The Extent of Mathematical Creativity and Aesthetics in Solving Problems among Students Attending the Mathematically Talented Youth Program

Author(s)
Einav Aizikovitsh-Udi

ABSTRACT

This study investigates the extent of mathematical creativity among 57 eight-grade talented students in the Mathematically Talented Youth Program. We examine the reasoning these students applied in solving a problem; the degree of mathematical creativity and aesthetic in their approach in solving a non-routine mathematical problem; and explore whether the students’ mathematical thinking is dependent solely upon previous mathematical knowledge and skills. We found that majority of the students relied on technical algorithm to solve the problem. Although talented students coped well with the thinking challenge, most of them operated at the basic level of creativity. One implication drawn from this study is the need to broaden and develop mathematical-logical thinking both as specific lessons and also as an integral part of other lessons in the program.

Cite this paper

Aizikovitsh-Udi, E. (2014) The Extent of Mathematical Creativity and Aesthetics in Solving Problems among Students Attending the Mathematically Talented Youth Program.*Creative Education*, **5**, 228-241. doi: 10.4236/ce.2014.54032.

Aizikovitsh-Udi, E. (2014) The Extent of Mathematical Creativity and Aesthetics in Solving Problems among Students Attending the Mathematically Talented Youth Program.

References

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http://cerme8.metu.edu.tr/wgpapers/WG7/WG7_Aizikovitsh_Udi.pdf

[2] Allan, S. D. (1991). Ability-Grouping Research Reviews: What Do You Say about Grouping and Gifted? Educational Leadership, 48, 60-65.

[3] Artzt, A. F., & Armour-Thomas, E. (1997). Mathematical Problem Solving in Small Groups: Exploring the Interplay of Students’ Metacognitive Behaviors, Perceptions, and Ability Levels. Journal of Mathematical Behavior, 16, 63-74.

http://dx.doi.org/10.1016/S0732-3123(97)90008-0

[4] Artzt, A. F., & Yaloz-Femia, S. (1999). Mathematical Reasoning during Small-Group Problem Solving. In L. V. Stiff, & F. R. Curcio (Eds.), Developing Mathematical Reasoning K-12 Yearbook (pp. 115-126). Reston, VA: National Council of Teachers of Mathematics.

[5] Binder, C. (1996). Behavioral Fluency: Evolution of a New Paradigm. The Behavior Analyst, 19, 163-197.

http://www.abainternational.org/TBA.asp

[6] Boyce, L. N., VanTassel-Baska, J., Burruss, J. D., Sher, B. T., & Johnson, D. T. (1997). A Problem-Based Curriculum: Parallel Learning Opportunities for Students and Teachers. Journal of the Education of the Gifted, 20, 363-379.

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[9] Chiu, M.-S. (2009). Approaches to the Teaching of Creative and Non-Creative Mathematical Problems. International Journal of Science and Mathematics Education, 7, 55-79.

http://dx.doi.org/10.1007/s10763-007-9112-9

[10] Dreyfus, T., & Eisenberg, T. (1986). On the Aesthetics of Mathematical Thought. For the Learning of Mathematics, 6, 2-10.

[11] Ervynck, G. (1991). Mathematical Creativity. In: D. Tall (Ed.), Advanced Mathematical Thinking (pp. 42-53). Dordrecht: Kluwer Academic.

[12] 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.

http://dx.doi.org/10.1177/001698620404800304

[13] Hwang, W. Y., Chen, N. S., Dung, J. J., & Yang, Y. L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving Using a Multimedia Whiteboard System. Educational Technology & Society, 10, 191-212.

[14] Kwon, O.-N., Park, J.-S., & Park, J.-H. (2006). Cultivating Divergent Thinking in Mathematics through an Open-Ended Approach. Asia Pacific Education Review, 7, 51-61.

http://dx.doi.org/10.1007/BF03036784

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http://dx.doi.org/10.1007/BF03217299

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http://www.informatik.unitrier.de/~ley/db/conf/candc/candc1999.html

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[25] Sinclair, N. (2004).The Role of the Aesthetics in Mathematical Inquiry. Mathematical Thinking and Learning, 6, 261-284.

http://dx.doi.org/10.1207/s15327833mtl0603_1

[26] 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.

[27] Shore, B. M., & Kanevsky, L. (1993). Thinking Processes: Being and Becoming Gifted. In K. A. Heller, F.J. Monks, & A. H. Passow (Eds.), International Handbook for Research and Development on Giftedness and Talent (pp. 133-148). London: Pergamon.

[28] Starko, J. A. (1994). Creativity in the Classroom. New York: Longman.

[29] Stepien, W. J., & Pike, S. L. (1997). Designing Problem-Based Learning Units. Journal for the Education of the Gifted, 20, 380-400.

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[31] The Technion Israel Institute of Technology (2005). Number 3 Unified Examination for Ninth Grade Students Studying Toward a 5-Point Matriculation Examination in the Program for Realizing Mathematical Excellence: 19 FILL IN Year Part 3 Enrichment. Haifa: The Technion Israel Institute of Technology.

[1] Aizikovitsh-Udi, E. (in Press). The Extent of Mathematical Creativity and Aesthetics in Solving Problems among Students Attending the Mathematically Talented Youth Program. Proceedings of the 2013 Conference for European Research in Mathematics Education (CERME-8). (To Be Published)

http://cerme8.metu.edu.tr/wgpapers/WG7/WG7_Aizikovitsh_Udi.pdf

[2] Allan, S. D. (1991). Ability-Grouping Research Reviews: What Do You Say about Grouping and Gifted? Educational Leadership, 48, 60-65.

[3] Artzt, A. F., & Armour-Thomas, E. (1997). Mathematical Problem Solving in Small Groups: Exploring the Interplay of Students’ Metacognitive Behaviors, Perceptions, and Ability Levels. Journal of Mathematical Behavior, 16, 63-74.

http://dx.doi.org/10.1016/S0732-3123(97)90008-0

[4] Artzt, A. F., & Yaloz-Femia, S. (1999). Mathematical Reasoning during Small-Group Problem Solving. In L. V. Stiff, & F. R. Curcio (Eds.), Developing Mathematical Reasoning K-12 Yearbook (pp. 115-126). Reston, VA: National Council of Teachers of Mathematics.

[5] Binder, C. (1996). Behavioral Fluency: Evolution of a New Paradigm. The Behavior Analyst, 19, 163-197.

http://www.abainternational.org/TBA.asp

[6] Boyce, L. N., VanTassel-Baska, J., Burruss, J. D., Sher, B. T., & Johnson, D. T. (1997). A Problem-Based Curriculum: Parallel Learning Opportunities for Students and Teachers. Journal of the Education of the Gifted, 20, 363-379.

[7] Bloom, B. S., et al. (1956). Taxonomy of Educational Objects: The Classification of Educational Goals, Vol. 1. London: Longman.

[8] Chamberlin, S. A., & Moon, S. (2005). Model-Eliciting Activities: An Introduction to Gifted Education. Journal of Secondary Gifted Education, 17, 37-47.

[9] Chiu, M.-S. (2009). Approaches to the Teaching of Creative and Non-Creative Mathematical Problems. International Journal of Science and Mathematics Education, 7, 55-79.

http://dx.doi.org/10.1007/s10763-007-9112-9

[10] Dreyfus, T., & Eisenberg, T. (1986). On the Aesthetics of Mathematical Thought. For the Learning of Mathematics, 6, 2-10.

[11] Ervynck, G. (1991). Mathematical Creativity. In: D. Tall (Ed.), Advanced Mathematical Thinking (pp. 42-53). Dordrecht: Kluwer Academic.

[12] 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.

http://dx.doi.org/10.1177/001698620404800304

[13] Hwang, W. Y., Chen, N. S., Dung, J. J., & Yang, Y. L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving Using a Multimedia Whiteboard System. Educational Technology & Society, 10, 191-212.

[14] Kwon, O.-N., Park, J.-S., & Park, J.-H. (2006). Cultivating Divergent Thinking in Mathematics through an Open-Ended Approach. Asia Pacific Education Review, 7, 51-61.

http://dx.doi.org/10.1007/BF03036784

[15] Lester, K. (1980). Research on Problem Solving. In: R. J. Shumway (Ed.), Research in Mathematics Education. Reston, VA: National Council of Teachers of Mathematics.

[16] Leung, S. S., & Silver, E. (1997). The Role of Task Format, Mathematics Knowledge, and Creative Thinking on the Arithmetic Problem Posing of Prospective Elementary School Teachers. Mathematics Education Research Journal, 9, 5-24.

http://dx.doi.org/10.1007/BF03217299

[17] Liljedahl, P., & Sriraman, B. (2006). Musings on Mathematical Creativity. For The Learning of Mathematics, 26, 20-23.

[18] Mann, E. L. (2006). Creativity: The Essence of Mathematics. Journal for the Education of the Gifted, 30, 236-262.

[19] Meissner, H. (2000). Creativity in Mathematics Education. The Meeting of the International Congress on Mathematics Education, Tokyo, Japan.

[20] National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

[21] 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 & Cognition (pp. 166-173). New York: ACM Press.

http://www.informatik.unitrier.de/~ley/db/conf/candc/candc1999.html

[22] Polya, G. (1957). How to Solve It: A New Aspect of Mathematical Method (2nd ed.) Princeton, NJ: Princeton University Press.

[23] Polya, G. (1968). Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving. New York: Wiley.

[24] Silver, E. (1997). Fostering Creativity through Instruction Rich in Mathematical Problem Solving and Problem Posing. ZDM, 3, 75-80. http://dx.doi.org/10.1007/s11858-997-0003-x

[25] Sinclair, N. (2004).The Role of the Aesthetics in Mathematical Inquiry. Mathematical Thinking and Learning, 6, 261-284.

http://dx.doi.org/10.1207/s15327833mtl0603_1

[26] 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.

[27] Shore, B. M., & Kanevsky, L. (1993). Thinking Processes: Being and Becoming Gifted. In K. A. Heller, F.J. Monks, & A. H. Passow (Eds.), International Handbook for Research and Development on Giftedness and Talent (pp. 133-148). London: Pergamon.

[28] Starko, J. A. (1994). Creativity in the Classroom. New York: Longman.

[29] Stepien, W. J., & Pike, S. L. (1997). Designing Problem-Based Learning Units. Journal for the Education of the Gifted, 20, 380-400.

[30] Sternberg, R. J., & Ben-Zeev, T. (1996). The Nature of Mathematical Thinking (335p). New York: Lawrence Erlbaum Assoc.

[31] The Technion Israel Institute of Technology (2005). Number 3 Unified Examination for Ninth Grade Students Studying Toward a 5-Point Matriculation Examination in the Program for Realizing Mathematical Excellence: 19 FILL IN Year Part 3 Enrichment. Haifa: The Technion Israel Institute of Technology.