Matematik Öğretmenlerinin İrrasyonel Sayılara Yönelik Kavram Bilgilerinin İncelenmesi

Öz

Bu araştırmanın amacı matematik öğretmenlerinin irrasyonel sayılara yönelik bilgi düzeylerini incelemektir. Araştırmanın verileri Türkiyenin İç Anadolu Bölgesinde görev yapan sekiz ilköğretim matematik öğretmeni ile yapılan yarı yapılandırılmış görüşmeler yardımıyla toplanmıştır. Öğretmenlerle yapılan mülakatlar ortalama 45 dakika sürmüştür. Yapılan mülakatlar öğretmenlerin izinleri alınarak ses kayıt cihazı ile kayıt edilmiştir. Mülakatların tamamlanmasının ardından ses kayıtları yazıya dökülerek verilerin analizine başlanmıştır. Veriler nitel içerik analizi yöntemi ile analiz edilmiştir. Araştırmacı tarafından görüşme formunun hazırlanması aşamasında ilk olarak literatürde yer alan çalışmalar ve Milli Eğitim Bakanlığı (MEB) tarafından hazırlanan ortaokul ve lise ders kitapları incelenmiştir. Araştırma sonucunda, matematik öğretmenlerinin irrasyonel sayıları tanımlama, tanıma, sayı doğrusu üzerinde irrasyonel sayıların tam yerinin bulunması ve irrasyonel sayılar kümesi üzerinde yaptıkları işlemlere yönelik güçlüklerinin olduğu görülmüştür. Öğretmenler formel matematiksel bilgiler kullanmak yerine daha çok sezgisel yanıtlar vermişlerdir. Matematik öğretmenlerinin irrasyonel sayılara yönelik bilgi düzeylerinin düşük olduğu ve kavram yanılgılarına sahip oldukları görülmüştür. Öğretmenlerin irrasyonel sayılarla ilgili tanımlama, tanıma, sayı doğrusu üzerinde irrasyonel sayıların tam yerinin göstermesi ve irrasyonel sayılar kümesi üzerinde yaptıkları işlemlere yönelik yaşadıkları güçlükler dikkate alınarak daha geniş katılımlı araştırmaların yapılması önerilmiştir.

Anahtar Kelimeler

• Matematik öğretmeni,irrasyonel sayı,rasyonel sayı,kavramsal anlama

An Evaluation of Mathematics Teachers’ Conceptual Understanding of Irrational Numbers

Öz

The objective of this study was to examine mathematics teachers’ conceptual understanding of irrational numbers. Data were gathered from semi-structured interviews with eight primary school mathematics teachers in Central Anatolia, Turkey. The interviews carried on with the teachers lasted about 45 minutes. To be able to record the interviews, permissions were taken from the teachers. After the interviews had been completed, they were decoded and begun to be analyzed. The data were analyzed via content analysis method. At the stage during which the interview form was prepared, at first the studies in the literature and the books prepared by the Ministry of National Education (MNE) for the secondary and high schools were examined.The results show that teachers have difficulty defining and recognizing irrational numbers, placing them on the number line, and doing operations with them. The teachers gave intuitive answers instead of using formal mathematics knowledge. Teachers’ knowledge about irrational numbers is insufficient and they have misconceptions. The teachers’ definitions, knowing of irrational numbers, showing the exact place of irrational numbers on number line and the difficulties they faced while doing operations on irrational set are taken into consideration so as to recommend providing studies involving a large number of participants.

Anahtar Kelimeler

• Mathematics teachers,irrational numbers,rational numbers,conceptual understanding

Kaynakça

1. Arcavi, A., Bruckheimer, M., & Ben-Zvi, R. (1987). History of mathematics for teacher: The case of irrational numbers. For the Learning of Mathematics, 7(2), 18-23.
2. Baki, A. (2008). From theory to practice mathematics education. Ankara: Alfa Publications.
3. Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2011). Scientific research methods. Pegem Akademi, Ankara.
4. Fischbein, E., Jehiam, R., & Cohen, D. (1995). The concept of irrational numbers in high school students and prospective teachers. Educational Studies in Mathematics, 29(1), 29-44.
5. Güler, G., Kar, T., & Işık, C. (2012). Qualitative study on determining the relationship between real and irrational numbers by the prospective mathematics teachers'. X. National Science and Mathematics Education Congress, 22-30 June, Niğde, Türkiye.
6. Güven, B., Çekmez, E., & Karataş, İ. (2011). Examining preservice elementary mathematics teachers’ understanding about irrational numbers. Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS), 21(5), 401-416. DOI: 10.1080/10511970903256928
7. Kara, F., & Delice, A. (June 2012). Is the definition of the concept? Or is the concept images? Represent irrational numbers. X. National Science and Mathematics Education Congress, 22-30 June, Niğde, Türkiye.
8. Ministry of National Education [MNE]. (2013a). Middle school (5-8). classes programs promotion handbook. Chairman of the Board of Education Ministry of Education. Ankara: Department of State Printing House Books.

9. Ministry of National Education [MNE], (2013b). Secondary (9-12). Classes Programs Promotion Handbook. Chairman of the Board of Education Ministry of Education. Ankara: Department of State Printing House Books.
10. Ministry of National Education [MNE]. (2015a). 8th grade mathematics textbook. Chairman of the Board of Education Ministry of Education. Ankara: Department of State Printing House Books.
11. Ministry of National Education [MNE]. (2015b). 9th grade mathematics textbook. Chairman of the Board of Education Ministry of Education. Ankara: Department of State Printing House Books.
12. National Council of Teachers of Mathematics [NCTM], (2000). Principles and standarts for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
13. Peled, I., & Hershkovitz, S. (1999). Difficulties in knowledge integration: Revisiting Zeno’s paradox with irrational numbers. International Journal of Mathematics Education, Science and Technology, 30(1), 39-46.
14. Sirotic, N., & Zazkis, R. (2007). Irrational numbers on the number line-Where are they?. International Journal of Mathematics Education, Science and Technology, 38(4), 477-488.
15. Srotic, N. (2004). Prospective secondary mathematics teachers’ understanding of irrationality. Unpublished Master Thesis, Simon Fraser University, British Colombia, Canada.
16. Temel, H., & Eroğlu, A. O. (2014). A study on 8th grade students’ explanations of concepts of number. Journal of Kastamonu Education, 22(3), 1263-1278.
17. Zazkis, R. (2005). Representing numbers: Prime and irrational. International Journal of Mathematics Education, Science and Technology, 36(2-3), 207-218.