Creative Problem Posing: Analysis of the Problems Posed Towards Different Strategies by Prospective Mathematics Teachers

Abstract

The purpose of this study is to analyze problems posed by prospective elementary mathematics teachers of towards different strategies in scope of creativity. Participants of the study are 36 prospective teachers, who take the course of “Problem Solving Strategies”. In this course they study problem-solving strategies. At the end of the course, they were asked to pose three problems suitable for the strategies. Each participant posed a total of 27 problems with three problems for each 9 problem-solving strategies. Problems posed by participants were analyzed in terms of the indicators of fluency, flexibility and originality and chi-square independence test was applied so as to determine whether the creativity of problem posing depends on the strategies. It was seen that fluency had the highest average among all strategies excluding the conscious guessing and control strategy. It was seen that the drawing strategy had the highest average among the strategies in scope of flexibility and the conscious guess and control strategy had the highest average among the strategies in scope of originality. Also it as seen that participants’ creativity levels for various strategies are usually high, and in some cases in the higher echelons of the medium category. This small variation is found to be statistically significant.

Keywords

• problem posing
• problem solving strategies
• creativity
• mathematical creativity

Yaratıcı Problem Kurma: Matematik Öğretmeni Adaylarının Farklı Stratejilere Yönelik Kurdukları Problemlerin Analizi

Abstract

Bu çalışmanın amacı, ilköğretim matematik öğretmeni adaylarının farklı stratejilere yönelik kurdukları problemlerin yaratıcılık bağlamında incelenmesidir. Araştırmanın katılımcıları “Problem Çözme Stratejileri” dersini alan 36 öğretmen adayıdır. Bu ders kapsamında problem çözme stratejilerine yönelik eğitim verilmektedir. Dersin sonunda katılımcılardan stratejilere uygun üçer problem kurmaları istenmiştir. Bu bağlamda her katılımcı, ele alınan 9 problem çözme stratejisinin her biri için üç problem olmak üzere toplam 27 problem kurmuştur. Katılımcıların kurdukları problemler akıcılık, esneklik ve özgünlük göstergeleri açısından analiz edilmiş ve problem kurma yaratıcılığının stratejilere bağlı olup olmadığını belirlemek için ki-kare bağımsızlık testi uygulanmıştır. Çalışma sonunda, esneklik bağlamında en yüksek ortalamaya sahip stratejinin çizim yapma stratejisi olduğu, özgünlük bağlamında ise en yüksek ortalamaya sahip stratejinin bilinçli tahmin ve kontrol stratejisi olduğu görülmüştür. Ayrıca, katılımcıların çeşitli stratejilere yönelik problem kurma yaratıcılıklarının genel olarak iyi düzeyde olduğu, bazı stratejiler için ise yüksek düzeyden az farkla orta düzeyde olduğu görülmüştür. Bu küçük varyasyon ise istatistiksel olarak anlamlı bulunmuştur.

Keywords

• problem kurma
• problem çözme stratejileri
• yaratıcılık
• matematiksel yaratıcılık

References

1. Akgül, S. (2014). Üstün yetenekli öğrencilerin matematik yaratıcılıklarını açıklamaya yönelik bir model geliştirilmesi [A model study to examine gifted and talented students’ mathematical creativity]. Doctorate Dissertation, İstanbul University.
2. Amaral, N. and Carreira, S. (2012). An essay on students’ creativity in problem solving beyond school: Proposing a framework of analysis. In Pre-Proceedings of the International Congress on Mathematical Education (ICME 12) 8-15 July 2012 (pp. 1584-1593).
3. Arıkan, E. (2013). İlköğretim 2. sınıf öğrencilerinin matematiksel problem kurma becerilerinin incelenmesi [The analysis of mathematical problem posing skill of elementary second grade Students]. Amasya Education Journal, 2(2), 305-325.
4. Balka, D. S. (1974). The development of an instrument to measure creative ability in mathematics. Ph.D. Thesis, University of Missouri, Columbia.
5. Baltacı, S., Yıldız, A. & Güven, B. (2014). Knowledge types used by eighth grade gifted students while solving problems. Bolema: Boletim de Educação Matemática, 28(50), 1032-1055.
6. Charles, R., & Lester, F. (1982). Teaching problem solving: What, why & how. Dale Seymour Publications.
7. Cildir, S. & Sezen, N. (2011). Skill levels of prospective physics teachers on problem posing. Hacettepe University Journal of Education, 40(40), 105-116.
8. Collins, A., Brown, J.S., & Newman, S.E. (1989). Cognitive apprenticeship: teaching the crafts of reading, writing, and mathematics. In L. B. Resnick (Ed.), Knowing, learning and instruction: Essays in honor of Robert Glaser (pp. 453–491). Lawrence Erlbaum Associates.

9. Çeker, F., & Çimen, E. E. (2017). Ortaokul matematik öğretmenlerinin problem çözme stratejilerine ilişkin görüşleri [Secondary school mathematics teachers’ opinions about problem solving strategies]. Journal of Education in Eskisehir Osmangazi University Turkic World Apply and Research Center, 2(1), 44-60.
10. Daher, W. & Anabousy, A. (2018). Creativity of pre-service teachers in problem posing. EURASIA Journal of Mathematics, Science and Technology Education, 14(7), 2929-2945.
11. Elias MJ., & Weissberg R.P. (2000). Primary prevention: educational approaches to enhance social and emotional learning. The Journal of School Health, 70(5), 186-190.
12. English, L. D. (1997). The development of fifth grade children’s problem posing abilities. Educational Studies in Mathematics. 34(1), 183–217.
13. English, L. D., Fox, J. L. & Watters, J. J. (2005). Problem posing and solving with mathematical modeling. Teaching Children Mathematics, 12(3), 156–163.
14. Ersoy, E. & Başer, N. E. (2009). İlköğretim 6. sınıf öğrencilerinin yaratıcı düşünme düzeyleri [The creatıve thınkıng levels of students at sixth class of prımary education]. The Journal of International Social Research, 2(9), 128-137.
15. Guilford, J. P. (1967). The nature of human intelligence. McGraw-Hill.
16. Gür, H., & Hangül, T. (2015). A study on secondary school students' problem solving strategies [A study on secondary school students’ problem solving strategies]. Pegem Journal of Education and Instruction, 5(1), 95-112.
17. Haavold, P. Ø. (2013). What are the characteristics of mathematical creativity? An emprical and theorical investigation of mathematical creativity? Doctorate Dissertation. University of Tromso.
18. Intaros, P., Inprasitha, M., & Srisawadi, N. (2014). Students’ problem solving strategies in problem solving-mathematics classroom. Procedia-Social and Behavioral Sciences, 116, 4119-4123.
19. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp.123–147). Lawrence Erlbaum Associates.
20. 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). Sense Publishers.
21. Leikin, R., & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In Proceedings of the 31st International Conference for the Psychology of Mathematics Education 8-13 July 2007 (Vol.3, pp.161– 168).
22. Leung, S.S. (2013). Teachers implementing mathematical problem posing in the classroom: challenges and strategies. Educational Studies in Mathematics, 83(1), 103-116. https://doi.org/10.1007/s10649-012-9436-4.
23. Mestre, J., P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. Applied Developmental Psychology, 3, 9–50.
24. Ministry of National Education. (2018). Matematik dersi öğretim programı (1.-8. sınıflar)[Mathematics curriculum: 1-8. Grades]. Devlet Kitapları Müdürlüğü.
25. National Council of Teachers of Mathematics, (2000). Principles and standards for school mathematics. Reston.
26. Özcan, F. M. (2005). İlköğretim 6-7-8. sınıf öğrencilerinin problem çözme stratejileri ve matematiksel modellemenin problem çözmedeki yeri ve önemi [The strategies of problem solving and the role and the importance of mathematical modelling inside these strategies in 2nd level (6th, 7th, 8th) Classes İn Primary Education]. Master’s Thesis, Dokuz Eylül University.
27. Partnership for 21st Century Skills (2009). Curriculum and instruction: A 21st century skills implementation guide. http://www.p21.org/storage/documents/p21- stateimp_curriculuminstruction.pdf
28. Pásztor, A., Molnár, G., & Csapó, B. (2015). Technology-based assessment of creativity in educational context: the case of divergent thinking and its relation to mathematical achievement. Thinking Skills and Creativity, 18, 32-42. https://doi.org/10.1016/j.tsc.2015.05.004.
29. Posamentier, A. S. & Krulik, S. (1998). Problem-solving strategies for efficient and elegant solutions: A Researce for the Mathematics Teacher. Corwin Press.
30. Schoenfeld, A.H. (1985). Mathematical problem solving. Academic Press.
31. Shriki, A. (2013). A model for assessing the development of students’ creativity in the context of problem posing. Creative Education, 4(7), 430-439. doi: 10.4236/ce.2013.47062.
32. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM—The International Journal on Mathematics Education, 29(3), 75–80.
33. Sing, R. R. (1991). Education for the twenty first century: Asia-Pacific perspectives. UNESCO Principal Regional Office for Asia and the Pacific.
34. Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? The Journal of Secondary Gifted Education, 17(1), 20–36.
35. Stoyanova, E. (2003). Extending students’ understanding of mathematics via problem posing. The Australian Mathematics Teacher, 59(2), 32-40.
36. Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australia.
37. Taşkın, D. (2016). Üstün yetenekli tanısı konulmuş ve konulmamış öğrencilerin matematikte yaratıcılıklarının incelenmesi: Bir özel durum çalışması [An analysis of the creativity of the students who assigned as gifted and the students who are not assigned as gifted in mathematics: A case study]. Doctorate Dissertation, Karadeniz Technical University.
38. Torrance, E. P. (1968). A longitudinal examination of the fourth grade slump in creativity. Gifted Child Quarterly, 12(4), 195-199.
39. Yıldız, A., Baltacı, S., Kurak, Y. & Güven, B. (2012). Üstün yetenekli ve üstün yetenekli olmayan 8. sınıf öğrencilerinin problem çözme stratejilerini kullanma durumlarının incelenmesi [Examining the usage of problem-solving strategies by the eighth grade gifted and non-gifted students]. Journal of Uludağ University Faculty of Education, 25(1), 123-143.