Connecting mathematical creativity to mathematical ability
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This study aims to investigate whether there is a relationship between mathematical ability and mathematical creativity, and to examine the structure of this relationship. Furthermore, in order to validate the relationship between the two constructs, we will trace groups of students that differ across mathematical ability and investigate the relationships amongst these students’ performance on a mathematical ability test and the components of mathematical creativity. Data were collected by administering two tests, a mathematical ability and a mathematical creativity test, to 359 elementary school students. Mathematical ability was considered as a multidimensional construct, including quantitative ability (number sense and pre-algebraic reasoning), causal ability (examination of cause–effect relations), spatial ability (paper folding, perspective and spatial rotation abilities), qualitative ability (processing of similarity and difference relations) and inductive/deductive ability. Mathematical creativity was defined as a domain-specific characteristic, enabling individuals to be characterized by fluency, flexibility and originality in the domain of mathematics. The data analysis revealed that there is a positive correlation between mathematical creativity and mathematical ability. Moreover, confirmatory factor analysis suggested that mathematical creativity is a subcomponent of mathematical ability. Further, latent class analysis showed that three different categories of students can be identified varying in mathematical ability. These groups of students varying in mathematical ability also reflected three categories of students varying in mathematical creativity.
- Bahar, A. K., & Maker, C. J. (2011). Exploring the relationship between mathematical creativity and mathematical achievement. Asia-Pacific Journal of Gifted and Talented Education, 3(1), 33–48.
- Baran, G., Erdogan, S., & Çakmak, A. (2011). A study on the relationship between six-year-old children’s creativity and mathematical ability. International Education Studies, 4(1), 105–111.
- Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
- Chi, M. T., Glaser, R., & Farr, M. J. (1988). The nature of expertise. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Cramond, B., Matthews-Morgan, J., Bandalos, D., & Zuo, L. (2005). A report on the 40-year follow-up of the Torrance Tests of Creative Thinking: Alive and well in the new millennium. Gifted Child Quarterly, 49, 283–291. CrossRef
- Haylock, D. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18(1), 59–74. CrossRef
- Haylock, D. (1997). Recognizing mathematical creativity in schoolchildren. ZDM—The International Journal on Mathematics Education, 29(3), 68–74. CrossRef
- Hong, E., & Aqui, Y. (2004). Cognitive and motivational characteristics of adolescents gifted in mathematics: Comparisons among students with different types of giftedness. Gifted Child Quarterly, 48, 191–201. CrossRef
- Iowa Department of Education (1989). A guide to developing higher order thinking across the curriculum. Des Moines, IA: Department of Education. Retrieved from ERIC database (ED 306 550).
- Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
- Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the fifth conference of the European Society for Research in Mathematics Education—CERME-5 (pp. 2330–2339). http://ermeweb.free.fr/Cerme5.pdf. Accessed 17 Sep 2012.
- Leung, S. S., & Silver, E. A. (1997). The role of task format, mathematics knowledge and creative thinking on the arithmetic problem posing on prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 1–20. CrossRef
- Levav-Waynberg, A., & Leikin, R. (2009). Multiple solutions for a problem: A tool for evaluation of mathematical thinking in geometry. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of sixth conference of European Research in Mathematics Education (pp. 776–785). Lyon: Institut National de Recherche Pédagogique.
- Mann, E. (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students. Doctoral dissertation. http://www.gifted.uconn.edu/siegle/Dissertations/Eric%20Mann.pdf. Accessed 17 Sep 2012.
- Marcoulides, G. A., & Schumacker, R. E. (1996). Advanced capacity equation modelling: Issues and techniques. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Murphy, K. R., & Davidshofer, C. O. (2001). Psychological testing: Principles and application (5th ed.). Upper Saddle River, NJ: Prentice-Hall.
- Muthén, L. K., & Muthén, B. O. (1998). Mplus user’s guide. Los Angeles, CA: Muthén & Muthén.
- Nakakoji, K., Yamamoto, Y., & Ohira, M. (1999). A framework that supports collective creativity in design using visual images. In E. Edmonds & L. Candy (Eds.), Proceedings of the 3rd conference on creativity and cognition (pp. 166–173). New York: ACM Press. CrossRef
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
- Pehkonen, E. (1997). The state-of-the-art in mathematical creativity. ZDM—The International Journal on Mathematics Education, 29(3), 63–67. CrossRef
- Sak, U., & Maker, C. J. (2006). Developmental variations in children’s creative mathematical thinking as a function of schooling, age, and knowledge. Creativity Research Journal, 18(3), 279–291. CrossRef
- Sheffield, L. (2009). Developing mathematical creativity—questions may be the answer. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 87–100). Rotterdam: Sense Publishers.
- 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. CrossRef
- Silver, E. A. (1997). Fostering creativity though instruction rich mathematical problem solving and problem posing. International Reviews on Mathematical Education, 29(3), 75–80.
- 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.
- Starko, J. A. (1994). Creativity in the classroom. New York: Longman.
- Sternberg, R. J. (1999). Handbook of creativity. New York: Cambridge University Press.
- Sternberg, R. J. (2006). The nature of creativity. Creativity Research Journal, 18(1), 87–98. CrossRef
- Torrance, E. P. (1995). The ‘beyonders’ in why fly? A philosophy of creativity. Norwood, NJ: Ablex.
- Weisberg, R. W. (1999). Creativity and knowledge: A challenge to theories. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 226–250). Cambridge: Cambridge University Press.
- Weisberg, R. W. (2006). Expertise and reason in creative thinking: Evidence from case studies and the laboratory. In J. C. Kauffman & J. Baer (Eds.), Creativity and reason in cognitive development (pp. 7–42). New York: Cambridge University Press. CrossRef
- Connecting mathematical creativity to mathematical ability
Volume 45, Issue 2 , pp 167-181
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