Abstract
In this chapter, we highlight the role of convergence in developing creativity and mathematical capacity. We renew our understanding of creativity from the relations of three creativity mechanisms: Convergence in divergence for emergence, and three principles of experience: Continuity, interaction and complementarity. Convergence in the context of creativity development is an incidence of learning for capacity building and knowledge construction. Examples of convergent processes in learning are: setting a plan, having a structure, and possessing coordinated capacity to complete a task. To elaborate, we refer to theories of development and creativity on how people develop their capacity in convergence (e.g., collaboration), through mathematical learning (e.g., with coherence, congruence), and for creativity (e.g., imagination). We make reference to convergent creativity of an eminent mathematician Srinivasa Ramanujan (1887–1920) for a reflection on developing creativity and building capacity for good life.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amabile, T. (1983). Social psychology of creativity: A componential conceptualization. Journal of Personality and Social Psychology, 45, 997–1013.
Andrew, G. (n.d.-a). An introduction to the loss notebook. http://www.personal.psu.edu/gea1/pdf/78.pdf. Downloaded on 2 Sep 2015.
Andrew, G. (n.d. b). The meaning of Ramanujan, now and the future. http://www.personal.psu.edu/gea1/pdf/274.pdf. Downloaded on 2 Sep 2015.
Bakhtin, M. (1981). The dialogical imagination. Austin: University of Taxes.
Baltes, P. (1987). Theoretical propositions of life-span developmental psychology: On the dynamics between growth and decline. Developmental Psychology, 23(5), 611–626.
Bandura, A. (2001). Social cognitive theory: An agentic perspective. Annual Review of Psychology, 52, 1–26.
Berndt, B. C. (n.d.). An overview of Ramanujan’s notebooks. http://www.math.uiuc.edu/~berndt/articles/aachen.pdf. Downloaded on 2 Sep 2015.
Bohr, N. (1950). On the notions of causality and complementarity. Science, 111(2873), 51–54.
Brinkmann, A., & Sriraman, B. (2009). Aesthetics and creativity: An exploration of the relationships between the constructs. In B. Sriraman & S. Goodchild (Eds.), Relatively and philosophically earnest: Festschrift in honor of Paul Ernest’s 65th birthday (pp. 57–80). Charlotte: Information Age Publishing.
Buber, M. (1937). I and thou (translated by Ronald Gregor Smith). Edinburg: Clark.
Christoff, K., Gordon, A., & Smith, R. (2008). The role of spontaneous thought in human cognition. In O. Vartanian & D. R. Mandel (Eds.), Neuroscience in decision making (pp. 259–284). New York: Psychology Press.
Craft, A. (1999). Creative development in the early years: Some implications of policy for practice. The Curriculum Journal, 10(1), 135–190.
Cropley, A. (2006). In praise of convergent thinking. Creativity Research Journal, 18(3), 391–404.
Csikszentmihalyi, M. (1988). Society, culture, and person: A system view of creativity. In R. J. Sternberg (Ed.), The nature of creativity (pp. 325–339). New York: Cambridge University Press.
Dewey, J (1937/1997). Experience and education. New York: Touchstone.
Frankl, V. (1984). Man’s search for meaning: An introduction to logotherapy. New York: Washington Square Press.
Fredrickson, B. (2001). The role of positive emotion in positive psychology: The broaden-and-build theory of positive emotion. American Psychologist, 56, 218–226.
Glaveanu, V. P. (2011). Creativity as cultural participation. Journal for the Theory of Social Behavior, 41(1), 48–67.
Guilford, J. P. (1950). Creativity. American Psychologist, 5, 444–454.
Guilford, J. P. (1957). Creative abilities in the arts. Psychological Review, 64(2), 110–118.
Hardy, G. H. (1937). The Indian mathematician Ramanujan. The American Mathematical Monthly, 44(3), 137–155.
Hennessey, B. A., & Amabile, T. M. (2010). Creativity. Annual Review of Psychology, 61, 569–598.
Hsu, P. L. (2012). Understanding creative culture divergence: A Bakhtinian reflection form a culture-crossing scholar. Cultural Studies of Science Education, 7, 103–110.
Jarczak, R. L. (2011). An information processing perspective on divergence and convergence in collaborative learning. Computer-Supported Collaborative Learning, 6, 207–221.
Kastenhofer, K. (2007). Converging epistemic cultures? A discussion drawing from empirical findings. Innovation: The European Journal of Social Science Research, 20(4), 359–373.
Kaufman, J., & Beghetto, R. (2009). Beyond big and little: The four C model of creativity. Review of General Psychology, 13(1), 1–2.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. (J. Teller, trans., J. Kilpatrick & I. Wirszup, Eds.). Chicago: University of Chicago Press.
Lubart, T. L. (2000–2001). Models of the creative process: Past, present and future. Creativity Research Journal, 13(3–4), 295–308.
May. (1975). The courage to create. New York: W.W. Norton & Co.
Mok, L. W. (2014). The interplay between spontaneous and controlled processing in creative cognition. Frontiers in Human Neuroscience, 8(663), 1–5. doi:10.3389/fnhum.2014.00663.
Nielsen, B. D., Pickett, C. L., & Simonton, D. K. (2008). Conceptual versus empirical creativity: Which works best on convergent and divergent thinking tasks? Psychology of Aesthetics, Creativity, and the Arts, 2(3), 131–138.
Nishitari, K. (1991). Nishida Kitaro. California: University of California Press.
Piaget, J. (1928). Judgement and reasoning in the child. London: Routledge & Kegan Paul.
Polanyi, M. (1968). Logic and psychology. American Psychologist, 23(1), 27–43.
Ponomerav, I. A. A. (2008a). Prospects of development of the psychology of creativity (I). Journal of Russian and East European Psychology, 46(3), 17–93.
Ponomerav, I. A. A. (2008b). Prospects of development of the psychology of creativity (II). Journal of Russian and East European Psychology, 46(4), 3–93.
Rhodes, M. (1961). An analysis of creativity. Phi Delta Kappan, 42(7), 305–310.
Rich, P. J., Leatham, K. R., & Wright, G. A. (2013). Convergent cognition. Instructional Sciences, 41, 431–453.
Rizzolatti, G., & Craighero, L. (2004). Mirror neuron system. Annual Review of Neuroscience, 27, 169–192.
Rogers, C. (1961). On becoming a person: A therapist view of psychotherapy. London: Constable.
Runco, M. (2004). Creativity. Annual Review of Psychology, 55, 657–687.
Sawyer, K. R. (1999). The emergence of creativity. Philosophical Psychology, 12(4), 447–469.
Sriraman, B. (2002). How do mathematically gifted students abstract and generalize mathematical concepts. NAGC 2002 Research Briefs (Distinguished Brief of the Year), 16, 83–87.
Sriraman, B. (2003). Can mathematical discovery fill the existential void? The use of conjecture, proof and refutation in a high school classroom (feature article). Mathematics in School, 32(2), 2–6.
Sriraman, B. (2004a). Discovering a mathematical principle: The case of Matt. Mathematics in School, 33(2), 25–31.
Sriraman, B. (2004b). Discovering Steiner triple systems through problem solving. The Mathematics Teacher, 97(5), 320–326.
Sriraman, B. (2004c). Reflective abstraction, uniframes and the formulation of generalizations. The Journal of Mathematical Behavior, 23(2), 205–222.
Sriraman, B. (2005). Are giftedness & creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17, 20–36.
Sriraman, B., & Lee, K. H. (2016). The Hobbesian trap in contemporary India and Korea: Implications for education in the 21st century. In D. Ambrose & R. Sternberg (Eds.), Giftedness and ralent in the 21st century: Adapting to the turbulence of globalization. Rotterdam: Sense Publishers. in press.
Sternberg, R. J. (1985). Implicit theory of intelligence, creativity, and wisdom. Journal of Personality and Social Psychology, 49(3), 607–627. doi:10.1037/0022-3514.49.3.607.
Sternberg, R., & Lubart, T. (1999). The concept of creativity: Prospect and paradigm. In R. Sternberg (Ed.), A handbook of creativity (pp. 3–15). Cambridge: Cambridge University Press.
Sundararajan, L., & Raina, M. K. (2013). Revolutionary creativity, east and west: A critique from indigenous psychology. Journal of Theoretical and Philosophical Psychology, 35(1), 3–19.
Tan, A. G. (2012). Constructive creativity for growth. In D. Ambrose & R. J. Sternberg (Eds.), How dogmatic beliefs harm creativity and higher level thinking (pp. 192–204). New York: Routledge.
Tan, A. G. (2014). Cross-disciplinary creativity. In E. Shiu (Ed.), An interdisciplinary and multidisciplinary research handbook (pp. 68–85). London: Routledge.
Tan, A. G. (2015a). Teaching mathematics creatively. In R. Wegriff, J. Kaufman, & L. Li (Eds.), The Routledge international handbook of research and teaching thinking (pp. 411–423). London: Routledge.
Tan, A. G. (2015b). Convergent creativity: From Arthur Cropley (1935–) onwards. Creativity Research Journal, 27(3), 271–280.
Torrance, E. P. (1966). The Torrance tests of creative thinking-norms-technical manual research education – verbal tests forms A and B, figural test, forms A and B. Princeton: Personnel Test.
Vygotsky, L. (1978). Mind in the society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Vygotsky, L. (2004). Imagination and creativity in childhood. Journal of Russian and East European Psychology, 42(1), 7–97.
Ward, T., Smith, S. M., & Finke, R. A. (1999). Creative cognition. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 189–212). Cambridge: Cambridge University Press.
Woodhouse, H. (2012). Mathematics as liberal education: Whitehead and the rhythm of life. Interchange, 43, 1–23.
Zittoun, T., Baucal, A., Cornish, F., & Gillespie, A. (2007). Collaborative research, knowledge and emergence. Integrative Psychological and Behavioral Science, 41, 208–217.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Tan, AG., Sriraman, B. (2017). Convergence in Creativity Development for Mathematical Capacity. 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_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-38840-3_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-38838-0
Online ISBN: 978-3-319-38840-3
eBook Packages: EducationEducation (R0)