ORTAOKUL MATEMATİK ÖĞRETMENLERİNİN KURDUKLARI PROBLEMLERİN GÜÇLÜK DÜZEYİNE YÖNELİK GÖRÜŞLERİNİN İNCELENMESİ

Yıl 2015, Cilt: 16 Sayı: 2, 63 - 81, 01.05.2015

Tuğrul Kar Cemalettin Işık

Öz

Bu araştırmada, ortaokul matematik öğretmenlerinin kesirlerle toplama veya çıkarma işlemlerine yönelik kurdukları problemlerin güçlük düzeylerini belirlerken dikkate aldıkları ölçütlerin tespit edilmesi amaçlanmıştır. Ayrıca kurulan problemlerin kavramsal analizi yapılarak, olası hatalarının belirlenmesi de hedeflenmiştir. Araştırmaya, Erzurum il merkezinde görev yapan beş öğretmen katılmıştır. Araştırmada veriler, serbest problem kurma etkinliğine yönelik hazırlanan problem kurma testi ve odak-grup görüşme sürecinin video kaydının yapılması yoluyla toplanmıştır. Veriler öğretim için matematik bilgisi teorik çerçevesine göre analiz edilmiştir. Öğretmenlerin problemin zorluk düzeyini arttırmada genel olarak işlem yapısına odaklandıkları, buna karşın farklı ölçütleri dikkate almada sınırlı bir bakış açısına sahip oldukları belirlenmiştir. Bunun yanında bazı öğretmenlerin kurulan problemlerde hatalar sergiledikleri de tespit edilmiştir.

Anahtar Kelimeler

problem kurma, kesirlerle toplama ve çıkarma, matematik öğretmenleri

The Investigation of Middle School Mathematics Teachers' Views on the Difficulty Levels of Posed Problems

Öz

The present study aimed to determine the criteria that middle school mathematics teachers considered in assessing the difficulty levels of problems they posed on the addition and subtraction of fractions. Furthermore, a conceptual analysis was made on the problems posed in order to identify potential errors. Five teachers from schools in the central districts of Erzurum participated in the study. Data were collected through videorecording the focus-group interviews, as well as the administration of the problem posing test designed for the free problem posing activity. Collected data were analyzed according to the theoretical framework of the mathematical knowledge for teaching. With respect to increasing the difficulty level of a problem, teachers were determined to focus on the structure of the operation in general and it was found that they had a limited perspective in considering different criteria. Some of the teachers were also identified to have errors in posing problems

Anahtar Kelimeler

problem posing, additon and subtraction with fractions, mathematics teachers

Kaynakça

• Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education, 25(1), 56-69.
• 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.
• Anderson, R. C., & Hoffmeister, A. M. (2007). Knowing and teaching middle school mathematics: A professional development coursefor in-service teachers. School Science and Mathematics, 107(5), 193-203.
• 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.
• Barlow, A. T., & Cates, J. M. (2006). The impact of problem posing on elementary teachers’ beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64–73.
• 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.
• Cankoy, O. (2013). Interlocked problem posing and children’s problem posing performance in free structured situations. International Journal of Science and Mathematics Education, 1-20.
• Cankoy, O. ve Darbaz, S. (2010). Problem kurma temelli problem çözme öğretiminin problemi anlama başarısına etkisi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 38, 11-24.
• Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149 – 158.
• 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.
• Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270.
• 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.
• Creswell, W. J. (2007). Qualitative inquiry and research design choosing among five traditions. California: Sage Publications.
• English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.
• Hancock, D. R. & Algozzine, B. (2006). Doing case study research. A practical guide for beginning researchers. Teachers College Press. New York.
• Hatch, J. A. (2002). Doing qualitative research in education settings. Albany, NY: SUNY press.
• Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243.
• Işık, C. ve Kar, T. (2012a). Matematik dersinde problem kurmaya yönelik öğretmen görüşleri üzerine nitel bir çalışma. Milli Eğitim Dergisi, 194, 199-215.
• Işık, C. ve Kar, T. (2012b). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin http://ilkogretim-online.org.tr/, adresinden 30/05/2012 tarihinde indirilmiştir.
• Işık, C. ve Kar, T. (2012c). İlköğretim matematik öğretmeni adaylarının kesirlerde analizi. İlköğretim Online, 11(4), 1021-1035. [Online]bölmeye yönelik kurdukları problemlerde hata analizi. Kuram ve Uygulamada Eğitim Bilimleri, 12(3), 2289-2309.
• Işık, C., Öcal, T. ve 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.
• Kar, T., Özdemir, E., Ipek, A. S. ve Albayrak, M. (2010). The relation between the problem posing and problem solving skills of prospective elementary mathematics teachers. Social and Behavioral Sciences, 2, 1577–1583.
• Kieboom, L. A. V. (2013). Examining the mathematical knowledge for teaching involved in pre-service teachers' reflections. Teaching and Teacher Education, 35,146-156.
• Kılıç, Ç. (2012). Investigating the problem posing reasons of pre-service primary school teachers in different problem posing contexts. Mustafa Kemal Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 9(20), 347-356.
• Kılıç, Ç. (2013a). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 1-10.
• Kılıç, Ç. (2013b). İlköğretim öğrencilerinin doğal sayılarla dört işlem gerektiren problem kurma etkinliklerindeki performanslarının belirlenmesi. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 20, 256-274.
• Knott, L. (2010). Problem posing from the foundations of mathematics. TMME, 7, 413- 432.
• Lee, J. E. (2011). A study of pre-kindergarten teachers’ mathematical knowledge for teaching (Unpublished doctoral dissertation). University of Texas, Austin.
• Leung, S. S. (2013). Teachers implementing mathematical problem posing in the classroom: challenges andstrategies. Educational Studies in Mathematics, 1- 14.
• Leung, S. K., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9, 5-24.
• Liu, W., & Neber, H. (2012). Estimation skills of Chinese and polish grade 6 students on pure fraction tasks. Journal of Mathematics Education, 5(1), 1-14.
• 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.
• 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.
• Milli Eğitim Bakanlığı [MEB], (2013). Ortaokul Matematik Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı. Ankara: MEB Basımevi.
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
• 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.
• Saxe, G., Gearhart, M., & Nasir, N. S. (2001). Enhancing students' understanding of mathematics: A study of three contrasting approaches to professional support. Journal of Mathematics Teacher Education, 4, 55–79.
• Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
• Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
• 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.
• 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.
• 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.
• Tobias, J. M. (2012). Prospective elementary teachers’ development of fraction language for deŞning the whole. Journal of Mathematics Teacher Education, 16(2), 85-103.
• Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.
• Zembat, İ. Ö. (2007). Sorun aynı–kavramlar; kitle aynı-öğretmen adayları. Elementer Education Online, 6(2), 305-312, [Online]: http://ilkogretim-online.org.tr adresinden 12 Aralık 2011 tarihinde indirilmiştir.