### DEVELOPING A MODEL TO EXPLAIN THE MATHEMATICAL CREATIVITY OF GIFTED STUDENTS

#### Abstract

The aim of this study is to investigate the relationships among students’ mathematics self-efficacy, their metacognitive skills in mathematics and their mathematics achievement in relation to their mathematical creativity. The study’s sample consisted of 445 gifted and talented middle school students who attended grades 5, 6, 7, and 8 at 13 Science and Art Centers in 11 cities. For such a correlational study, Mathematics Self-efficacy Scale, Mathematical Creativity Scale, Young Pupils’ Metacognitive Abilities in Mathematics Scale were used. The research findings indicated that mathematical creativity is significantly correlated with mathematical achievement, mathematical metacognition skills and self-efficacy in mathematics, including the three sub-dimensions of self-efficacy, positive self-efficacy, negative self-efficacy and self-efficacy in the use of mathematics in daily tasks. Because the adaptive values of the model are within reasonable boundaries, the model can be regarded as valid. The research model suggests that students’ mathematical creativity is significantly predicted by mathematics self-efficacy, mathematical achievement and mathematical metacognition skills.

** Article visualizations:**

#### Keywords

#### References

Airasian, P., Gay, L. R., & Mills, G. E. (2000). Educational research: Competencies for analysis and applications. Upper SaddleRiver, NJ:Prentice Hall.

Akgül, S. (2014). Üstün yetenekli öğrencilerin matematik yaratıcılıklarını açıklamaya yönelik bir model geliştirilmesi [A model study to examine gifted and talented students’ mathematical creativity]. Doctoral dissertation. Istanbul University, Istanbul, Turkey.

Akgül, S. & Kahveci, N. G. (2016). A study on the development of a mathematics creativity scale. Eurasian Journal of Educational Research, 62, 57-76.doi: 10.14689/ejer.2016.62.5

Balka, D. S. (1974). The development of an instrument to measure creative ability in mathematics. Dissertation Abstracts International, 36, 98. (UMI No. AAT 7515965).

Bandura, A. (1997). Self-efficacy: The exercise of control. New York, NY: W.H. Freeman.

Banghart, F. W., & Spraker, H. S. (1963). Group influence on creativity in mathematics. Journal of Experimental Education, 31, 257-263. doi:10.1080/00220973.1963.11010773

Baykul, Y. (1999). İlkögretimde matematik ögretimi [Elemantary and middle school mathematics education] (3rd ed.). Ankara, Turkey: Anı Yayıncılık.

Benbow, C. E. (1988). Sex differences in mathematical reasoning ability in intellectually talented preadolescents: Their nature, effects, and possible causes. Behavioral and Brain Sciences, 11, 169-232. doi:10.1017/S0140525X00049244

Büyüköztürk, Ş. (2015). Sosyal bilimler için veri analizi el kitabı: İstatistik, araştırma deseni, SPSS uygulamaları ve yorum (Gözden geçirilmiş yirmi birinci baskı). [Handbook of data analysis for social sciences: Statistics, research design, SPSS and comments] Ankara: Pegem Yayıncılık.

Carr, M., Alexander, J., & Folds-Bennett, T. (1994). Metacognition and mathematics strategy use. Applied Cognitive Psychology, 8, 583-595. doi:10.1002/acp.2350080605

Clark, B. (2012). Growing up gifted (8th ed). Upper Saddle River, NJ: Pearson-Merrill-Prentice Hall.

Coleman, L. J. (1995). The power of specialized educational environments in the development of giftedness: The need for research on social context. Gifted Child Quarterly, 39, 171-176. doi:10.1177/001698629503900307

Cornoldi, D. L. C. (1997). Mathematics and metacognition: What is the nature of the relationship? Mathematical Cognition, 3, 121-139. doi:10.1080/135467997387443

Dai, D. Y. (2004). A comparison of gender differences in academic self-concept and motivation between high-ability and average Chinese adolescents. The Journal of Secondary Gifted Education, 13, 22-32. doi:10.4219/jsge-2001-361

Downing, K. J. (2009). Self-efficacy and metacognitive development. The International Journal of Learning, 16(4). 185-189.

Hacker, D. J. (1998). Definition and empirical foundations. Metacognition in Educational Theory and Practise. ed. Douglas J Hacker, John Dunlosky, Arthur C Graesser. ABD: Lawrence Erlbaum Associates, Publishers: 1-23

Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self-efficacy/mathematics performance correspondence. Journal for Research in Mathematics Education, 20, 261-273. doi:10.2307/749515

Hadamard, J. (1945). The psychology of invention in the mathematical field. Princeton, NJ: Princeton University Press.

Halmos, P. R. (1968). Mathematics as a creative art. American Scientist, 56, 375-389.

Halpern, D. F., Benbow, C. P., Geary, D. C., Gur, R., Hyde, J. S., & Gernsbacher, M. A. (2007). The science of sex differences in science and mathematics. Psychological Science in the Public Interest, 8, 1-51. doi:10.1111/j.1529-1006.2007.00032.x

Hammouri, H. (2004). Attitudinal and motivational variables related to mathematics achievement in Jordan: findings from the Third International Mathematics and Science Study (TIMSS). Educational Research, 46, 241-257. doi:10.1080/0013188042000277313

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 (3), 191-201.

Jacobse, A. E., & Harskamp, E. G. (2009). Student-controlled metacognitive training for solving word problems in primary school mathematics. Educational Research and Evaluation, 15, 447-463. doi:10.1080/13803610903444519

Jensen, L. R. (1973). The relationships among mathematical creativity, numerical aptitude and mathematical achievement. Dissertation Abstracts International, 34, 2168. (UMI No AAT 7326021).

Junge, M. E., & Dretzke, B. J. (1995). Mathematical self-efficacy: Gender differences in gifted/talented adolescents. Gifted Child Quarterly, 39, 22-28. doi:10.1177/001698629503900104

Kahveci, N. G., & Akgül, S. (2014) Gifted and talented students’ perceptions on their schooling: A survey study. Gifted and Talented International, 29,79-91.doi:10.1080/15332276.2014.11678431

Karnes, F. A., & Wherry, J. N. (1981). Self-concepts of gifted students as measured by the Piers-Harris Children’s Self-Concept Scale. Psychological Reports, 49, 903-906.doi:10.2466/pr0.1981.49.3.903

Kelly, R., & Colangelo, N. (1984). Academic and social self-concepts of gifted, general, and special students. Exceptional Children, 50, 551-554.doi:10.1177/001440298405000612

Kerr, B., & Gagliardi, C. (2003). Measuring creativity in research and practice.

Laskey, M. L., & Hetzel, C. J. (2010). Self-regulated learning, metacognition, and soft skills: The 21st century learner. Retrieved from http://eric.ed.gov/?id=ED511589

Leikin, R. & Pitta- Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM, 45(2), 159-166.

Livne, N. L., & Milgram, R. M. (2006). Academic versus creative abilities in mathematics: Two components the same construct? Creative Research Journal, 18, 192-212. doi:10.1207/s15326934crj1802_6

Lubinski, D., & Benbow, C. P. (1992). Gender differences in abilities and preferences among the gifted: Implications for the math/science pipeline. Current Directions in Psychological Science, 1, 61-66. doi:10.1111/1467-8721.ep11509746

Lucas, R. E. (1988). On the mechanics of economic development. Journal of Monetary Economics, 22, 25-50. doi:10.1016/0304-3932(88)90168-7

Maker, C. J. (1982). Teaching models in education of the gifted. Rockville, MD: Aspen Systems Corp.

Malpass, J. R., O’Neil, H. F., & Hocevar, D. (1999). Self-regulation, goal orientation, self-efficacy, worry and high stakes math achievement for mathematically gifted high school students. Roeper Review, 21, 281-288.doi:10.1080/02783199909553976

Maier, S. R., & Curtin,P. (2005). Self-efficacy theory: A prescriptive model for teaching research methods. Journalism and Mass Communication Educator, 59, 351-364.http://dx.doi.org/10.1177/107769580405900405

Mann, E. L. (2005). Mathematical creativity and school mathematics: indicators of mathematical creativity in middle school students (Doctoral dissertation). University of Connecticut, Mansfield, CT.

Mann, E. L. (2009). The search for mathematical creativity: Identifying creative potential in middle school mathematics. Creativity Research Journal,21, 338-348.

Monette, D.R., Sullivan, T.J., & De Jong, C.R. (1990). Applied social research. New York, NY: Harcourt Brace Jovanovich.

Moores, T. T., Chang, J. C. J., &Smith, D. K. (2006). Clarifying the role of self-efficacy and metacognition as predictors of performance: Construct development and test. Databases for Advances in Information Systems, 37, 125-132. doi:10.1145/1161345.1161360

Muir, A. (1988). The psychology of mathematical creativity. The Mathematical Intelligence, 10, 33-37. doi:10.1007/BF03023849

Nelson, L. L. (2012). The effectiveness of metacognitive strategies on 8th grade students in mathematical achievements and problem solving skills (Doctoral dissertation).Southern University and A & M College, Baton Rouge, LA.

Özcan, Z. Ç. (2010). The construct validity of the scale of young pupils’ metacognitive abilities in mathematics. Procedia Social and Behavioral Sciences, 2, 2997-3002.

Ozsoy, G., & Ataman, A. (2009). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2). Retrieved from http://files.eric.ed.gov/fulltext/ED508334.pdf

Pajares, F. (1996). Self-efficacy beliefs and mathematical problem-solving of gifted students. Contemporary Educational Psychology, 21, 325-344. doi:10.1006/ceps.1996.0025

Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86, 193-203. doi:10.1037/0022-0663.86.2.193

Panoura, A. and Philippou, G. (2005). The measurement of young pupils’ metacognitive ability in mathematics: the case of self-representation end self-evaluation. Sant-Feliu-de-Guixols: CERME 4.

Pehkonen, E. (1997). The state-of-art in mathematical creativity. ZDM Mathematics Education, 29 (3), 63-67.

Pintrich, P. R. (1999). The role of motivation in promoting and sustaining self-regulated learning. International Journal of Educational Research, 31,459-470. doi:10.1016/S0883-0355(99)00015-4

Pintrich, P. R., & De Groot, E. V. (1990). Motivational and self-regulated learning components of classroom academic performance. Journal of Educational Psychology, 82, 33-40. doi:10.1037/0022-0663.82.1.33

Pintrich, P. R., & Garcia, T. (1991). Student goal orientation and self-regulation in the college classroom. In M. L. Maehr & P. R. Pintrich(Eds.), Advances in motivation and achievement: Goals and self-regulatory processes(vol.7,pp.371-402). Greenwich, CT: JAI Press.

Pitta-Pantazi, D., Christou, C., Kontoyianni, K., & Kattou, M. (2011). A model of mathematical giftedness: Integrating natural, creative, and mathematical abilities. Canadian Journal of Science, Mathematics and Technology Education, 11, 39-54. doi:10.1080/14926156.2011.548900

Singh, B. (1985). Change in some characteristics of teacher behaviour and its effect on pupil creativity. Indian Journal of Applied Psychology, 22, 31-35.

SPSS Inc. (2010). SPSS 19.0 Computer software. Chicago. IL: Author.

Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, 17, 20-36.

Sternberg, R. J. (1996). What is mathematical thinking? The nature of mathematical thinking, 303-318.

Sternberg, R. J., Kaufman, J.C., & Grigorenko, E. L. (2008). Applied intelligence. New York, NY: Cambridge University Press.

Tuna, Y. (2003). Kalkınma planlarında yükseköğretim [Higher Education in the development plan]. Milli Eğitim Dergisi, 160.

Türkiye Büyük Millet Meclisi. (2006, July 1). Dokuzuncu Kalkınma Planı 2007-2013 [The strategy of the Ninth Development Plan 2077-2013]. T. C. Resmi Gazete, 26215.

Usher, E. L. (2009). Sources of middle school students’ self-efficacy in mathematics: A qualitative investigation. American Educational Research Journal, 46, 275-314.

Usiskin, Z. (2000). The development into the mathematically talented. Journal of Secondary Gifted Education, 11, 152-162.

Williams, J. E. (1998). Self-concept-performance congruence: An exploration of patterns among high-achieving adolescents. Journal for the Education of the Gifted, 21, 415-422.

Wolters, C., & Pintrich, P.R. (1998). Contextual differences in student motivation and self-regulated learning in mathematics, English, and social studies classroom. Instructional Science, 26, 27-47.

Yabaş, D. (2008). Farklılaştırılmış öğretim programının öğrencilerin özyeterlik algıları, biliş-üstü becerileri ve akademik başarılarına etkisinin incelenmesi[The effects of differentiated instructional design on students’ self-efficacy beliefs, metacognitive skills and academic achievement]. Yüksek Lisans Tezi. Yıldız Teknik Üniversitesi, Istanbul, Turkey.

Yi, M. Y., & Davis, F. D. (2003). Developing and validating an observational learning model of computer software training and skill acquisition. Information Systems Research, 14, 146-169. doi:10.1287/isre.14.2.146.16016

DOI: http://dx.doi.org/10.46827/ejes.v0i0.868

### Refbacks

- There are currently no refbacks.

Copyright (c) 2018 Savaş Akgül, Nihat Gürel Kahveci

This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2015-2018. **European Journal of Education Studies** (ISSN 2501 - 1111) is a registered trademark of **Open Access Publishing Group**. All rights reserved.

This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).