Creativity and Giftedness pp 225-238 | Cite as

# The Interplay Between Excellence in School Mathematics and General Giftedness: Focusing on Mathematical Creativity

## Abstract

Observation that the interrelations between mathematical creativity, mathematical expertise and general giftedness are vague is what motivated a large-scale study that explores the relationship between mathematical creativity and mathematical ability. The study employs Multiple Solution Tasks (MSTs) as a tool for the evaluation of mathematical creativity in high-school students. We discuss the links between mathematical creativity, excellence in school mathematics and general giftedness as reflected in an empirical study of senior high-school students in Israel, which implemented the MST tool. The study demonstrated that between-group differences are task-dependent and are a function of mathematical insight integrated in the mathematical task.

## Keywords

Mathematical creativity Multiple Solution Tasks (MST) General giftedness Excellence in mathematics## Notes

### Acknowledgments

This project was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the author(s) and do not necessarily reflect the views of the John Templeton Foundation. We extend our thanks to the Foundation and to the Israeli Ministry of Education and the University of Haifa for their generous financial support to this project.

## References

- Davis, G., & Rimm, S. (2004).
*Education of the gifted and talented*(5th ed.). Needham Heights: Allyn & Bacon.Google Scholar - Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.),
*Advanced mathematical thinking*(pp. 42–53). Dordrecht: Kluwer.Google Scholar - Geary, D. C., & Brown, S. C. (1991). Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children.
*Developmental Psychology, 27*, 398–406.CrossRefGoogle Scholar - Guberman, R., & Leikin, R. (2012). Interest and difficulty: Changes in teachers’ views of multiple solution tasks.
*Journal of Mathematics Teacher Education, 16*(1), 33–56.CrossRefGoogle Scholar - Krutetskii, V. A. (1976).
*The psychology of mathematical abilities in schoolchildren*. Translated from Russian by J. Teller; edited by J. Kilpatrick and I. Wirszup. Chicago: The University of Chicago Press.Google Scholar - 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). (CD-ROM and on-line.) http://ermeweb.free.fr/Cerme5.pdf. Accessed 4 Sept 2012. - Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.),
*Creativity in mathematics and the education of gifted students*(pp. 129–145). Rotterdam: Sense Publishers.Google Scholar - Leikin, R. (2013). Evaluating mathematical creativity: The interplay between multiplicity and insight.
*Psychological Test and Assessment Modeling, 55*(4), 385–400.Google Scholar - 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*(2), 183–197.CrossRefGoogle Scholar - Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art.
*ZDM – The International Journal on Mathematics Education, 45*(2), 159–166.CrossRefGoogle Scholar - Leikin, M., Waisman, I., Shaul, S., & Leikin, R. (2014a). Brain activity associated with translation from a visual to a symbolic representation in algebra and geometry.
*Integrative Neoro-Science, 13*(1), 35–59.CrossRefGoogle Scholar - Leikin, R., Leikin, M., Lev, M., Paz, N., & Waisman, I. (2014b). On the relationships between mathematical creativity, excellence and giftedness. In S. Oesterle & D. Allan (Eds.),
*Post-proceedings of the 2013 annual conference of the Canadian Mathematics Education Study Group (CMESG)*. Burnaby: CMESG/GCEDM.Google Scholar - Leikin, R., Paz-Baruch, N., & Leikin, M. (2014c). Cognitive characteristics of students with superior performance in mathematics.
*Journal of Individual Differences, 35*(3), 119–129.CrossRefGoogle Scholar - Levav-Waynberg, A., & Leikin, R. (2012a). The role of multiple solution tasks in developing knowledge and creativity in geometry.
*Journal of Mathematical Behavior, 31*, 73–90.CrossRefGoogle Scholar - Levav-Waynberg, A., & Leikin, R. (2012b). Using multiple solution tasks for the evaluation of students’ problem-solving performance in geometry.
*Canadian Journal of Science, Mathematics, and Technology Education, 12*(4), 311–333.CrossRefGoogle Scholar - Marland, S. P., Jr. (1972). Education of the gifted and talented: Report to the Congress of the United States by the U.S. Commissioner of Education and background papers submitted to the U.S. Office of Education, 2 vols. Washington, DC: U.S. Government Printing Office.Google Scholar
- Paz-Baruch, N., Leikin, M., Aharon-Peretz, J., & Leikin, R. (2014). Speed of information processing in generally gifted and excelling in mathematics adolescents.
*High Abilities Studies, 25*(2), 143–167.CrossRefGoogle Scholar - Piirto, J. (1999). Identification of creativity. In J. Piirto (Ed.),
*Talented children and adults: Their development and education*(pp. 136–184). Upper Saddle River: Prentice Hall.Google Scholar - Polya, G. (1973).
*How to solve it: A new aspect of mathematical method*. Princeton: Princeton University Press.Google Scholar - Raven, J., Raven, J. C., & Court, J. H. (2000).
*Manual for Raven’s progressive matrices and vocabulary scales*. Oxford: Oxford Psychologists.Google Scholar - Renzulli, J. (1978). What makes giftedness? Re-examining a definition.
*Phi Delta Kappan, 60*, 180–184, 261.Google Scholar - Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing.
*ZDM – The International Journal on Mathematical Education, 29*(3), 75–80.CrossRefGoogle Scholar - 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 - Torrance, E. P. (1974).
*Torrance tests of creative thinking*. Bensenville: Scholastic Testing Service.Google Scholar - Vygotsky, L. S. (1930/1984). Imagination and creativity in adolescent. In D. B. Elkonin (Ed.),
*The collected works of L. S. Vygotsky*(Child psychology, Vol. 4, pp. 199–219). Moscow: Pedagogika. (In Russian).Google Scholar - Waisman, I., Leikin, M., Shaul, S., & Leikin, R. (2014). Brain activity associated with translation between graphical and symbolic representations of functions in generally gifted and excelling in mathematics adolescents.
*International Journal of Science and Mathematics Education, 12*(3), 669–696.CrossRefGoogle Scholar - Zohar, A. (1990).
*Mathematical reasoning ability: Its structure, and some aspects of its genetic*17*transmission*. Unpublished doctoral dissertation, Hebrew University, JerusalemGoogle Scholar