Investigation of Secondary School Students' Strategies for Solving Routine and Non-Routine Problems

Abstract

The aim of this study is to determine the situations of secondary school students in solving routine and non-routine problems and the strategies they use while solving these problems. The research is in the survey model. The sample of the study consists of 430 students studying in the 6th, 7th and 8th grades of two official secondary schools by homogeneous sampling, one of the purposeful sampling methods. Routine and non-routine problem test and problem evaluation rubric were used as data collection tools in the study. As a result of the research, it was concluded that students were more successful in routine problems and that students mostly used arithmetic strategies in solving routine and non-routine problems. In addition, it was revealed that students used the equation strategy in solving routine problems, and the guess and check strategy in solving non-routine problems. As a result of the study, it was revealed that non-routine problems should be included more in the classroom and in the textbooks in mathematics lessons. In addition, it was concluded that students never used drawing, make a list, logical reasoning strategies in the process of problem solving, but never using the strategies of find a pattern, elimination, and working backwards.

Keywords

• Routine problem
• ,non routine problem
• problem solving strategies
• mathematics
• secondary school students

Ortaokul Öğrencilerinin Rutin ve Rutin Olmayan Problemleri Çözme Stratejilerinin İncelenmesi

Abstract

Bu araştırmanın amacı, ortaokul öğrencilerinin rutin ve rutin olmayan problemleri çözme durumlarını ve bu problemleri çözerken kullandıkları stratejileri belirlemektir. Araştırma tarama modelindedir. Araştırmanın örneklemini, amaçlı örnekleme yöntemlerinden homojen örnekleme ile belirlenen 6., 7. ve 8. sınıflarında öğrenim görmekte olan toplam 430 öğrenci oluşturmaktadır. Araştırmada veri toplama aracı olarak rutin ve rutin olmayan problem testi ve problem değerlendirme rubriği kullanılmıştır. Araştırmada öğrencilerin rutin problemlerde daha başarılı oldukları ve öğrencilerin rutin ve ve rutin olmayan problemlerin çözümünde en çok aritmetiksel strateji kullandıkları sonucuna ulaşılmıştır. Ayrıca rutin problemlerin çözümünde öğrencilerin denklem kurma stratejisini kullanırken rutin olmayan problemlerin çözümünde ise tahmin kontrol stratejisini kullandıkları ortaya çıkmıştır. Çalışmanın sonucunda matematik derslerinde rutin olmayan problemlere sınıf içerisinde ve ders kitaplarında daha fazla yer verilmesi gerekliliği ortaya çıkmıştır. Ayrıca öğrencilerin çizim yapma, sistematik liste yapma, mantıksal akıl yürütme stratejilerini problem çözme sürecinde kullanmakla beraber bağıntı bulma, eleme ve geriye doğru çalışma stratejilerini hiç kullanmadıkları sonucuna ulaşılmıştır.

Keywords

• Rutin problem
• rutin olmayan problem
• problem çözme stratejileri
• matematik,
• ortaokul öğrencileri

References

1. Altun, M. (2015). Ortaokullarda 5, 6, 7 ve 8. sınıflarda matematik öğretimi [Teaching mathematics in 5th, 6th, 7th and 8th grades in secondary schools]. Alfa Aktüel Yayınları.
2. Altun, M. Memnun, D. S. (2008). Mathematics teacher trainees’ skills and opinions on solving non-routine mathematical problems. Journal of Theory and Practice in Education, 4(2), 213-238.
3. Altun, M., Memnun, D. S., & Yazgan, Y. (2007). Primary school teacher trainees’ skills and opinions on solving non-routine mathematical problems. Elementary Education Online, 6(1), 127-143.
4. Anderson, J. (2009). Mathematics curriculum development and the role of problem solving. ACSA Conference. Retrieved from ://acsa.edu.au/pages/images/judy%20anderson%20-%20mathematics% 20curriculum%20development.
5. Andrade R.R, Fortes, E. C. ve Mabilangan R. A. (2020). Problem solving heuristics and mathematical abilities of heterogeneous learners. Universal Journal of Educational Research, 8(11), 5114-5126.
6. Arslan, C. ve Yazgan, Y. (2015). Common and flexible use of mathematical non routine problem solving strategies. American Journal of Educational Research, 3(12), 1519-1523.
7. Artut, P. D. ve Tarım, K. (2006). Investigation of elementary school students' level of solving non-routine verbal problems, solution strategies and error types. Cukurova University Journal of Social Sciences Institute, 15(2), 39-50.
8. Atay, H. (2017). Ortaokul öğrencilerinin problem çözmede çözüm stratejileri kullanma becerilerinin incelenmesi [Examination of middle school students' skills of using solution strategies in problem solving]. Master Thesis, Akdeniz University, Antalya.

9. Avcu, S. (2012). An investigation of prospective elementary mathematics teachers’strategies used in mathematical problem solving. Master Thesis, Orta Doğu Teknik University, Ankara.
10. Baykul, Y. (2019). Ortaokulda matematik öğretimi (5-8. sınıflar) [Teaching mathematics in secondary school (5th-8th grades)]. Ankara: Pegem Akademi.
11. Biddlecomb, B. & Carr, M. (2011). A longitudinal study of the development of mathematics strategies and underlying counting schemes. International Journal of Science and Mathematics Education, 9(1), 1-24. doi: 10.1007/s10763-010- 9202y.
12. Blum, W. & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects state, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68.
13. Bozkurt, A. & Topal, A. (2019). Investigation of middle school 6th grade students' mathematical thoughts on problems that can be solved with a standard algorithm. International Journal of Educational Studies in Mathematics, 6(2), 44-59.
14. Cai, J. (2000). Mathematical Thinking Involved in U.S. and Chinese Students’Solving of Process-Constrained and Process-Open Problems. Mathematical Thinking and Learning, 2(4), 309–340.
15. Demir, G. (2019). 8. sınıf öğrencilerinin kullandıkları problem çözme stratejileri ve problem çözme sürecinde karşılaştıkları hatalar [Problem solving strategies used by 8th grade students and the mistakes they encountered in the problem solving process]. Master Thesis, Uşak University, Uşak.
16. Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41,605-618.
17. Fan, L. & Zhu, Y. (2007). Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks. Educ Stud Math, 66, 61–75.
18. Fong, H. K. & Hsui, V. (1999). Strategy preferences and their association with hierarchical difficulties of fraction problems. Science, Mathematics and Technical Education, 5, 3–12.
19. Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). New York: McGram-Hill Companies.
20. Fülöp E. (2015). Teaching problem-solving strategies in mathematics. LUMAT, 3(1):37– 54.
21. Gür, H. & Hangül, T. (2015). A study on problem solving strategies of middle school students. Pegem Journal of Education and Instruction, 5(1), 95-112.
22. Gürbüz, R., & Güder, Y. (2016). Strategies used by math teachers in problem solving. Ahi Evran University Kırşehir Eğitim Fakültesi Dergisi, 17(2), 371-386.
23. Gürsan, S. & Yazgan, Y. (2020). Non-routine problem-solving skills of ninth grade students: An experimental study. Academy Journal of Educational Sciences, 4(1), 23-29.
24. IBM Corp. (2017).IBM SPSS Statistics for Windows. IBM Corp.
25. Karakoca, A. (2011). Altıncı sınıf öğrencilerinin problem çözmede matematiksel düşünmeyi kullanma durumları [Sixth grade students' use of mathematical thinking in problem solving]. Master Thesis, Eskişehir Osmangazi University, Eskişehir.
26. Laterell, C. M. (2013). What is problem solving ability? Retrieved from http://www.lamath.org/journal/Vol1/What_IS_P_S_Ability.pdf
27. Lee, J. & Kim, K. (2005). Elementary school teacher candidates’ perception of good problems. IUMPST: The Journal 1. Retrieved from http://www.k-12prep.math.ttu.edu/journal/contentkno wledge/lee01/article.pdf
28. Mayer, R. E. & Hegarty, M. (1996). The process of understanding mathematical problem solving. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 29–54). Mahwah, NJ: Erlbaum.
29. Miles, M, B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded Sourcebook. (2nd ed). Thousand Oaks, CA: Sage
30. Milli Eğitim Bakanlığı [MEB] (2009). İlköğretim matematik dersi 6-8. sınıflar öğretim programı ve kılavuzu [Elementary math lesson 6th - 8th grades curriculum and guide]. Talim ve Terbiye Başkanlığı. Milli Eğitim Bakanlığı [MEB] (2019a). Ortaöğretim kurumları yönetmeliği [Secondary education institutions regulation]. MEB Yayınları.
31. Mogari D. & Chirove M. (2017). Comparing grades 10–12 mathematics learners’ non- routine problem solving. EURASIA Journal of Mathematics Science and Technology Education, 13(8), 4523-4551.
32. Morgan, C. T. (1995). Psikolojiye giriş (10. basım). Hacettepe University Psikoloji Bölümü Yayınları.
33. Olkun, S. & Toluk Uçar, Z. (2003). İlköğretimde etkinlik temelli matematik öğretimi [Activity-based mathematics teaching in primary education]. Anı Yayıncılık.
34. Özdamar, K. (2013). Paket programlar ile istatistiksel veri analizi [Statistical data analysis with package programs]. 1. Kaan Kitabevi.
35. Patton, M. (2014). Nitel araştırma ve değerlendirme yöntemleri [Qualitative research and evaluation methods]. Ankara: Pegem Akademi.
36. Polya, G. (1957). How to solve it: A new aspect of mathematical methos. Anchor Books
37. Posamentier, A. S. & Krulik, S. (2008). Problem solving strategies for efficient and elegant solutions, grades 6-12. A resource for the mathematics teachers. Corwin Press Inc.
38. Reusser, K., & Stebler, R. (1997). Every word problem has a solution the social rationality of mathematical modeling in schools. Learning and Instruction, 7(4), 309-3
39. Sappaile, B. I. & Djam’an, N. (2017). The Influence of problem-solving methods on students’ mathematics learning outcomes. Global Journal of Engineering Education, 19(3), 267-272.
40. Saygılı, S. (2017). Examining the problem solving skills and the strategies used by high school students in solving non-routine problems. E-International Journal of Educational Research, 8(2), 91-114.
41. Schroeder, T L, & Lester, F K. (1989). Developing understanding in mathematics via problem solving. In P.R. Trafton (Eds) New directions for elementary school mathematics, (pp 31-42) Reston, VA: NCTM.
42. Schunk, D. H. (2012). Learning theories: An educational perspective (Sixth Edition). New York: Prentice Hall.
43. Sita Pramayudi A. A. A., Sudiarta IGP ve Astawa IWP (2020). Classification of students’ non-routine problem solving skills. Journal of Physics: Conference Series. doi:10.1088/1742-6596/1503/1/012016
44. Tabachnick, B. G. & Fidell, L. S. (2013). Using multivariate statiscs (sixth ed.). Boston: Pearson.
45. Taşkın, D., Aydın, F., Akşan, E. & Güven, B. (2012). Investigation of the relationship between secondary school students' perceptions of belief and self-efficacy towards problem solving and their success in routine and non-routine problems. E-Journal of New World Sciences Academy, 7(1), 50-61.
46. Türk Dil Kurumu (TDK) (2020). Güncel Türkçe Sözlük [Current Turkish Dictionary]. Retrieved from http://www.tdk.gov.tr.
47. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Pearson.
48. Yazgan, Y., & Arslan, Ç. (2019). Matematiksel sıradışı problem çözme stratejileri ve örnekleri [Mathematical unusual problem solving strategies and examples]. Pegem Akademi.
49. Yıldırım, A., Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences]. Seçkin Yayınları.
50. Yılmaz, R. (2019). Strategies used by prospective classroom teachers in problem solving: routine problem solving situations. Kastamonu Education Journal, 27(1), 85-94.