Matematik Öğretmen Adaylarının Lineer Kongrüanslara İlişkin Soyutlamayı İndirgeme Eğilimleri

Abstract

Matematik öğretmen adaylarının lisans eğitimi süresince alan bilgilerinin şekillenmesinde önemli rolü olan derslerden birisi de Sayılar Teorisi dersidir. Bu çalışmada, matematik öğretmen adaylarının, Sayılar Teorisi dersi kapsamında verilen lineer kongrüanslar ile ilgili algılayışları, Hazzan’ın (1999) geliştirdiği soyutlamanın indirgenmesi teorisi çerçevesinde incelenmiştir. Soyutlamanın indirgenmesi düşüncesi öğrencilerin, kavramların derste verildiği soyutlama seviyesinden daha düşük seviyedeki bir soyutlamayla çalışma eğilimlerine dayanmaktadır. Araştırmamızda, ilköğretim ve ortaöğretim matematik eğitimi bölümlerinde okuyan öğretmen adaylarından oluşan bir çalışma grubuna sorulan üç tane lineer kongrüans denkleminin çözümüne yönelik yazılı cevaplar, betimsel analiz ve içerik analizi yöntemleri ile incelenmiştir. Elde edilen bulgulardan, öğretmen adaylarının birçoğunun, denklemlerin çözümünün varlığı için gerekli şartları belirten teoremleri kullanmadan veya yanlış kullanarak çözüme ulaşmaya çalıştıkları görülmüştür. Bu durum, soyutlama seviyesinin indirgendiğinin bir göstergesidir

Keywords

• Soyutlamanın indirgenmesi, lineer kongrüanslar

Pre-Service Mathematics Teachers’ Tendencies of Reducing Abstraction about Linear Congruence

Abstract

Number theory is one of the courses that play an important role in forming the content knowledge of the pre-service mathematics teachers during their undergraduate education. In this research, the conception of the pre-service mathematics teachers about linear congruence which is given in the number theory course is examined through the framework of the theory of reducing abstraction. The theme of reducing abstraction is based on students’ tendencies to work on a lower level of abstraction than the one in which concepts are introduced in class. The answers of a study group to the questions related with linear congruence are analyzed with the methods of content and descriptive analysis. From the obtained findings, it was observed that many of the pre-service teachers try to solve the equations without using the theorems about the existence of the solutions of a linear congruence or they misused them. This situation is an indication that the level of abstraction is reduced

Keywords

• Reducing abstraction, linear congruence

References

1. Baki, A. ve Gökçek, T. (2012). Karma yöntem araştırmalarına genel bir bakış. Elektronik Sosyal Bilimler Dergisi, 11(42), 1-21.
2. Bolte, L. (1999). Enhancing and assessing preservice teachers’ integration and expression of mathematical knowledge. Journal of Mathematics Teacher Education, 2(2), 167-185.
3. Brown, A., Thomas, K., and Tolias, G. (2002). Conceptions of divisibility: Success and understanding. In S. R. Campbell & R. Zazkis (Eds.), Learning and Teaching Number Theory: Research in Cognition and Instruction, 41-82. Westport, CT: Ablex.
4. Creswell, J. W. (2003). Research design: Qualitative, quantitative, and mixed methods approaches (2nd ed.). Thousand Oaks, CA: Sage.
5. Hazzan, O. (1999). Reducing abstraction level when learning abstract algebra concepts. Educational Studies in Mathematics, 40, 71–90.
6. Hazzan, O. (2001). Reducing abstraction: The case of constructing an operation table for a group. Journal of Mathematical Behaviour, 20(2), 163-172.
7. Hazzan, O. (2003a). How students attempt to reduce abstraction in the learning of mathematics and in the learning of computer science. Computer Science Education, 13(2), 95-122.
8. Hazzan, O. (2003b). Reducing abstraction when learning computability theory. Journal of Computers in Mathematics and Science Teaching, 22(2), 95-117.

9. Hazzan, O. and Zaskis, R. (2005). Reducing abstraction: The case of school mathematics. Educational Studies in Mathematics, 58, 101–119.
10. Kurz, T. L. and Garcia, J. (2012). The complexities of teaching prime decomposition and multiplicative structure with tools to preservice elementary teachers. Journal of Research in Education, 22(2), 169-193.
11. Meel, D. E. (2003). Models and theories of mathematical understanding: Comparing Pirie and Kieren’s model of the growth of mathematical understanding and APOS theory. CBMS Issues in Mathematics Education, 12, 132-181.
12. Milli Eğitim Bakanlığı (2013). Ortaokul Matematik Dersi (5,6,7 ve 8. Sınıflar) Öğretim Programı. Ankara.
13. Milli Eğitim Bakanlığı (2013). Ortaöğretim Matematik Dersi (9,10,11 ve 12. Sınıflar) Öğretim Programı. Ankara.
14. Papadopoulos, I. and Iatridou, M. (2010). Modelling problem-solving situations into number theory tasks: The route towards generalisation. Mathematics Education Research Journal, Vol. 22/3, 85-110.
15. Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
16. Smith, J. C. (2002). An investigation of undergraduates’ understanding of congruence of integers. Unpublished doctoral dissertation. The Graduate College of The University of Arizona.
17. Şenay, H. (2007). Sayılar Teorisi Dersleri. Konya: Dizgi Ofset Matbaacılık.
18. Zazkis, R. and Campbell, S. R. (2011). Number theory in Mathematics Education: Perspectives and Prospects. In R. Zaskis & S. R. Campbell (Eds.), Number theory in Mathematics Education: Perspectives and Prospects. (Chp. 1). New York: Routledge.