson, M. (1999). Ordinary creativity. In A. Montuori & R. Purser (Eds.), Social creativity (Vol. I, pp. 153–171). Cresskill: Hampton Press.

    Google Scholar 

  • Csikszentmihalyi, M. (1996). Creativity, flow, and the psychology of discovery and invention. New York: Harper Collins.

    Google Scholar 

  • Eisenhardt, K. M., Furr, N. R., & Bingham, C. B. (2010). Microfoundations of performance: Balancing efficiency and flexibility in dynamic environments. Organization Science, 21(6), 1263–1273.

    Article  Google Scholar 

  • Furr, N. R. (2009). Cognitive flexibility: The adaptive reality of concrete organization change. Ph.D. dissertation, Stanford University. http://gradworks.umi.com/33/82/3382938.html.

  • Gardner, H. (1993). Creating minds: An anatomy of creativity as seen through the lives of Freud, Einstein, Picasso, Stravinsky, Eliot, Graham, and Ghandi. New York: Basic Books.

    Google Scholar 

  • Gardner, H. (2006). Five minds for the future. Boston, MA: Harvard Business School Press.

    Google Scholar 

  • Gardner, H., Csikszentmihalyi, M., & Damon, M. (2001). Good work: When excellence and ethics meet. New York: Basic Books.

    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.

    Article  Google Scholar 

  • Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2011). Indicators of creativity in mathematical problem posing: How indicative are they. In M. Avotina, D. Bonka, H. Meissner, L. Sheffield, & E. Velikova (Eds.), Proceedings of the 6th International Conference Creativity in Mathematics Education and the Education of Gifted Students (pp. 120–125). Latvia: Latvia University.

    Google Scholar 

  • Krems, J. F. (1995). Cognitive flexibility and complex problem solving. In P. A. Frensch & J. Funke (Eds.), Complex problem solving: The European perspective (pp. 201–218). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–145). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Leikin, R., Koichu, B., & Berman, A. (2009). Mathematical giftedness as a quality of problem-solving acts. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 115–128). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM Mathematics Education, 45(2), 159–166.

    Article  Google Scholar 

  • Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26(1), 20–23.

    Google Scholar 

  • Martin, M. O., Mullis, I. V., & Foy, P. (in collaboration with Olson, J. F., Preuschoff, C., Erberber, E., Arora, A., & Galia, J.). (2008). TIMSS 2007 international mathematics report: Findings from IEA’s trends in international mathematics and science study at the fourth and eighth grades. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

    Google Scholar 

  • Pelczer, I., Singer, F. M., & Voica, C. (2013). Cognitive framing: A case in problem posing. Procedia-Social and Behavioral Sciences, 78, 195–199.

    Article  Google Scholar 

  • Piirto, J. (1999). Talented children and adults: Their development and education (2nd ed.). Upper Saddle River, NJ: Merrill.

    Google Scholar 

  • Roskos-Ewoldsen, B., Black, S. A., & McCown, S. M. (2008). Age-related changes in creative thinking. The Journal of Creative Behavior, 42, 33–59.

    Article  Google Scholar 

  • Sak, U., & Maker, C. J. (2006). Developmental variation in children’s creative mathematical thinking as a function of schooling, age, and knowledge. Creativity Research Journal, 18(3), 279–291.

    Article  Google Scholar 

  • Sheffield, L. J. (2009). Developing mathematical creativity—Questions may be the answer. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 87–100). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Silver, E. A., Mamona-Downs, J., Leung, S., & Kenny, P. A. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27(3), 293–309.

    Article  Google Scholar 

  • Singer, F. M. (2007). Balancing globalisation and local identity in the reform of education in Romania. In B. Atweh, M. Borba, A. Barton, D. Clark, N. Gough, C. Keitel, C. Vistro-Yu, & R. Vithal (Eds.), Internationalisation and globalisation in mathematics and science education (pp. 365–382). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Singer, F. M., Pelczer, I., & Voica, C. (2015). Problem posing: Students between driven creativity and mathematical failure. In CERME 9—Ninth Congress of the European Society for Research in Mathematics Education (pp. 1073–1079).

    Google Scholar 

  • Singer, F. M., & Voica, C. (2015). Is problem posing a tool for identifying and developing mathematical creativity? In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 141–174). New York: Springer.

    Chapter  Google Scholar 

  • Singer, F. M., & Voica, C. (2017). When mathematics meets real objects: How does creativity interact with expertise in problem solving and posing. In Roza Leikin and Bharath Sriraman (Eds.), Creativity and giftedness. Interdisciplinary perspectives from mathematics and beyond (pp. 75–103). Springer International Publishing Switzerland.

    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, 49(1), 37–52. https://doi.org/10.1007/s11858-016-0820-x.

  • Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34.

    Google Scholar 

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

    Article  Google Scholar 

  • Sternberg, R. J., & Lubart, T. I. (1996). Investing in creativity. American Psychologist, 51, 677–688.

    Article  Google Scholar 

  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Tall, D. (1993). Success and failure in mathematics: The flexible meaning of symbols as process and concept. Mathematics Teaching, 14, 6–10.

    Google Scholar 

  • Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville, IL: Scholastic Testing Service.

    Google Scholar 

  • Voica, C., & Singer, F. M. (2012). Creative contexts as ways to strengthen mathematics learning. Procedia-Social and Behavioral Sciences, 33, 538–542.

    Article  Google Scholar 

  • Voica, C., & Singer, F. M. (2013). Problem modification as a tool for detecting cognitive flexibility in school children. ZDM Mathematics Education, 45(2), 267–279.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bucharest, 14 Academiei Street, 010014, Bucharest, Romania

    Cristian Voica

  2. Faculty of Letters and Science, University of Ploiesti, 39 Bucharest Boulevard, 100680, Ploiesti, Romania

    Florence Mihaela Singer

Authors
  1. Cristian Voica
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  2. Florence Mihaela Singer
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Correspondence to Cristian Voica .

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Editors and Affiliations

  1. Faculty of Letters and Science, Oil & Gas University of Ploiești, Ploiești, Romania

    Florence Mihaela Singer

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Voica, C., Singer, F.M. (2018). Cognitive Variety in Rich-Challenging Tasks. In: Singer, F. (eds) Mathematical Creativity and Mathematical Giftedness. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73156-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-73156-8_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73155-1

  • Online ISBN: 978-3-319-73156-8

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