An Investigation of Sixth Grade Students' Skills of Solving and Posing Problems Which Require Using the Knowledge of Order of Operations

Abstract

The aim of this research is to examine sixth grade students’ skills of solving and posing problems which require using the knowledge of the order of operations to solve. The case study design, one of the qualitative research methods, was adopted in the research. The study group consisted of 44 sixth grade students attending a public secondary school in Eskisehir. Within the scope of the application, the forms including the questions to measure their problem solving and posing skills were directed to the study group. The data were analyzed by thematic analysis method. According to the results obtained, it was found that while most of the students were successful in solving problems which require the knowledge of the order of operations, they were not successful in posing such type of problems. In addition, it was found that students made mistakes in Turkish language grammar and expressions and in using the mathematical language. Students made mathematical terminology mistakes generally in subtraction and division operations. As a result, it is recommended to increase the problem posing and order of operations activities in mathematics lessons.

Keywords

• mathematics education
• sixth grade students
• four basic operations
• order of operations
• problem solving
• problem posing.

References

1. Akben, N. (2020). Effects of the problem-posing approach on students’ problem solving skills and metacognitive awareness in science education. Research in Science Education, 50(3), 1143-1165.
2. Amini, A., Gabriel, S., Lin, P., Koncel-Kedziorski, R., Choi, Y., & Hajishirzi, H. (2019). MathQA: Towards interpretable math word problem solving with operation-based formalisms. arXiv preprint arXiv:1905.13319.
3. Andrade Medeiros, A. M., & Muniz, C. A. (2022). Mathematical learning difficulties: a subjective production. The Mathematics Enthusiast, 19(1), 28-54.
4. Barwell, R. (2020). Language background in mathematics education. Encyclopedia of mathematics education, 441-447.
5. Blando, J. A., Kelly, A. E., Schneider, B. R., & Sleeman, D. (1989). Analyzing and modeling arithmetic errors. Journal of Research in Mathematics Education, 20(3), 301-308.
6. Boyatzis, R. E. (1998). Transforming qualitative information: Thematic analysis and code development. London and New Delhi: Sage Publications.
7. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101.
8. Bunar, N. (2011). Altıncı sınıf öğrencilerinin kümeler, kesirler ve dört işlem konularında problem kurma ve çözme becerileri (Yayınlanmamış yüksek lisans tezi). Afyon Kocatepe Üniversitesi, Sosyal Bilimler Enstitüsü, Afyon.

9. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401-421.
10. Cai, J., & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 101391.
11. Carroll, W. M., & Isaacs, A. (2020). Achievement of students using the university of Chicago school mathematics project’s Everyday Mathematics. In Standards-based school mathematics curricula (pp. 79-108). Routledge.
12. Chen, T., & Cai, J. (2020). An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition. International Journal of Educational Research, 102, 101420.
13. Chinn, S. (2020). The trouble with maths: A practical guide to helping learners with numeracy difficulties. Routledge.
14. Çetinkaya, A. ve Soybaş, D. (2018). İlköğretim 8. sınıf öğrencilerinin problem kurma becerilerinin incelenmesi. Kuramsal Eğitimbilim Dergisi, 11(1), 169-200.
15. Deringöl, Y. (2020). Problem posing activities in primary school mathematics textbooks. Ilkogretim Online, 19(3).
16. Dinç, B. (2018). Yedinci sınıf öğrencilerinin gerçek yaşam durumlarına uygun problem kurma becerilerinin incelenmesi (Yayınlanmamış yüksek lisans tezi). Eskişehir Osmangazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Eskişehir.
17. Dogan-Coskun, S. (2019). The Analysis of the Problems Posed by Pre-Service Elementary Teachers for the Addition of Fractions. International Journal of Instruction, 12(1), 1517-1532. https://doi.org/10.29333/iji.2019.12197a
18. Ekinci, O. ve Bal, A. P. (2019). 2018 yılı liseye geçiş sınavı (LGS) matematik sorularının öğrenme alanları ve yenilenmiş Bloom taksonomisi bağlamında değerlendirilmesi. Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi, 7(3), 9-18.
19. English, L. (1997a) Promoting a problem-posing classroom, Teaching Children Mathematics, 3, 172-179.
20. Ev Çimen, E. ve Yıldız, Ş. (2018). Altıncı sınıf öğrencilerinin sütun grafiğine uygun problem kurma becerilerinin incelenmesi. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 48, 325-354.
21. Gökkurt, B. Örnek T., Hayat, F. ve Soylu, Y. (2015). Öğrencilerin problem çözme ve problem kurma becerilerinin değerlendirilmesi. Bartın Üniversitesi Eğitim Fakültesi Dergisi, 4(2), 751-774.
22. Holt, K. J. (2021). The Impact of STEM Integrated Instruction on Elementary Student Outcomes in Reading and Mathematics (Doctoral dissertation, Trevecca Nazarene University).
23. Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243.
24. Işık, C., Kar, T., Işık, A. ve Albayrak, M. (2012). İlköğretim 6. sınıf öğrencilerinin doğal sayılarda kalanlı bölme işlemine yönelik problem kurma ve çözme becerilerinin araştırılması. 11. Ulusal Sınıf Öğretmenliği Eğitimi Sempozyumu’nda sunulan bildiri, Rize.
25. Keşan, C., Kaya, D. ve Güvercin, S. (2010). The effect of problem posing approach to the gifted student’s mathematical abilities. International Online Journal of Educational Science, 2(3), 677-687.
26. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A.H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp. 123-148). Hillsdale, NJ: Lawrence Erlbau.
27. Korkmaz, E. ve Gür, H. (2006). Öğretmen adaylarının problem kurma becerilerinin belirlenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8(1), 65-74.
28. Li, X., Song, N., Hwang, S., & Cai, J. (2020). Learning to teach mathematics through problem posing: Teachers’ beliefs and performance on problem posing. Educational Studies in Mathematics, 105(3), 325-347.
29. Milli Eğitim Bakanlığı [MEB]. (2005). İlköğretim matematik dersi (6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB Basımevi.
30. Milli Eğitim Bakanlığı [MEB]. (2009). Ortaokul matematik dersi (6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB Basımevi.
31. Millî Eğitim Bakanlığı [MEB]. (2018). Matematik dersi (1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB Basımevi.
32. Millî Eğitim Bakanlığı [MEB]. (2018). Matematik dersi (1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB Basımevi.
33. National Council of Teachers of Mathematics [NCTM] (2000). Principles and standarts for school mathematics. Reston, VA20191-1502.
34. Özsoy, G. (2005). Problem çözme becerisi ile matematik başarısı arasındaki ilişki. Gazi Eğitim Fakültesi Dergisi, 25(3), 179-190.
35. Pietsch, J. (2020). Teaching and learning mathematics together: Bringing collaboration to the centre of the mathematics classroom. Cambridge Scholars Publishing.
36. Darhim, Prabawanto, S., & Susilo, B. E. (2020). The Effect of Problem-based Learning and Mathematical Problem Posing in Improving Student’s Critical Thinking Skills. International Journal of Instruction, 13(4), 103-116. https://doi.org/10.29333/iji.2020.1347a
37. Putra, H. D., Herman, T., & Sumarmo, U. (2020). The Impact of Scientific Approach and What-If-Not Strategy Utilization towards Students' Mathematical Problem Posing Ability. International Journal of Instruction, 13(1), 669-684. https://doi.org/10.29333/iji.2020.13143a
38. Putri, A. L., Lukito, A., & Wijayanti, P. (2020, February). Students’ specializing in mathematics problem solving. In Journal of Physics: Conference Series (Vol. 1470, No. 1, p. 012075). IOP Publishing.
39. Rashidov, A. S. (2020). Development of creative and working with information competences of students in mathematics. European Journal of Research and Reflection in Educational Sciences, 8(3).
40. Renatovna, A. G., & Renatovna, A. S. (2021). Pedagogical and psychological conditions of preparing students for social relations on the basis of the development of critical thinking. Psychology and Education Journal, 58(2), 4889-4902.
41. Russo, J., & Minas, M. (2020). Student Attitudes Towards Learning Mathematics Through Challenging, Problem Solving Tasks:“It’s so Hardin a Good Way”. International Electronic Journal of Elementary Education, 13(2), 215-225.
42. Sullivan, P. (2020). Leading Improvement in Mathematics Teaching and Learning. ACER Press.
43. Şengül-Akdemir, T. ve Türnüklü, E. (2017). Ortaokul 6. sınıf öğrencilerinin açılar ile ilgili problem kurma süreçlerinin incelenmesi. International Journal of New Trends in Arts, Sports and Science Education, 6(2), 17-39.
44. Tabak, S. (2019). 6th, 7th and 8th grade students’ misconceptions about the order of operations. International Journal of Educational Methodology, 5(3), 363-373. https://doi.org/10.12973/ijem.5.3.363.
45. Tertemiz, N. I. (2017). İlkokul öğrencilerinin dört işlem becerisine dayalı kurdukları problemlerin incelenmesi. Journal of Turkish Educational Sciences, 15(1), 1-25.
46. Tulaev, B., Daminov, O., Khakimov, J., & Turdiev, J. (2020). Developing competencies in the development of information and communication technologies. Journal of critical reviews. ISSN-2394-5125, 7(2), 296-298.
47. Türnüklü, E., Aydoğdu, M. Z. ve Ergin, A. S. (2017). 8. sınıf öğrencilerinin üçgenler konusunda problem kurma çalışmalarının incelenmesi. Bayburt Eğitim Fakültesi Dergisi, 12(24), 467-486.
48. Ulu, M. (2011). İlköğretim 5. sınıf öğrencilerinin rutin olmayan problemlerde yaptıkları hataların belirlenmesi ve giderilmesine yönelik bir uygulama (Yayınlanmamış doktora tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
49. Voica, C., Singer, F. M., & Stan, E. (2020). How are motivation and self-efficacy interacting in problem-solving and problem-posing?. Educational Studies in Mathematics, 105(3), 487-517.
50. Yenilmez, K. ve Çoksöyler, A. (2018) Altıncı sınıf öğrencilerinin işlem önceliği konusunda karşılaştığı zorluklar. Eğitim ve Öğretim Araştırmaları Dergisi, 7(2), 155-166.
51. Yıldırım, A. ve Şimşek, H. (2011). Sosyal bilimlerde nitel araştırma yöntemleri (8. Baskı). Ankara: Seçkin Yayıncılık.
52. Yin, R. K. (2017). Durum çalışması araştırması uygulamaları. (Çev. Günbayı, I.), 3.Baskıdan Çeviri, Ankara: Nobel Yayınları.
53. Zulnaidi, H., Heleni, S., & Syafri, M. (2021). Effects of SSCS Teaching Model on Students’ Mathematical Problem-solving Ability and Self-efficacy. International Journal of Instruction, 14(1). https://doi.org/10.29333/iji.2021.14128a