题名

數學創造力的文獻回顧與探究

并列篇名

Survey and Discussion of Mathematical Creativity

DOI

10.6278/tjme.2050313.002

作者

劉宣谷(Hsuan-Ku Liu)

关键词

創造力指標 ； 創造力階段理論 ； 創造貢獻 ； 數學創造力 ； creative indicator ； creative process ； creative contribution ； mathematical creativity

期刊名称

臺灣數學教育期刊

卷期/出版年月

2卷1期（2015 / 04 / 01）

页次

23 - 40

内容语文

繁體中文
中文摘要

數學創造力的描述至今尚未明確，本文將從四個不同的觀點回顧數學創造力。數學創造產出的新穎與一般創造力無中生有的新穎性不同，且數學創造力的「新穎」並非全然的無中生有而是將重點放在舊知識的「再結合」。使用創造力量表測量學童的創造力可能窄化了創造力的豐富內涵，部分學者改以「多元解題」的方法分析數學上的創造力指標。從創造力階段理論學童在數學創造的醞釀過程中藉由重組過去的知識與比對題目的條件，在反覆的組合和比對的過程中對學童對於舊知識產生新的認識。創造力的貢獻分為歷史上和心理上的貢獻，學校層次的研究焦點在國小孩童是否具備「心理上的數學創造力」。數學知識與數學創造力同等重要，提供學童發散性思考和連結舊經驗的環境有助於提升學童的數學創造力。
英文摘要

Specific descriptions of mathematical creativity have not been proposed. This article reviews mathematical creativity from four aspects: products, indicators, processes, and contributions. A description of novelty in mathematical creativity is different from that of original creativity; novelty focuses on the recombination of ＂old＂ knowledge in mathematical creativity. The use of creativity tests for measuring creativity indicators may lead the field into a narrow and limited conception of creativity. Recently, scholars have begun to use the multiple-solution task to analyze indicators of mathematical creativity. Regarding creative processes, students recombine mathematical knowledge and compare the recombinations by using the requirements of problems during the incubation period. Through these recombination processes, students obtain new understanding regarding the old knowledge. Creative contributions exist in two forms: historical creativity and psychological creativity. At the school level, the concept of psychological creativity has been adapted for researching the mathematical creativity of elementary school students. Mathematical knowledge and mathematical creativity are both critical. Fostering an environment that encourages divergent thinking and connects to related mathematical knowledge assists in nurturing a student's mathematical creativity abilities.
主题分类 基礎與應用科學 > 數學
社會科學 > 教育學
参考文献
  1. 陳李綢(2006)。國小數學創造力診斷與認知歷程工具研發。教育心理學報，38(1)，1-17。
    連結：
  2. Wallas, G. (1926). The art of thought. New York, NY: Harcourt Brace.
  3. Dodds, A. Rebecca, Ward, B. Thomas, & Smith, M. Steven (2004). A Review of Experimental Research on Incubation in Problem Solving and Creativity. Texas A&M University. Retrieved January 30, 2015, from http://ecologylab.net/research/publications/DoddsSmithWardChapter.pdf
  4. Amabile, T. M.(1989).Growing up creativity: Nurturing a lifetime of creativity.New York, NY:Crown.
  5. Amabile, T. M.(1996).Creativity in context: Update to the social psychology of creativity.Boulder, CO:Westview Press.
  6. Barbeau, E. J.(ed.),Taylor, P. J.(ed.)(2009).Challenging mathematics in and beyond the classroom: The 16th ICMI Study.New York, NY:Springer.
  7. Barnes, M.(2000).'Magical' moments in mathematics: Insights into the process of coming to know.For the Learning of Mathematics,20(1),33-43.
  8. Barron, F. X.,Harrington, D. M.(1981).Creativity, intelligence and personality.Annual Review of Psychology,32,439-476.
  9. Bloom, B. S.(Ed.).(1985).Development talent in young people.New York, NY:Ballantine.
  10. Boden, M. A.(Ed.)(1996).Dimension of creativity.Cambridge, MA:MIT Press.
  11. Brinkmann, A.(2004).The experience of mathematical beauty.the 10th International Congress of Mathematics Education,Roskilde, Denmark:
  12. Chamberlin, S. A.,Moon, S. M.(2005).Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians.Journal of Secondary Gifted Education,17(1),37-47.
  13. Csikszentmihalyi, M.(1996).Creativity: Flow and the psychological of discovery and invention.NewYork, NY:HarperCollins.
  14. Csikszentmihalyi, M.(Ed.),Csikszentmihalyi, I. S.(Ed.)(1988).Optimal experience: Psychological studies of flow in consciousness.Cambridge, UK:Cambridge University Press.
  15. Gardner, H.(1993).Creating minds: An anatomy of creativity seen through the lives of Freud, Einstein, Picasso, Stravinsky, Eliot, Graham, and Gandhi.New York, NY:Basic Books.
  16. Glover, J. A.(ed.),Ronning, R. R.(ed.),Reynolds, C. R.(ed.)(1989).Handbook of creativity.New York, NY:Plenum Press.
  17. Guilford, J. P.(1950).Creativity.American Psychologist,5(9),444-454.
  18. Hausman, C. R.(1984).A discourse on novelty and creativity.Albany, NY:State University of New York Press.
  19. Haylock, D. W.(1987).A framework for assessing mathematical creativity in school children.Educational Studies in Mathematics,18(1),59-74.
  20. Helsinki, E. P.(1997).The state-of-art in mathematical creativity.ZDM - The International Journal on Mathematics Education,29(3),63-67.
  21. Hollands, R.(1972).Educational technology: Aims and objectives in teaching mathematics.Mathematics in School,1(6),22-23.
  22. Idris, N.,Mohd Nor, N.(2010).Mathematical creativity: Usage of technology.Procedia - Social and Behavioral Sciences,2(2),1963-1967.
  23. Jackson, P. W.,Messick, S.(1965).The person, the product, and the response: Conceptual problems in the assessment of creativity.Journal of Personality,33(3),309-329.
  24. Kaufman, J. C.,Beghetto, R. A.(2009).Beyond big and little: The four c model of creativity.Review of General Psychology,13(1),1-12.
  25. Kerr, B.(Ed.)(2009).Encyclopedia of giftedness, creativity and talent.Thousand Oaks, CA:Sage.
  26. Krutetskii, V. A.,Kilpatrick, J.(ed.),Wirzup, I.(ed.),Teller, J.(trans.)(1976).The psychology of mathematical abilities in school children.Chicago, IL:University of Chicago Press.
  27. Lee, K. S.,Hwang D. J.,Seo, J. J.(2003).A development of the test for mathematical creative problem solving ability.Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education,7(3),163-189.
  28. Leikin, R.(2007).Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks..Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education,Larnaca, Cyprus:
  29. Leikin, R.(ed.),Berman, A.(ed.)(2009).Creativity in mathematics and the education of gifted students.Rotterdam, The Netherlands:Sense.
  30. Leikin, R.,Lev, M.(2013).Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference?.ZDM - The International Journal on Mathematics Education,45,183-197.
  31. Leikin, R.,Levav-Waynberg, A.,Gurevich, I.,Mednikov, L.(2006).Implementation of multiple solution connecting tasks: Do students' attitudes support teachers' reluctance?.Focus on Learning Problems in Mathematics,28(1)
  32. Levav-Waynberg, A.,Leikin, R.(2012).The role of multiple solution tasks in developing knowledge and creativity in geometry.The Journal of Mathematical Behavior,31(1),79-90.
  33. Mann, E. L.(2005).Storrs, CT.,University of Connecticut.
  34. Morgan, S.,Forster, L.(1999).Creativity in the classroom.Gifted Educational International,14(1),29-43.
  35. Nadjafikhah, M.,Yaftian, N.,Bakhshalizadeh, S.(2012).Mathematical creativity: Some definitions and characteristics.Procedia - Social and Behavioral Sciences,31,285-291.
  36. Neumann, C. J.(2007).Fostering creativity: A model for developing a culture of collective creativity in science.EMBO Reports,8(3),202-206.
  37. Peressini, D.,Knuth, E.(2000).The role of tasks in developing communities of mathematical inquiry.Teaching Children Mathematics,6(6),391-396.
  38. Pitta-Pantazi, D.,Sophocleous, P.,Christou, C.(2013).Spatial visualizers, object visualizers and verbalizers: their mathematical creative abilities.ZDM - The International Journal on Mathematics Education,45,199-213.
  39. Poincaré, H.,Maitland, F.(trans.)(1952).Science and method.Mineola, NY:Dover.
  40. Rieber, R. W.(ed.)(1984).The collected works of L. S. Vygotsky: Vol. 5, child psychology.New York, NY:Springer.
  41. Romey, W. D.(1970).What is your creativity quotient?.School Science and Mathematics,70(1),3-8.
  42. Runco, M. A.(Ed.)(1997).The creativity research handbook.Cresskill, NJ:Hampton Press.
  43. Shriki, A.(2010).Working like real mathematicians: Developing prospective teachers' awareness of mathematical creativity through generating new concepts.Educational Studies in Mathematics,73(2),159-179.
  44. Sio, U. N.,Ormerod, T. C.(2009).Does incubation enhance problem solving? A meta-analytic review.Psychological Bulletin,135(1),94-120.
  45. Skemp, R. R.(1971).The psychology of learning mathematics.Baltimore, MD:Penguin Books.
  46. Sriraman, B.(2009).The characteristics of mathematical creativity.ZDM - The International Journal on Mathematics Education,41(1-2),13-27.
  47. 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.
  48. Sriraman, B.(2004).The characteristics of mathematical creativity.The Mathematics Educator,14(1),19-34.
  49. Sriraman, B.(2005).Are giftedness and creativity synonyms in mathematics?.Journal of Secondary Gifted Education,17(1),20-36.
  50. Sriraman, B.(Ed.)(2008).Creativity, giftedness, and talent development in mathematics.Charlotte, NC:Information Age Publishing.
  51. Sriraman, B.,Haavold, P.,Lee, K.(2013).Mathematical creativity and giftedness: A commentary on and review of theory, new operational views, and ways forward.ZDM - The International Journal on Mathematics Education,45(2),215-225.
  52. Sternberg, R. J.(Ed.)(1999).Handbook of creativity.Cambridge, UK:Cambridge University Press.
  53. Sternberg, R. J.(Ed.)(1999).Handbook of creativity.Cambridge, UK:Cambridge University Press.
  54. Sternberg, R. J.(Ed.)(1999).Handbook of creativity.Cambridge, UK:Cambridge University Press.
  55. Sternberg, R. J.(Ed.)(1999).Handbook of creativity.Cambridge, UK:Cambridge University Press.
  56. Sternberg, R. J.(Ed.)(1999).Handbook of creativity.Cambridge, UK:Cambridge University Press.
  57. Sternberg, R. J.,Lubart, T. I.(1996).Investing in creativity.American Psychologist,51(7),677-688.
  58. Sternberg, R. J.,Lubart, T. I.(1995).Defying the crowd: Cultivating creativity in a culture of conformity.New York, NY:Free Press.
  59. Sternberg, R. J.,Lubart, T. I.(1991).An investment theory of creativity and its development.Human Development,34(1),1-31.
  60. Tall, D.(Ed.)(1991).Advanced mathematical thinking.Dodrecht, The Netherlands:Kluwer Academic Publishers.
  61. Torrance, E. P.(1962).Guiding creative talent.Englewood Cliffs, NJ:Prentice-Hall.
  62. Usiskin, Z.(2000).The development into the mathematically talented.Journal of Secondary Gifted Education,11(3),152-162.
  63. Vul, E.,Pashler, H.(2007).Incubation benefits only after people have been misdirected.Memory & Cognition,35(4),701-710.
  64. 張雨霖、陳學志、徐芝君(2010)。教師創造力信念、創造力教學自我效能對創造力教學行為之影響。復興崗學報，99，151-172。
  65. 郭明采(2014)。碩士論文(碩士論文)。臺北市，國立臺北教育大學。
  66. 詹志禹(2002)。影響創造力的相關因素―從小學教育環境與脈絡來考量。學生輔導，79，32-47。
  67. 蕭佳純(2002)。國小學生內在動機、學科知識與創造力表現關聯之研究：教師創造力教學的調節效果。特殊教育研究學刊，37(3)，89-113。
  68. 魏明通(1994)。高級中學數學與科學資優學生創造力研究。師大學報，39，525-544。
被引用次数
  1. 潘裕豐(2019)。高中美術資優班學生創造力、學業成就與藝術表現之關係研究。教育科學研究期刊，64(1)，267-285。
  2. (2024)。國中八年級學生在數學創造力問題表現之分析。臺灣數學教育期刊，11(2)，59-80。
  3. (2024)。國中生數學符號運算素養的創造思考表現。臺灣數學教育期刊，11(1)，1-36。
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