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  • Barnes, M. (2000). Magical moments in mathematics: Insights into the process of coming to know. For the Learning of Mathematics, 20(1), 33–43.
  • Barnett, L. B., & Corazza, L. (1993). Identification of mathematical talent and programmatic efforts to facilitate development of talent. European Journal for High Ability, 4, 48–61.
  • Behr, M., & Khoury, H. (1986). Children’s inferencing behavior. Journal for Research in Mathematics Education, 17, 369–381.
  • Benbow, C. P., Lubinski, D. & Sushy, B. (1996). The impact of SMPY’s educational programs from the perspective of the participant. In C. P. Benbow & D. Lubinski (Eds.), Intellectual talent (pp. 266–300). Baltimore, MD: Johns Hopkins University Press.
  • Birkhoff, G. D. (1956). Mathematics of aesthetics. In J. R. Newman (Ed.), The world of mathematics, Vol. 4 (7th ed., pp. 2185–2197). New York: Simon and Schuster.
  • Birkhoff, G. D. (1969). Mathematics and psychology. Society for Industrial and Applied Mathematics Review, 11, 429–469.
  • Brinkmann, A. (2004). The experience of mathematical beauty. In P. C. Clarkson & M. Hannula (Organizers), Students’ motivation and attitudes toward mathematics and its study: Proceedings of the 10th International Congress of Mathematics Education (Topics Study Group 24 [CD-ROM]). Copenhagen, Denmark.
  • Brower, R. (1999). Dangerous minds: Eminently creative people who spent time in jail. Creativity Research Journal, 12, 3–14.
  • Burton, L. (1999a). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37, 121–143.
  • Burton, L. (1999b). Why is intuition so important to mathematics but missing from mathematics education? For the Learning of Mathematics, 19(3), 27–32.
  • Chambers, J. A. (1964). Relating personality and biographical factors to scientific creativity. Psychological Monographs, 78(7, Whole No. 584).
  • Chang, L. L. (1985). Who are the mathematically gifted elementary school children? Roeper Review, 8, 76–79.
  • Craft, A. (2002). Creativity in the early years: A lifewide foundation. London: Continuum.
  • Craft, A. (2003). The limits to creativity in education: Dilemmas for the educator. British Journal of Educational Studies, 51, 113–127.
  • Cramond, B. (1994). Attention-deficit hyperactivity disorder and creativity—What is the connection? Journal of Creative Behavior, 28, 193–210.
  • Creme, P. (2003). Why can’t we allow students to be more creative? Teaching in Higher Education, 8, 273–277.
  • Csikszentmihalyi, M. (1988). Society, culture, and person: A systems view of creativity. In R. J. Sternberg (Ed.), The nature of creativity: Contemporary psychological perspectives (pp. 325–339). New York: Cambridge University Press.
  • Csikszentmihalyi, M. (2000). Implications of a systems perspective for the study of creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 313–338). New York: Cambridge University Press.
  • Davis, G. A. (1997). Identifying creative students and measuring creativity. In N. Colangelo & G. A. Davis (Eds.), Handbook of gifted education (2nd ed., pp. 269–281). Boston: Allyn & Bacon.
  • Davis, P. J., & Hersh, R. (1981). The mathematical experience. New York: Houghton Mifflin.
  • Davydov, V. V. (1988). The concept of theoretical generalization and problems of educational psychology. Studies in Soviet Thought, 36, 169–202.
  • Davydov, V. V. (1990). Type of generalization in instruction: Logical and psychological problems in the structuring of school curricula. In J. Kilpatrick (Ed.), Soviet studies in mathematics education (Vol. 2). Reston, VA: National Council of Teachers of Mathematics.
  • Diezmann, C., & Watters, J. (2003). The importance of challenging tasks for mathematically gifted students. Gifted and Talented International, 17, 76–84.
  • Dreyfus, T., & Eisenberg, T. (1986). On the aesthetics of mathematical thought. For the Learning of Mathematics, 6(1), 2–10.
  • Einstein, A., & Inheld, L. (1938). The evolution of physics. New York: Simon and Schuster.
  • English, L. D. (in press). Problem posing in the elementary curriculum. In F. Lester & R. Charles (Eds.), Teaching mathematics through problem solving. Reston, VA: National Council of Teachers of Mathematics.
  • Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.). Advanced mathematical thinking. (pp. 42–53). Dodrecht, The Netherlands: Kluwer Academic Publishers.
  • Frensch, P., & Sternberg, R. (1992). Complex problem solving: Principles and mechanisms. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Goldberg, A., & Suppes, P. (1972). A computer assisted instruction program for exercises on finding axioms. Educational Studies in Mathematics, 4, 429–449.
  • Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28(6), 14–17.
  • Grouws, D. A. (Ed.). (1992). Handbook of research on mathematics teaching and learning. New York: McMillan.
  • Gruber, H. E. (1981). Darwin on man. Chicago: University of Chicago Press.
  • Gruber, H. E. (1989). The evolving systems approach to creative work. In D. B. Wallace & H. E. Gruber (Eds.), Creative people at work: Twelve cognitive case studies (pp. 3–24). Oxford, England: Oxford University Press.
  • Gruber, H. E., & Wallace, D. B. (2000). The case study method and evolving systems approach for understanding unique creative people at work. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 93–115). New York: Cambridge University Press.
  • Hadamard, J. W. (1945). Essay on the psychology of invention in the mathematical field. Princeton, NJ: Princeton University Press.
  • Hardy, G. H. (1940). A mathematician’s apology. London: Cambridge University Press.
  • Heid, M. K. (1983). Characteristics and special needs of the gifted student in mathematics. The Mathematics Teacher, 76, 221–226.
  • Hershkowitz, R. (1989). Visualization in geometry—two sides of the coin. Focus on Learning Problems in Mathematics, 11, 61– 76.
  • Hewitt, E. (1948). Rings of real-valued continuous functions. Transactions of the American Mathematical Society, 64, 45–99.
  • Hilbert, D. (1900). Mathematische Probleme: Vortrag, gehalten auf dem internationalen Mathematiker-Congress zu Paris 1900 [Mathematical problems: Lecture held at the International Congress of Mathematicians in Paris 1900]. Gött. Nachr. 253–297.
  • Jackson, L. (2002). Freaks, geeks and Asperger syndrome: A user guide to adolescence. London: Jessica Kingsley.
  • James, I. (2003). Autism in mathematicians. The Mathematical Intelligencer, 25(4), 62–65.
  • Kajander, A. (1990) Measuring mathematical aptitude in exploratory computer environments. Roeper Review, 12, 254–256.
  • Kanevsky, L. S. (1990). Pursuing qualitative differences in the flexible use of a problem solving strategy by young children. Journal for the Education of the Gifted, 13, 115–140.
  • Kerr, B. A. (1997). Developing talents in girls and young women. In N. Colangelo & G. A. Davis (Eds.), Handbook of gifted education (2nd ed., pp. 483–497). Boston: Allyn & Bacon.
  • Kieren, T., & Pirie, S. (1991). Recursion and the mathematical experience. In L. P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 78–102). New York: Springer-Verlag.
  • Kiesswetter, K. (1985). Die förderung von mathematisch besonders begabten und interessierten Schülern-ein bislang vernachlässigtes sonderpädogogisches problem [The advancement of mathematically talented and interested students: A neglected and special pedagogical problem]. Der mathematische und naturwissenschaftliche Unterricht, 38, 300–306.
  • Kiesswetter, K. (1992). Mathematische Begabung. Über die Komplexität der Phänomene und die Unzulänglichkeiten von Punktbewertungen [Mathematical giftedness: On the complexity of the phenomenon and the inadequacies of extant evaluations]. Mathematik-Unterricht, 38, 5–18.
  • 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.
  • Kuhn, T. S. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.
  • Lesh, R., Kaput, J., & Hamilton, E. (Eds.). (in press). Foundations for the future: The need for new mathematical understandings & abilities in the 21st century. Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Lesh, R., & Sriraman, B. (2005a). John Dewey revisited—Pragmatism and the models-modeling perspective on mathematical learning. In A. Beckmann, C. Michelsen, & B. Sriraman (Eds.), Proceedings of the 1st International Symposium on Mathematics and its Connections to the Arts and Sciences (pp. 32–51). University of Schwaebisch Gmuend, Germany: Franzbecker Verlag.
  • Lesh, R., & Sriraman, B. (2005b). Mathematics education as a design science. International Reviews on Mathematical Education (Zentralblatt für Didaktik der Mathematik), 37, 490–505.
  • Lester, F. K., & Kehle, P. E. (2003). From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 501–518). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Marshak, D. (2003). No child left behind: A foolish race into the past. Phi Delta Kappan, 85, 229–231.
  • Massé, L., & Gagné, F. (2002). Gifts and talents as sources of envy in high school settings. Gifted Child Quarterly, 46, 15–29.
  • Minsky, M. (1985). The society of mind. New York: Simon & Schuster.
  • National Council of Teachers of Mathematics (1989). Curriculum and standards for school mathematics. Reston, VA: Author.
  • Nickerson, R. S. (2000). Enhancing creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 392–430). New York: Cambridge University Press.
  • No Child Left Behind Act, 20 U.S.C. §6301 (2001).
  • Plucker, J., & Beghetto, R. A. (2004). Why creativity is domain general, why it looks domain specific, and why the distinction does not matter. In R. J. Sternberg, E. L. Grigorenko, & J. L. Singer (Eds.), Creativity: From potential to realization (pp.153–168). Washington, DC: American Psychological Association.
  • Policastro, E., & Gardner, H. (2000). From case studies to robust generalizations: An approach to the study of creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 213–225). New York: Cambridge University Press.
  • Poincaré, H. (1948). Science and method. New York: Dover.
  • Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.
  • Polya, G. (1954). Mathematics and plausible reasoning: Induction and analogy in mathematics (Vol. II). Princeton, NJ: Princeton University Press.
  • Presmeg, N. C. (1986). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17, 297–311.
  • Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60, 180–184, 261.
  • Renzulli, J. S. (1986). The three-ring conception of giftedness: A developmental model for creative productivity. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 332–357). New York: Cambridge University Press.
  • Ripple, R. E. (1989). Ordinary creativity. Contemporary Educational Psychology, 14, 189–202.
  • Root-Bernstein, R. S. (1989). Discovering. Cambridge, MA: Harvard University Press.
  • Root-Bernstein, R. S. (1996). The sciences and arts share a common creative aesthetic. In A. I. Tauber (Ed.), The elusive synthesis: Aesthetics and science (pp. 49–82). Dodrecht, The Netherlands: Kluwer Academic Publishers.
  • Root-Bernstein, R. S. (2000). Art advances science. Nature, 407, 134.
  • Root-Bernstein, R. S. (2001). Music, science, and creativity. Leonardo, 34, 63–68.
  • Root-Bernstein, R. S. (2003). The art of innovation: Polymaths and the universality of the creative process. In L. Shavanina (Ed.), International handbook of innovation (pp. 267–278). Amsterdam: Elsevier.
  • Rowe, D., & Gray, J. (2000). The Hilbert challenge. Oxford, England: Oxford University Press.
  • Schoenfeld, A. (1985). Mathematical problem solving. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: McMillan.
  • Shapiro, S. I. (1965). A study of pupils’ individual characteristics in processing mathematical information. Voprosy Psikhologii, No. 2.
  • Shaw, M. P. (1994). Affective components of scientific creativity. In M. P. Shaw & M. A. Runco (Eds.), Creativity and affect (pp. 3–43), Norwood, NJ: Ablex.
  • Sheffield, L. J., Bennett, J., Berriozabal, M., DeArmond, M., & Wertheimer, R. (1995). Report of the task force on the mathematically promising. Reston, VA: National Council of Teachers of Mathematics.
  • Silver, E. A. (Ed.). (1985). Teaching and learning mathematical problem solving: Multiple research perspectives. Hillsdale, NJ: Laurence Erlbaum Associates.
  • Smith, J. M. (1966). Setting conditions for creative teaching in the elementary school. Boston: Allyn and Bacon.
  • Sowell, T. (2001). The Einstein syndrome. New York: Basic Books.
  • Sriraman, B. (2002). How do mathematically gifted students abstract and generalize mathematical concepts? National Association for Gifted Children 2002 Research Briefs, 16, 83–87.
  • Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations. Journal of Secondary Gifted Education. 14, 151–165.
  • Sriraman, B. (2004a). Reflective abstraction, uniframes and the formulation of generalizations. The Journal of Mathematical Behavior, 23, 205–222.
  • Sriraman, B. (2004b). Discovering a mathematical principle: The case of Matt. Mathematics in School, 33(2), 25–31.
  • Sriraman, B. (2004c). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19–34.
  • Sriraman, B. (2004d). Gifted ninth graders’ notions of proof. Investigating parallels in approaches of mathematically gifted students and professional mathematicians. Journal for the Education of the Gifted, 27, 267–292.
  • Sriraman, B. (2005). Philosophy as a bridge between mathematics arts and the sciences. In A. Beckmann, C. Michelsen, & B. Sriraman (Eds.), Proceedings of the 1st International Symposium on Mathematics and its Connections to the Arts and Sciences (pp. 7–31). University of Schwaebisch Gmuend, Germany: Franzbecker Verlag.
  • Sriraman, B. (in press). Implications of research on mathematics gifted education for the secondary curriculum. To appear in C. Callahan & J. Plucker (Editors) What the Research Says: Encyclopedia on Research in Gifted Education. Prufrock Press.
  • Sriraman, B., & English, L. (2004). Combinatorial mathematics: Research into practice. The Mathematics Teacher, 98, 182–191.
  • Sriraman, B., & Strzelecki, P. (2004). Playing with powers. The International Journal for Technology in Mathematics Education, 11(1), 29–34.
  • Steen, L. A. (2001). Revolution by stealth. In D. A. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 303–312). Dodrecht, The Netherlands: Kluwer Academic Publishers.
  • Steen, L. A. (2005). Math & Bio 2010: Linking undergraduate disciplines. Washington, DC: Mathematical Association of America.
  • Sternberg, R. J. (1997). A triarchic view of giftedness: Theory and practice. In N. Colangelo & G. A. Davis (Eds.), Handbook of gifted education (2nd ed., pp. 43–53). Boston: Allyn and Bacon.
  • Sternberg, R. J., & Lubart, T. I. (2000). The concept of creativity: Prospects and paradigms. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 93–115). New York: Cambridge University Press.
  • Sternberg, R. J., & Lubart, T. I. (1996). Investing in creativity. American Psychologist, 51, 677–688.
  • Suppes, P., & Binford, F. (1965). Experimental teaching of mathematical logic in the elementary school. The Arithmetic Teacher, 12, 187–195.
  • Torrance, E. P. (1974). Torrance tests of creative thinking: Norms-technical manual. Lexington, MA: Ginn.
  • Torrance, E. P. (1981). Non-test ways of identifying the creatively gifted. In J. C. Gowan, J. Khatena, & E. P. Torrance (Eds.), Creativity: Its educational implications (2nd ed., pp. 165–170). Dubuque, IA: Kendall/Hunt.
  • Usiskin, Z. (2000). The development into the mathematically talented. Journal of Secondary Gifted Education, 11, 152–162.
  • Vitale, B. (1989). Elusive recursion: A trip in a recursive land. New Ideas in Psychology, 7, 253–276.
  • Vygotsky, L. (1962). Thought and language. Cambridge, MA: MIT Press.
  • Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
  • Wallas, G. (1926). The art of thought. New York: Harcourt Brace.
  • Wason, P. C., & Johnson-Laird, P. N. (1972). Psychology of reasoning. Cambridge, MA: Harvard University Press.
  • Wertheimer, M. (1945). Productive thinking. New York: Harper.
  • Weisberg, R. W. (1993). Creativity: Beyond the myth of genius. New York: Freeman.
  • Yakimanskaya, I. S. (1970). Individual differences in solving geometry problems on proof. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics (Vol. 4). Stanford, CA: School Mathematics Study Group.
  • Ypma, E. G. (1968). Predictions of the industrial creativity of research scientists from biographical information. Dissertation Abstracts International, 30, 5731B–5732B.
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  • Volume 17
  •  Issue 1
  • Publication Date: Fall 2005



Are Giftedness and Creativity Synonyms in Mathematics?

Bharath Sriraman

At the K–12 level one assumes that mathematically gifted students identified by out-of-level testing are also creative in their work. In professional mathematics, “creative” mathematicians constitute a very small subset within the field. At this level, mathematical giftedness does not necessarily imply mathematical creativity but the converse is certainly true. In the domain of mathematics, are the words creativity and giftedness synonyms? In this article, the constructs of mathematical creativity and mathematical giftedness are developed via a synthesis and analysis of the general literature on creativity and giftedness. The notions of creativity and giftedness at the K–12 and professional levels are compared and contrasted to develop principles and models that theoretically “maximize” the compatibility of these constructs. The relevance of these models is discussed with practical considerations for the classroom. The paper also significantly extends ideas presented by Usiskin (2000).


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