Yaratıcı Problem Çözme Sürecinde Analojik ve Seçici Düşünme: Seçici Problem Çözme Modelinin Matematik Eğitiminde Uygulama Örneği

Öz

Sıra dışı ve etkileyici çözümler üretme, orijinal problemler oluşturma ya da var olan problemleri farklı bir bakış açısı ile yeniden tasarlama matematikte yaratıcı olan öğrencilerden beklenilen temel beceriler olarak değerlendirilebilir. Bu becerilerin geliştirilmesinde yaratıcı problem çözme süreçleri ön plana çıkmaktadır. Yaratıcı problem çözme bir dizi algoritmik işlemin uygulanmasından öte orijinal düşünmeyi gerektiren bir eylem olarak tanımlanabilir. Problem çözme sürecine yönelik birçok yaklaşım olduğu gibi yaratıcılık için önemli görülen analojik düşünme ve seçici düşünme becerilerinin önemi araştırmacılar tarafından vurgulanmaktadır. Bu çalışmada yeni bir yaratıcı problem çözme modeli olan, matematiksel yaratıcılık eğitimi için önerilen Seçici Problem Çözme (SPÇ) modeli incelenmiştir. Bu doğrultuda alan yazın taraması yöntemi kullanılmıştır. Modelin yapısı ve işleyişi bir matematik problemi uygulama örneği ile ayrıntılı olarak açıklanmıştır. SPÇ modeli matematiksel yaratıcılığın gelişimi için önemli görülen problem çözme, problem oluşturma, seçici düşünme ve analojik düşünme becerilerini geliştirmeyi hedefleyen bir yaratıcı problem çözme modelidir.

Anahtar Kelimeler

• matematiksel yaratıcılık
• analojik düşünme
• seçici düşünme
• yaratıcı problem çözme
• Seçici Problem Çözme Modeli

Analogical and Selective Thinking in Creative Problem Solving Process: The Use of Selective Problem Solving Model in Mathematics Education

Öz

Creating unusual and insightful solutions to a given problem, construction original problems or reformulation an old problem with a new perspective can be evaluated as basic skills expected from students who are creative in mathematics. Creative problem-solving processes come to the fore in the development of these skills. Creative problem solving can be defined as an action that requires original thinking rather than applying a series of algorithmic operations. As there are many approaches to the problem-solving process, the importance of analogical thinking and selective thinking, which are considered important for creativity, is emphasized by the researchers. In this study, the Selective Problem Solving (SPS) model, which is a new creative problem-solving model, proposed for mathematical creativity education was reviewed. The structure and functioning of the model is examined in detail with an example of a math problem. SPS model is a creative problem-solving model aims to develop problem solving, problem posing, selective thinking and analogical thinking skills that are considered important for the development of mathematical creativity.

Anahtar Kelimeler

• mathematical creativity
• analogical thinking
• selective thinking
• creative problem solving
• selective problem-solving model.

Kaynakça

1. Bal-Sezerel, B., & Sak, U. (2013). The selective problem solving model (SPS) and its social validity in solving mathematical problems. The International Journal of Creativity and Problem Solving, 23(1), 71-87.
2. Bassok, M. (2003). Analogical transfer in problem solving. In J. E. Davidson ve R.J. Sternberg (Eds), The psychology of problem solving (pp. 343-369). UK: Cambridge University Press.
3. Bernardo, A. B. (2001). Analogical problem construction and transfer in mathematical problem solving. Educational Psychology, 21(2), 137-150.
4. Chen, Z. (1996). Children's analogical problem solving: The effects of superficial, structural, and procedural similarity. Journal of Experimental Child Psychology, 62(3), 410-431.
5. Chiu, M. S. (2009). Approaches to the teaching of creative and non- creative mathematical problems. International Journal of Science and Mathematics Education,7(1), 55–79.
6. Davidson, J.E. (1986). The role of insight in giftedness. In R.J. Sternberg, & J.E. Davidson (Eds.), Conceptions of giftedness. Cambridge, UK: Cambridge University Press.
7. Davidson, J. E., and Sternberg, R. J. (1984). The role of insight in intellectual giftedness. Gifted Child Quarterly, 28(2), 58-64.
8. Endardini, U. (2017). Pengaruh model pembelajaran selective problem solving (sps) terhadap kemampuan higher order thinking skill dan disposisi matematika. (Unpublished master’s thesis). Fakultas Ilmu Tarbiyah dan Keguruan, Jakartha.

9. English, L. (1997). Analogies, metaphors, and images: vehicles for mathematical reasoning. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 191–220). Mahwah, NJ: Lawrence Erlbaum Associates Inc.
10. Ferguson, R. W. (1994). MAGI: Analogy-based encoding using regularity and symmetry. In Proceedings of the 16th annual conference of the cognitive science society (pp. 283-288).
11. Gentner, D. (1998). Analogy. In W. Bechtel, & G. Graham (Eds), A companion to cognitive science (pp. 107-113). Malden, MA, USA: Blackwell Publication.
12. Gentner, D., & Gentner, D. R. (1983). Flowing waters or teaming crowd: Mental models of electricity. In D. Gentner, & A. L., Ès Stevens (Eds.), Mental Models. (pp. 99-129). Lawrence Erlbaum, Hillsdale.
13. Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology, 95(2), 393-408
14. Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12(3), 306-355.
15. Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1–38
16. Gorodetsky, M., & Klavir, R. (2003). What can we learn from how gifted/average pupils describe their processes of problem solving?. Learning and Instruction, 13(3), 305-325.
17. Harrison, A. G., & Treagust, D. F. (2006). Teaching and learning with analogies. In P.J. Aubusson, A. G. Harrison, & S. M. Ritchie (Eds), Metaphor and analogy in science education (pp. 11-24). Dordrecht: Springer.
18. Haylock, D. W. (1997). Recognising mathematical creativity in schoollchildren. ZDM, 29(3), 68-74.
19. Karabacak, F., & Kirişçi, N. (2019). A Comparison of Gifted and non-Gifted Students’ Satisfaction about the Use of Selective Problem Solving Model in Mathematics. Turkish Journal of Giftedness and Education, 9(2), 131-144.
20. Kılıç, A., & Ayas, M. B. (2017). Fen bilimlerinde analojik ve seçici düşünme: Seçici problem çözme modelinin fen bilimlerine uyarlanması. Turkish Journal of Giftedness and Education, 7(2), 127-140.
21. Kirişçi, N. (2019). Seçici problem çözme modeli’nin yaratıcılık becerileri üzerindeki etkisinin ortaokul matematik dersinde incelenmesi. Yayımlanmamış Doktora Tezi, Eskişehir: Anadolu Üniversitesi.
22. Klavir, R., & Gorodetsky, K. (2011). Features of creativity as expressed in the construction of new analogical problems by intellectually gifted students. Creative Education, 2(3), 164-173.
23. Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago: University of Chicago Press. Loewenstein, J., Thompson, L., & Gentner, D. (1999). Analogical encoding facilitates knowledge transfer in negotiation. Psychonomic Bulletin & Review, 6(4), 586-597.
24. Novick, L. R., & Holyoak, K. J. (1991). Mathematical problem solving by analogy. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17(3), 398-415.
25. Pambudiarso, R. B., Mariani, S., & Prabowo, A. (2016). Komparasi kemampuan pemecahan masalah materi geometri antara model SPS dan model sps dengan hands on activity. Kreano, Jurnal Matematika Kreatif-Inovatif, 7(1), 1-9.
26. Polya, G. (1957). How to solve it. (2nd ed.). New Jersey: Princeton University Press.
27. Richland, L. E., & McDonough, I. M. (2010). Learning by analogy: Discriminating between potential analogs. Contemporary Educational Psychology, 35(1), 28-43.
28. Richland, L. E., Holyoak, K. J., & Stigler, J. W. (2004). Analogy use in eighth-grade mathematics classrooms. Cognition and Instruction, 22(1), 37-60.
29. Sak, U. (2011). Selective Problem Solving (SPS): A Model for teaching creative problem-solving. Gifted Education International, 27(3), 349-357.
30. Schank, R. C. (1982). Dynamic memory. Cambridge: Cambridge University Press.
31. Schwartz, L. S., & Baer, D. M. (1991). Social validity assessments: Is current practice state of the art? Journal of Applied Behavior Analysis, 24(2), 189-204.
32. Sheffield, L. J. (2013). Creativity and school mathematics: some modest observations. ZDM, 45(2), 325-332.
33. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. The International Journal on Mathematical Education, 29(3), 75–80.
34. Sriraman, B., Yaftian, N., & Lee, K. H. (2011). Mathematical creativity and mathematics education: A derivative of existing research. In The elements of creativity and giftedness in mathematics (pp. 119-130). Brill Sense.
35. Threlfall, J., & Hargreaves, M. (2008). The problem‐solving methods of mathematically gifted and older average‐attaining students. High Ability Studies, 19(1), 83-98.
36. Vosniadou, S. (1989). Analogical reasoning as a mechanism in knowledge acquisition: A developmental perspective. In S. Vosniadou, & A. Ortony (Eds), Similarity and Analogical Reasoning (pp. 413-437). Cambridge: Cambridge University Press.
37. Wong, S. S. H., Ng, G. J. P., Tempel, T., & Lim, S. W. H. (2019). Retrieval practice enhances analogical problem solving. The Journal of Experimental Education, 87(1), 128-138.
38. Zaenuri, Z., Nastiti, P. A., & Suhito, S. (2019). Mathematical creative thinking ability based on students’ characteristics of thinking style through selective problem solving learning model with ethnomatematics nuanced. Unnes Journal of Mathematics Education, 8(1), 49-5.