For the gifted mathematics student, early mastery of concepts and skills in the mathematics curriculum usually results in getting more of the same work and/or moving through the curriculum at a faster pace. Testing, grades, and pacing overshadow the essential role of creativity involved in doing mathematics. Talent development requires creative applications in the exploration of mathematics problems. Traditional teaching methods involving demonstration and practice using closed problems with predetermined answers insufficiently prepare students in mathematics. Students leave school with adequate computational skills but lack the ability to apply these skills in meaningful ways. Teaching mathematics without providing for creativity denies all students, especially gifted and talented students, the opportunity to appreciate the beauty of mathematics and fails to provide the gifted student an opportunity to fully develop his or her talents. In this article, a review of literature defines mathematical creativity, develops an understanding of the creative student of mathematics, and discusses the issues and implications for the teaching of mathematics.
Get full access to this article
View all access options for this article.
References
1.
AmabileT. M. (1989). Growing up creative: Nurturing a lifetime of creativity.Buffalo, NY: C.E.F. Press
2.
BalkaD. S. (1974). Creative ability in mathematics. Arithmetic Teacher, 21, 633–636.
3.
BassokM.HolyoakK. J. (1989). Interdomain transfer between isomorphic topics in algebra and physics. Journal of Experiment Psychology: Learning, Memory, and Cognition, 15(1), 153–166
4.
BeckerJ. P.ShimadaS. (Eds.). (1997). The open-ended approach: A new proposal for teaching-mathematics.Reston, VA: National Council of Teachers of Mathematics
5.
Ben-ZeevT. (1996). When erroneous mathematical thinking is just as “correct”: The oxymoron of rational errors. In SternbergR. J.Ben-ZeevT. (Eds.), The nature of mathematical thinking (pp. 55–80. Mahwah, NJ: Lawrence Erlbaum
6.
BrodyL. E.MillsC. J. (2005). Talent search research: What have we learned ?High Ability Studies, 16, 97–111
7.
BronsanP. A.FitzsimmonsJ. A. (2001). Creativity. In GrinsteinL. S.LipseyS. I. (Eds.), Encyclopedia of mathematics education (pp. 164–166. New York: RoutledgeFalmer
8.
CarrollJ. B. (1996). Mathematical abilities: Some results from factor analysis. In SternbergR. J.Ben-ZeevT. (Eds.), The nature of mathematical thinking (pp. 3–25. Mahwah, NJ: Lawrence Erlbaum
9.
ChingT. P. (1997). An experiment to discover mathematical talent in a primary school in Kampong Air. International Reviews on Mathematical Education, 29(3), 94–96. Retrieved March 10, 2003, from http://www.fizkarlsruhe.de/fix/publications/zdm/adm97
10.
CrosswhiteF. J. (1987). Cognitive science and mathematics education: A mathematician's perspective. In SchoenfeldA. H. (Ed.), Cognitive science and mathematics education (pp. 253–277. Mahwah, NJ: Lawrence Erlbaum
11.
CsikszentmihalyiM.RathundeK.WhalenS. (1993). Talented teenagers: The roots of success and failure.New York: Cambridge University Press
12.
DavisG. A. (1969). Thinking creatively in adolescence: A discussion of strategy. In GrinderR. E. (Ed.), Studies in adolescence (pp. 538–545. New York: Macmillan
13.
DavisR. B.MaherC. A.NoddingsN. (1990). Suggestions for the improvement of mathematics education. In DavisR. B.MaherC. A.NoddingsN. (Eds.), Constructivist views on the teaching of mathematics. Journal for Research in Mathematics Education Monograph No. 4 (pp. 187–191). Reston, VA: National Council of Teachers of Mathematics
14.
de MorganA. (1866). Sir W. R. Hamilton. Gentleman's Magazine and Historical Review, 1, 128–134
15.
DienesZ. P. (2004). Mathematics as an art form. An essay about the stages of mathematics learning in an artistic evaluation of mathematical activity. Retrieved September 1, 2004, from http://www.zoltandienes.com/Mathematics_as_an_art_form.pdf
16.
DreyfusT.EisenbergT. (1996). On different facets of mathematical thinking. In SternbergR. J.Ben-ZeevT. (Eds.), The nature of mathematical thinking (pp. 253–284. Mahwah, NJ: Lawrence Erlbaum
17.
FordD. Y.HarrisJ. J.III (1992). The elusive definition of creativity. Journal of Creative Behavior, 26, 186–198
18.
FoucheK. K. (1993). Problem solving and creativity: Multiple solution methods in a cross-cultural study in middle level mathematic. Unpublished doctoral dissertation, University of Florida, Gainesville
19.
FrahmR. A. (2004, March 21). Feverishly fixing an error: Company races to correct inaccurate scoring of Connecticut's mastery test. The Hartford Courant, p. A1
20.
GinsburgH. P. (1996). Toby's math. In SternbergR. J.Ben-ZeevT. (Eds.), The nature of mathematical thinking (pp. 175–282. Mahwah, NJ: Lawrence Erlbaum
21.
HadamardJ (1945). The psychology of invention in the mathematical field.Mineola, NY: Dover
22.
HashimotoY (1997). The methods of fostering creativity through mathematical problem solving. International Reviews on Mathematical Education, 29(3), 86–87. Retrieved March 10, 2003, from http://www.flz-karlsruhe.de/fix/publications/zdm/adm97
23.
HaylockD. W. (1985). Conflicts in the assessment and encouragement of mathematical creativity in schoolchildren. International Journal of Mathematical Education in Science and Technology, 16, 547–553
24.
HaylockD. W. (1987). A framework for assessing mathematical creativity in school children. Education Studies in Mathematics, 18(1), 59–74
25.
HaylockD (1997). Recognizing mathematical creativity in schoolchildren. International Reviews on Mathematical Education, 29(3), 68–74. Retrieved March 10, 2003, from http://www.fizkarlsruhe.de/fix/publications/zdm/adm97
26.
HongE.AquiY. (2004). Cognitive and motivational characteristics of adolescents gifted in mathematics: Comparisons among students with different types of giftedness. Gifted Child Quarterly, 48, 191–201
27.
ImaiT (2000). The influence of overcoming fixation in mathematics towards divergent thinking in open-ended mathematics problems on Japanese junior high school students. International Journal of Mathematical Education in Science and Technology, 31, 187–193
28.
JensenL. R. (1973). The relationships among mathematical creativity, numerical aptitude and mathematical achievement. Unpublished doctoral dissertation, University of Texas at Austin
29.
KilpatrickJ (1987). Problem formulating: Where do good problems come from? In SchoenfeldA. H. (Ed.), Cognitive science and mathematics education (pp. 123–148. Mahwah, NJ: Lawrence Erlbaum
30.
KimH.ChoS.AhnD. (2003). Development of mathematical creative problem solving ability test for identification of gifted in math. Gifted Education International, 18, 184–174
KrutetskiiV. A. (1976). The psychology of mathematical abilities in school children.Chicago: University of Chicago Press
33.
Learning Point Associates. (2004). All students reaching the top: Strategies for closing academic achievement gaps. A report of the national study group for the affirmative development of academic ability. Retrieved October 18, 2004, from http://www.ncrel.org/gap/studies/allstudents.pdf
34.
MannE. L. (2003). The impact of mathematical experiences as a child on the teaching practices of elementary schoolteachers. Unpublished manuscript, University of Connecticut, Storrs
35.
MayerR. E.HegartyM. (1996). The process of understanding mathematical problems. In SternbergR. J.Ben-ZeevT. (Eds.), The nature of mathematical thinking (pp. 29–54. Mahwah, NJ: Lawrence Erlbaum
36.
MeissnerH (2000, July–August). Creativity in mathematics education. Paper presented at the meeting of the International Congress on Mathematical Education, Tokyo, Japan
37.
National Council of Teachers of Mathematics. (1980). An agenda for action.Reston, VA: Author
38.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.Reston, VA: Author
PoincaréH. (1913). The foundations of science.New York: The Science Press
42.
PolyaG (1962). Mathematical discover: On understanding, learning and teaching problem solving (Vol. 1). Hoboken, NJ: John Wiley & Sons
43.
ReisS. M.GentryM.MaxfieldL. R. (1998). The application of enrichment clusters to teachers' classroom practices. Journal for Education of the Gifted, 21, 310–324
44.
RenzulliJ. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60, 180–184, 261
45.
RenzulliJ. S. (1997). How to develop an authentic enrichment cluster.Storrs: University of Connecticut, National Research Center on the Gifted and Talented. Retrieved November 12, 2002, from http://www.gifted.uconn.edu/sem/semart01.html
46.
RenzulliJ. S. (1998). The three-ring conception of giftedness. In BaumS. M.ReisS. M.MaxfieldL. R. (Eds.), Nurturing the gifts and talents of primary grade students (pp. 1–27. Mansfield Center, CT: Creative Learning Press
47.
RenzulliJ. S.GentryM.ReisS. M. (2003). Enrichment clusters: A practical plan for real-world, student-driven learning.Mansfield Center, CT: Creative Learning Press
48.
RenzulliJ. S.GentryM.ReisS. M. (2004). A time and place for authentic learning. Educational Leadership, 62(1), 73–77
49.
RenzulliJ. S.LeppienJ. H.HaysT. S. (2000). The Multiple Menu Model: A practical guide for developing differentiated curriculum.Mansfield Center, CT: Creative Learning Press
50.
RuncoM. A. (1993). Creativity as an educational objective for disadvantaged students (RBDM 9306).Storrs: University of Connecticut, The National Research Center on the Gifted and Talented
51.
SchoenfeldA. H. (1988). When good teaching leads to bad results: The disasters of “well-taught” mathematics courses. Educational Psychologist, 23, 145–166
52.
SheffieldL. J.BennettJ. Berioz AabalM.DeArmondM.WertheimerR. (1999). Report of the task force on the mathematically promising. In SheffieldL. J. (Ed.), Developing mathematically promising students (pp. 309–316). Reston, VA: National Council of Teachers of Mathematics
53.
ShimadaS (1997). The significance of an open-ended approach. In BeckerJ. P.ShimadaS. (Eds.), The open-ended approach: A new proposal for teaching mathematics (pp. 1–9. Reston, VA: National Council of Teachers of Mathematics
54.
SilverE. A. (1997). Fostering creativity though instruction rich mathematical problem solving and problem posing. International Reviews on Mathematical Education, 29, 75–80. Retrieved March 10, 2003, from http://www.fiz-karlsruhe.de/fix/publications/zdm/adm97
55.
SinghB (1988). Teaching-learning strategies and mathematical creativity.Delhi, India: Mittal Publications
56.
SkempR. R. (1987). The psychology of learning mathematics.Mahwah, NJ: Lawrence Erlbaum
57.
StarkoA. J. (2001). Creativity in the classroom: Schools of curious delight.Mahwah, NJ: Lawrence Erlbaum
58.
SternbergR. J. (1996). What is mathematical thinking? In SternbergR. J.Ben-ZeevT. (Eds.), The nature of mathematical thinking (pp. 303–318. Mahwah, NJ: Lawrence Erlbaum
TorranceE. P. (1966). Torrance test on creative thinking: Norms-technical manual (Research ed.). Lexington, MA: Personal Press
61.
TreffingerD. J.RenzulliJ. S.FeldhusenJ. F. (1971). Problems in the assessment of creative thinking. The Journal of Creative Behavior, 5, 104–112
62.
TreffingerD. J.YoungG. C.SelbyE. C.ShepardsonC. (2002). Assessing creativity: A guide for educators (RM02170).Storrs: University of Connecticut, The National Research Center on the Gifted and Talented
63.
TuliM. R. (1980). Mathematical creativity as related to aptitude for achievement in and attitude towards mathematics (Doctoral dissertation, Panjab University, 1980). Dissertation Abstracts International, 42 (01), 122
64.
UsiskinZ (1999). The mathematically promising and the mathematically gifted. In SheffieldL. J. (Ed.), Developing mathematically promising students (pp. 57–69. Reston, VA: National Council of Teachers of Mathematics
