ORTAOKUL MATEMATİK ÖĞRETMENLERİNİN KESİRLERLE ÇIKARMA İŞLEMİNE YÖNELİK PROBLEM KURMA BECERİLERİNİN İNCELENMESİ

Öz

Bu araştırmada, ortaokul matematik öğretmenlerinin kesirlerle çıkarma işlemine yönelik kurdukları problemlerdeki hataların ve bu hatalara yönelik görüşlerinin belirlenmesi amaçlanmıştır. Araştırma, Erzurum merkezde görev yapan yedi ortaokul matematik öğretmeniyle yürütülmüştür. Kesirlerle çıkarma işlemine yönelik hazırlanan Problem Kurma Testi ve öğretmenlerle yürütülen odak-grup görüşme sürecinin video kayıtları, veri toplama araçlarını oluşturmuştur. Öğretmenlerin kurdukları problemlerde sekiz hata türü tespit edilmiştir. Kurulan problemlerde, kesir sayılarının farklı bütünler üzerinden ifade edilmesi, parça-bütün ilişkisini kuramama ve birim kargaşası şeklindeki hatalar ön plana çıkarılmıştır. Bunun yanında öğretmenlerin hatalara yönelik yaptıkları açıklamalarda farklı hatalar sergiledikleri de tespit edilmiştir.

Anahtar Kelimeler

• Ortaokul matematik öğretmenleri,kesirlerle çıkarma işlemi,problem kurma

Investigating Middle School Mathematics Teachers’ Problem Posing Ability in the Context of Subtraction Operation with Fractions

Öz

In this study, it was aimed to determine the errors posed by middle school mathematics teachers for the subtraction operation with fractions and their opinions about these errors. The study was conducted with seven middle school mathematics teachers working in the city center of Erzurum province. The Problem Posing Test (PPT) prepared for subtraction operations with fractions and the video records of the focus group interviews used as data collection tools. Eight types of errors were determined in the problems posed. The most frequent error types made by middle school mathematics teachers are as follows: expressing the fractions over the different wholes, failure in establishing part-whole relation and confusion about units. Additionally middle school mathematics teachers made different errors in explaining the errors.

Anahtar Kelimeler

• Middle school mathematics teachers,subtraction operation with fractions,problem posing

Kaynakça

1. Akay, H. (2006). Problem kurma yaklaşımı ile yapılan matematik öğretiminin öğrencilerin akademik başarısı, problem çözme becerisi ve yaratıcılığı üzerindeki etkisinin incelenmesi (Yayınlanmamış doktora tezi). Gazi Üniversitesi, Ankara.
2. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
3. Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. Handbook of research on teaching, 4, 433-456.
4. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401– 421.
5. Cankoy, O., & Darbaz, S. (2010). Effect of a problem posing based problem solving instruction on understanding problem. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 38, 11-24.
6. Capraro, M. M., & Joffrion, H. (2006). Algebraic equatıons: Can middle-school students meanıngfully translate from words to mathematical symbols? Reading Psychology, 27, 147–164.
7. Charalambous, C. Y., Delaney, S., Hsu, H. Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12, 117–151.
8. Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149 – 158.

9. Contreras, J. (2007). Unraveling the mystery of the origin of mathematical problems: Using a problem-Posing framework with prospective mathematics teachers. The mathematics Educator, 17(2), 15-23.
10. Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal Mathematics Teacher Education, 11, 395–415.
11. Creswell, W. J. (2007). Qualitative inquiry and research design choosing among five traditions. California: Sage Publications.
12. Gonzales, N. A. (1998). A blueprint for problem posing. School Science and Mathematics, 94(2), 78- 85.
13. Işık, C., & Kar, T. (2012a). Matematik Dersinde Problem Kurmaya Yönelik Öğretmen Görüşleri Üzerine Nitel Bir Çalışma. Milli Eğitim Dergisi, 194, 199-215.
14. Işık, C., & Kar, T. (2012b). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. İlköğretim Online, 11(4), 1021-1035. [Online] http://ilkogretim-online.org.tr/, retrieved on 30/05/2012.
15. Işık, C., & Kar, T. (2012c). İlköğretim matematik öğretmeni adaylarının kesirlerde bölmeye yönelik kurdukları problemlerde hata analizi. Kuram ve Uygulamada Eğitim Bilimleri (KUYEB), 12(3), 2289- 2309.
16. Işık, C., Kar, T., Işık, A., & Güler, G. (2012). İlköğretim matematik öğretmeni adaylarının kesirlerde toplama işlemine yönelik kurulan problemlerdeki hataları belirleyebilme becerileri. Turkish Journal of Computer and Mathematics Education, 3(3), 161-182.
17. Işık, C., Öcal, T., & Kar, T. (2013). Analysis of pre-service elementary teachers’ pedagogical content knowledge in the context of problem posing. Paper presented at the meeting of Eighth Congress of European Research in Mathematics Education (CERME 8), Antalya, Turkey.
18. Kar, T. (2014). Ortaokul matematik öğretmenlerinin öğretim için matematiksel bilgisinin problem kurma bağlamında incelenmesi: kesirlerle toplama işlemi örneği (Yayınlanmamış doktora tezi). Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum, Türkiye.
19. Kar, T., & Işık, C. (2014a). Ortaokul yedinci sınıf öğrencilerinin kesirlerle çıkarma işlemine kurdukları problemlerin analizi. İlköğretim http://dergipark.ulakbim.gov.tr/ilkonline/article/view/500007527 1 13(4), 1223-1239. [Online]
20. Kar, T., & Işık, C. (2014b). Analysis of problems posed by pre-service primary teachers about adding fractions in terms of semantic structures. Mathematics Education, 9(2), 135-146.
21. Kılıç, Ç. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 1-10. Lamon, S. J. (2005). Teaching fractions and ratios for understanding:Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum Associates.
22. Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. Paper presented at the meeting of 31st Conference of the International Group for the Psychology of Mathematics Education, Seoul.
23. Luo, F. (2009). Evaluating the effectiveness and insights of pre-service elementary teachers’ abilities to construct word problems for fraction multiplication. Journal of Mathematics Education, 2(1), 83–98.
24. MacGregor, M., & Stacey, K. (1993). Cognitive models underlying students' formulation of simple linear equations. Journal for Research in Mathematics Education, 24 (3), 217- 232.
25. McAllister, C. J., & Beaver, C. (2012). Identification of error types in preservice teachers' attempts to create fraction story problems for specified operations. School Science and Mathematics 112(2), 88-98.
26. Milli Eğitim Bakanlığı [MEB], (2013). Ortaokul Matematik Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı. Ankara: MEB Basımevi.
27. National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
28. Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychology, 40(1), 27–52.
29. Osana, H. P., & Royea, D. A. (2011). Obstacles and challenges in preservice teachers’ explorations with fractions: A view from a small-scale intervention study. The Journal of Mathematical Behavior, 30, 333–352.
30. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
31. Stoyanova, E. (1998). Problem posing in mathematics classrooms. In A. McIntosh, & N. Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp.164-185). Perth: MASTEC Publication.
32. Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in Mathematics Education (pp.518–525). Melbourne: Mathematics Education Research Group of Australasia.
33. Ticha, M., & Hospesova, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. Paper presented at the meeting of CERME 6, Lyon.
34. Tobias, J. M. (2013). Prospective elementary teachers’ development of fraction language for deŞning the whole. Mathematics Teacher Education, 16(2), 85-103. Journal of
35. Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.
36. Ward, J. & Thomas, G. (2007). What do teachers know about fractions? In Findings from the New Zealand Numeracy Development Projects (pp. 128-138). Wellington: Learning Media.
37. Yin, R. K. (2011). Qualitative research from start to finish. The guilford press, New York: USA.
38. Zembat, İ.Ö. (2007). Sorun Aynı–Kavramlar; Kitle Aynı-Öğretmen Adayları. İlköğretim Online, 6(2), 305-312, [Online]: http://ilkogretim-online.org.tr adresinden 12 Aralık 2011 tarihinde indirilmiştir.