An Investigation of the Complexity of the Problems Posed by Prospective Teachers: The Case of Whole Number

Abstract

The aim of this case study is to examine the linguistic and mathematical complexity of the problems that prospective primary school teachers posed related to four operations with whole numbers. A Problem Posing Questionnaire was administered to 64 participants and semi-structured interviews were conducted with 20 of 64 participants. The data was analyzed through frequency analysis and descriptive analysis. The findings of the study revealed that many prospective teachers posed problems based on the single-statement problem root, without any relation/condition. That is, the linguistic complexity of the problems written by the prospective teachers is in the lowest level which is regarded as assignment category, regardless of the complexity of the problem situation. Furthermore, if the problem situations do not contain any relationship, then many prospective teachers had preferred to pose one-step problems. On the other hand, when the information in the problem situation is related to each other, then they were able to pose multi-step problems which could be regarded as complex problems in terms of mathematically. It can be concluded that although the complexity of the problem situation given to the prospective teachers does not affect the linguistic complexity of the problems they pose; it affects the mathematical complexity.

Keywords

• Problem posing
• linguistic complexity
• mathematical complexity
• whole numbers
• prospective primary school teachers

Project Number

2018/010

Sınıf Öğretmeni Adaylarının Kurdukları Problemlerin Karmaşıklığının İncelenmesi: Doğal Sayılar Örneği

Abstract

Bu durum çalışmasının amacı, sınıf öğretmeni adaylarının doğal sayılarda dört işlemle ilgili kurdukları problemlerin dilsel ve matematiksel karmaşıklığını incelemektir. 64 katılımcıya Problem Kurma Anketi uygulanmış ve 64 katılımcıdan 20'si ile yarı yapılandırılmış görüşmeler yapılmıştır. Veriler frekans analizi ve betimsel analiz yoluyla analiz edilmiştir. Araştırmanın bulguları, birçok öğretmen adayının herhangi bir ilişki/koşul olmaksızın tek ifadeli problem köküne dayalı problemler kurduklarını ortaya koymuştur. Yani öğretmen adayları tarafından yazılan problemlerin dilsel karmaşıklığı, problem durumunun karmaşıklığına bakılmaksızın, ödev kategorisi olarak kabul edilen en düşük düzeydedir. Ayrıca problem durumları herhangi bir ilişki içermiyorsa birçok öğretmen adayı tek adımlı problemler kurmayı tercih etmiştir. Öte yandan, problem durumundaki bilgiler birbiriyle ilişkili olduğunda matematiksel olarak karmaşık problemler olarak kabul edilebilecek çok adımlı problemler kurabilmişlerdir. Öğretmen adaylarına verilen problem durumunun karmaşıklığı, oluşturdukları problemlerin dilsel karmaşıklığını etkilemese de; matematiksel karmaşıklığı etkilemektedir.

Keywords

• Problem kurma
• dilsel karmaşıklık
• matematiksel karmaşıklık
• doğal sayılar
• ilkokul öğretmen adayları

Supporting Institution

Kırıkkale Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi

Project Number

2018/010

References

1. Abu-Elwan, R. (1999). The development of mathematical problem posing abilities for prospective middle school teachers. In proceedings of the International conference on Mathematical Education into the 21st Century: Social challenges, Issues and approaches (Vol. 2, pp. 1-8).
2. Albayrak, M., Ipek, A. S., & Isik, C. (2006). Problem designing-solving studies in teaching of basic operation skills. Erzincan University Journal of Education Faculty, 8 (2), 1-11.
3. Australian Education Council, Curriculum Corporation (Australia). (1991). A national statement on mathematics for Australian schools: A joint project of the states, territories and the Commonwealth of Australia/initiated by the Australian Education Council. Carlton, Vic: Curriculum Corporation for the Australian Education Council.
4. Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466.
5. Brown, S. I., & Walter, M. I. (1993). Problem posing: Reflections and applications. Hillsdale, NJ: Erlbaum.
6. Chapman, O. (2002). Belief structure and in-service high school mathematics teacher growth. In Beliefs: A Hidden Variable in Mathematics Education? (pp. 177-193). Springer, Dordrecht.
7. Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149-158.
8. Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395-415.

9. Creswell, J. W. (2007). Qualitative inquiry & research design: Choosing among five approaches (2nd ed.). Thousand Oaks, CA: Sage.
10. Creswell, J. W., & Clark, V. L. P. (2007). Designing and conducting mixed methods research.Thousand Oaks, CA: SAGE.
11. English, L. D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1) 83-106.
12. Isik, C., Isik, A. & Kar, T. (2011). Analysis of the problems related to verbal and visual representations posed by pre-service mathematics teachers. Pamukkale University Journal of Education,30(30), 39-49.
13. Kilic, C. (2013). Prospective primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22(4), 677-686.
14. Korkmaz, E., & Gur, H. (2006). Determining of prospective teachers’ problem posing abilities. Journal of Balikesir University Institute of Science and Technology, 8(1), 64–74.
15. Lin, P. J. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students' mathematical learning. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 3, pp. 257-2644). Norway: Bergen.
16. Mayer, R. E., Lewis, A. B., & Hegarty, M. (1992). Mathematical misunderstandings: Qualitative reasoning about quantitative problems. In J. I. D. Campbell (Ed.), The nature and origins of mathematical abilities (pp.137–154). Amsterdam: Elsevier.
17. Milli Eğitim Bakanlığı [Ministry of National Education] (MoNE) (2017). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Primary and middle school grades 1 to 8]. Ankara, Turkey: Author.
18. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA.
19. National Council of Teachers of Mathematics [NCTM]. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
20. Ngah, N., Ismail, Z., Tasir, Z., & Mohamad Said, M. N. H. (2016). Students’ ability in free, semi-structured and structured problem posing situations. Advanced Science Letters, 22(12), 4205-4208. Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education,20(4), 338-355.
21. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
22. Silver, E. A. & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education,27(5), 521-539.
23. Stoyanova, E. (2003). Extending students' understanding of mathematics via problem posing. Australian Mathematics Teacher, 59(2), 32-40.
24. Strauss, A., & Corbin, J. M. (1990), Basics of qualitative research: Grounded theory procedures and techniques. Thousand Oaks: Sage.
25. Tekin-Sitrava, R., & Isik, A. (2018). An investigation into prospective primary school teachers’ free problem posing skills. Gazi University Journal of Gazi Educational Faculty, 38(3), 919-947.
26. Ticha, M., & Hošpesova, A. (2009, January). Problem posing and development of pedagogical content knowledge in prospective teacher training. In meeting of CERME (Vol. 6, pp. 1941-1950).
27. Van Harpen, X. Y., & Sriraman, B. (2012). Creativity and mathematical problem posing: An analysis of high school students’ mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201-221.
28. Yin, R.K. (2003). Case study research: Design and methods. Thousand Oaks, CA: SAGE.
29. Yüksek Öğretim Kurumu [Higher Education Institution (HEI)]. (YÖK) (2007). Eğitim fakültesi öğretmen yetiştirme lisans programları. [Education faculty teacher education degree programs]. Ankara, Turkey: HEI.
30. Wilson, S. M., & Berne, J. (1999). Teacher Learning and the Acquisition of Professional Knowledge: An Examination of Research on Contemporary Professional Development. Review of Research in Education, 24(1), 173-209.