Educational Studies in Mathematics

, Volume 82, Issue 2, pp 201–221 | Cite as

Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA



In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in mathematics by analyzing their problem-posing abilities in geometric scenarios. The participants in this study were from one location in the USA and two locations in China. All participants were enrolled in advanced mathematical courses in the local high school. Differences in the problems posed by the three groups are discussed in terms of quality (novelty/elaboration) as well as quantity (fluency). The analysis of the data indicated that even mathematically advanced high school students had trouble posing good quality and/or novel mathematical problems. We discuss our findings in terms of the culture and curricula of the respective school systems and suggest implications for future directions in problem-posing research within mathematics education.


Advanced high school students Cross-cultural thinking Creativity Geometry Mathematical creativity Novelty Problem posing Problem solving US and Chinese students Rural and urban Chinese students 


  1. Allender, J. S. (1969). A study of inquiry activity in elementary school children. American Educational Research Journal, 6, 543–558.Google Scholar
  2. Anderson, J. R., Boyle, C. B., & Reiser, B. J. (1985). Intelligent tutoring systems. Science, 228, 456–462.CrossRefGoogle Scholar
  3. Andreasen, N. C., & Glick, I. D. (1988). Bipolar affective disorder and creativity: Implications and clinical management. Comprehensive Psychiatry, 29, 207–217.CrossRefGoogle Scholar
  4. Ariete, S. (1976). Creativity: The magic synthesis. New York: Basic Books.Google Scholar
  5. Barnes, M. (2000). Magical moments in mathematics: Insights into the process of coming to know. For the Learning of Mathematics, 20(1), 33–43.Google Scholar
  6. Biggs, J. B. (1991). Approaches to learning in secondary and tertiary students in Hong Kong: Some comparative studies. Educational Research Journal, 6, 27–39.Google Scholar
  7. Birkhoff, G. D. (1956). Mathematics of aesthetics. In J. R. Newman (Ed.), The world of mathematics (pp. 2185–2197). New York: Simon and Schuster.Google Scholar
  8. Bolden, D. S., Harries, T. V., & Newton, D. P. (2010). Pre-service primary teachers' conceptions of creativity in mathematics. Educational Studies in Mathematics, 73(2), 143–157.CrossRefGoogle Scholar
  9. Brinkmann, A., & Sriraman, B. (2009). Aesthetics and creativity: An exploration of the relationship between the constructs. In B. Sriraman & S. Goodchild (Eds.), Festschrift celebrating Paul Ernest ' s 65th birthday (pp. 57–80). Charlotte: Information Age Publishing.Google Scholar
  10. Brown, S., & Walter, M. (1983). The art of problem posing. Philadelphia: Franklin Press.Google Scholar
  11. Bunge, M. (1967). Scientific research, 1. Berlin, NY: Springer.Google Scholar
  12. Cai, J. (1995). A cognitive analysis of U.S. and Chinese students' mathematical performance on tasks involving computation, simple problem solving, and complex problem solving. Journal for Research in Mathematics Education monograph series. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  13. Cai, J. (1997). Beyond computation and correctness: Contributions of open-ended tasks in examining U.S. and Chinese students' mathematical performance. Educational Measurement: Issues and Practice, 16(1), 5–11.CrossRefGoogle Scholar
  14. Cai, J. (1998). An investigation of U.S. and Chinese students' mathematical problem posing and problem solving. Mathematics Education Research Journal, 10(1), 37–50.CrossRefGoogle Scholar
  15. Cai, J. (2000). Mathematical thinking involved in U.S. and Chinese students' solving process-constrained and process-open problems. Mathematical Thinking and Learning, 2, 309–340.CrossRefGoogle Scholar
  16. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students'mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21(4), 401–421.CrossRefGoogle Scholar
  17. Csikszentmihalyi, M. (1996). Creativity, flow and the psychology of discovery and invention. New York: Harper Collins.Google Scholar
  18. Ellerton, N. F. (1986). Children's made-up mathematics problems: A new perspective on talented mathematicians. Educational Studies in Mathematics, 17, 261–271.CrossRefGoogle Scholar
  19. English, L. D. (1997). The development of 5th grade students problem-posing abilities. Educational Studies in Mathematics, 34, 183–217.CrossRefGoogle Scholar
  20. English, L. D. (2007). Complex systems in the elementary and middle school mathematics curriculum: A focus on modeling. In B. Sriraman (Ed.), Festschrift in honor of Gunter Törner. The Montana mathematics enthusiast (pp. 139–156). Charlotte, NC: Information Age Publishing.Google Scholar
  21. English, L. D., & Sriraman, B. (2010). Problem solving for the 21st century. In B. Sriraman & L. D. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 263–285). Berlin, London: Springer.Google Scholar
  22. Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. New York: Basic Books.Google Scholar
  23. Ghiselin, B. (1952). The creative process. New York: Mentor.Google Scholar
  24. Guilford, J. P. (1950). Creativity. American Psychologist, 5, 444–454.CrossRefGoogle Scholar
  25. Hadamard, J. (1945). Mathematician ' s mind: The psychology of invention in the mathematical field. Princeton, NJ: Princeton University Press.Google Scholar
  26. Hewitt, E. (1948). Rings of real-valued continuous functions. Transactions of the American Mathematical Society, 64, 45–99.CrossRefGoogle Scholar
  27. 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]. Göttingen Nachrichten, 253–297.Google Scholar
  28. Hofstede, G. (1980). Culture ' s consequences: International differences in work related values. Beverly Hills, CA: Sage.Google Scholar
  29. Huang, R., & Leung, K. S. F. (2004). Cracking the paradox of Chinese learners: Looking into the mathematics classrooms in Hong Kong and Shanghai. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 348–381). Singapore: World Scientific.CrossRefGoogle Scholar
  30. Husen, T. (1967). International study of achievement in mathematics: A comparison of twelve countries (vol. 1–2). New York: Wiley.Google Scholar
  31. Jay, E. S., & Perkins, D. N. (1997). Problem finding: The search for mechanism. In M. A. Runco (Ed.), The creativity research handbook (Vol. 1, pp. 257–293). Cresskill, NJ: Hampton Press.Google Scholar
  32. Kaufman, J. C., & Sternberg, R. J. (Eds.). (2006). The international handbook of creativity. Cambridge: Cambridge University Press.Google Scholar
  33. Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago: The University of Chicago Press.Google Scholar
  34. Leikin, R., Berman, A., & Koichu, B. (2010). Creativity in mathematics and the education of gifted students. Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  35. Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem solving behavior. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 75–88). New York: Springer.CrossRefGoogle Scholar
  36. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers ' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  37. Mathematics Curriculum Development Group of Basic Education of Education Department [教 育部基础教育司数学课程标准研制组]. (2002). The interpretation of mathematics curriculum (Trial Version).[数学课程标准(实验稿)解读]. Beijing: Beijing Normal University Press.Google Scholar
  38. National Center for Education Development. (2000). Report on developing students ' creativity and teacher training in the U.S. [关于美国创造性人才培养与教师培训的考察报告].Google Scholar
  39. National Center for Educational Statistics. (2009). The National Assessment of Educational Progress Overview. Retrieved August 28, 2009, from
  40. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  41. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  42. Oakland, T., Glutting, J., & Horton, C. (1996). Student styles questionnaire. San Antonio, TX: The Psychological Corporation.Google Scholar
  43. Oakland, T., & Lu, L. (2006). Temperament styles of children from the People's Republic of China and the United States. School Psychology, 27, 192–208.CrossRefGoogle Scholar
  44. Peverly, S. (2005). Moving past cultural homogeneity: Suggestions for comparisons of students' educational outcomes in the United States and China. Psychology in the Schools, 42(3), 241–249.CrossRefGoogle Scholar
  45. Plucker, J., & Zabelina, D. (2009). Creativity and interdisciplinarity: One creativity or many creativities? ZDM: The International Journal on Mathematics Education, 41, 5–12.CrossRefGoogle Scholar
  46. Poincaré, H. (1948). Science and method. New York: Dover Books.Google Scholar
  47. Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.Google Scholar
  48. Presmeg, N. C. (1986). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17(3), 297–311.CrossRefGoogle Scholar
  49. Richards, R., Kinney, D. K., Lunde, I., Benet, M., & Merzel, A. C. (1988). Creativity in manic depressives, cyclothymes, their normal relatives and control subjects. Journal of Abnormal Psychology, 97, 281–288.CrossRefGoogle Scholar
  50. Robitaille, D. E., & Garden, R. A. (1989). The IEA study of mathematics 11: Contexts and outcomes of school mathematics. New York: Pergamon.Google Scholar
  51. Runco, M. A. (1994). Problem finding, problem solving, and creativity. Norwood, NJ: Ablex Publishing Corporation.Google Scholar
  52. 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.CrossRefGoogle Scholar
  53. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM: The International Journal on Mathematics Education, 97(3), 75–80.CrossRefGoogle Scholar
  54. Sio, U. N., & Ormerod, T. C. (2007). Does incubation enhance problem solving? A meta-analytic review. Psychological Bulletin, 135(1), 94–120.CrossRefGoogle Scholar
  55. Sriraman, B. (2003). Can mathematical discovery fill the existential void? The use of conjecture, proof and refutation in a high school classroom. Mathematics in School, 32(2), 2–6.Google Scholar
  56. Sriraman, B. (2004). Discovering a mathematical principle: The case of Matt. Mathematics in School, 33(2), 25–31.Google Scholar
  57. Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17, 20–36.Google Scholar
  58. Sriraman, B. (2008). Creativity, giftedness and talent development in mathematics. Charlotte, NC: Information Age Publishing.Google Scholar
  59. Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM: The International Journal on Mathematics Education, 41(1&2), 13–27.CrossRefGoogle Scholar
  60. Sriraman, B., & English, L. (2004). Combinatorial mathematics: Research into practice. The Mathematics Teacher, 98(3), 182–191.Google Scholar
  61. Sriraman, B., & Lee, K. (2011). The elements of giftedness and creativity in mathematics. Rotterdam, The Netherlands: Sense Publishers.CrossRefGoogle Scholar
  62. Stevenson, H. W. (1993). Why Asian students still outdistance Americans. Educational Leadership, 50(5), 63–65.Google Scholar
  63. Stevenson, H. W., & Stigler, J. W. (1992). The learning gap: Why our schools are failing and what we can learn from Japanese and Chinese education. New York: Summit Books.Google Scholar
  64. Stillman, G., Kwok-cheung, C., Mason, R., Sheffield, L., Sriraman, B., & Ueno, K. (2009). Classroom practice: Challenging mathematics classroom practices. In E. Barbeau & P. Taylor (Eds.), Challenging mathematics in and beyond the classroom: The 16th ICMI Study (pp. 243–284). Berlin: Springer.CrossRefGoogle Scholar
  65. Stoyanova, E. (1997). Extending and exploring students ' problem solving via problem posing: A study of Years 8 and 9 students involved in Mathematics Challenge and Enrichment Stages of Euler Enrichment Program for Young Australians. (Unpublished doctoral dissertation). Perth, Australia: Edith Cowan University.Google Scholar
  66. Stoyanova, E. (1998). Problem posing in mathematics classrooms. In N. Ellerton & A. McIntosh (Eds.), Research in mathematics education in Australia: A contemporary perspective (pp. 164–185). Perth: Edith Cowan University.Google Scholar
  67. Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (Proceedings of the 19th annual conference of the Mathematics Education Research Group of Australasia) (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia.Google Scholar
  68. Taylor, I. A. (1972). A theory of creative transactualization: A systematic approach to creativity with implications for creative leadership. Occasional Paper. Buffalo, NY: Creative Education Foundation.Google Scholar
  69. Torrance, E. P. (1988). The nature of creativity as manifest in its testing. In R. J. Sternberg (Ed.), The nature of creativity: Contemporary psychological perspectives (pp. 43–75). New York: Cambridge University Press.Google Scholar
  70. Usiskin, Z. (2000). The development into the mathematically talented. Journal of Secondary Gifted Education, 11(3), 152–162.Google Scholar
  71. Van Harpen, X. Y., & Presmeg, N. (2011). Insights into students' mathematical problem posing process. In B. Ubuz (Ed.), Proceedings of the 35th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 289–296). Ankara, Turkey: PME.Google Scholar
  72. Vital, D. H., Lummis, M., & Stevenson, H. W. (1988). Low and high mathematics achievement in Japanese, Chinese, and American elementary-school children. Developmental Psychology, 24(3), 335–342.CrossRefGoogle Scholar
  73. Vul, E., & Pashler, H. (2007). Incubation benefits only after people have been misdirected. Memory and Cognition, 35(4), 701–710.CrossRefGoogle Scholar
  74. Wallas, G. (1926). The art of thought. Harmondsworth, UK: Penguin Books Ltd.Google Scholar
  75. Wong, N. Y. (2004). The CHC learner's phenomenon: Its implications on mathematics education. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 503–534). Singapore: World Scientific.CrossRefGoogle Scholar
  76. Wong, N. Y. (2006). From “Entering the Way” to “Exiting the Way”: In search of a bridge to span “basic skills” and “process abilities”. In F. K. S. Leung, G. D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions: The 13th ICMI Study (pp. 111–128). New York: Springer.CrossRefGoogle Scholar
  77. Yang, G. (2007). A comparison and reflection on the school education of China and the U.S. [中 美基础教育的比较与思考].Google Scholar
  78. Yuan, X. (2009). An exploratory study of high school students ' creativity and mathematical problem posing in China and the United States. (Unpublished doctoral dissertation). Illinois State University.Google Scholar
  79. Yuan, X., & Presmeg, N. (2010). An exploratory study of high school students' creativity and mathematical problem posing in China and the United States. In M. Pinto & T. Kawasaki (Eds.), Proceedings of the 34th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 321–328). Belo Horizonte, Brazil: PME.Google Scholar
  80. Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students' creativity and mathematical problem posing abilities—Comparing Chinese and U.S students. In B. Sriraman & K. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5–28). Rotterdam, The Netherlands: Sense Publishers.CrossRefGoogle Scholar
  81. Zhang, D. (2005). The “two basics”: Mathematics teaching in Mainland China. Shanghai, China: Shanghai Educational Publishing House.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Illinois State UniversityNormalUSA
  2. 2.The University of MontanaMissoulaUSA

Personalised recommendations