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Ortaokul Öğrencilerinin Matematiksel Anlamalarının Farklı Değişkenler Açısından İncelenmesi

The Analysis Of Middle School Students’ Mathematical Understanding In Terms Of Different Variables

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Abstract (2. Language): 
Mathematical understanding which is dynamic, refined but non-linear and which is passed through different levels is a self-renewing process. Determining the factors which affects this process can be seen as the first steps of understanding the mathematical understanding. With this regard, in this study, it is aimed to analyze mathematical understandings of middle school students in terms of different variables (gender, academic achievement etc.). In this research relational screening model was used. The study group is consisted of 466 students who are studying in different grades of a public middle school in Zeytinburnu region of İstanbul. The data was obtained by using ‘Demographics Information Form (DIF)’ and ‘Determining the Mathematical Understanding Levels Scale (DMULS)’. According to research results it was appeared that the mathematical understandings of male students were lower than female students. In addition to that, it was determined that mathematical understandings of middle school students differed significantly according to their grade levels, their academic achievements, whether they received extra help for the mathematics lessons other than the school or not and educational levels of their parents.
Abstract (Original Language): 
Kendisini yenileyen bir süreç olan matematiksel anlama, dinamik, seviyeli fakat doğrusal olmayan bir yapıda olup ve farklı aşamalardan geçer. Bu süreci etkileyen faktörlerin belirlenmesi ise, matematiksel anlamayı anlamanın ilk adımları olarak görülebilir. Bu bağlamda araştırmada, ortaokul öğrencilerinin matematiksel anlamalarının farklı değişkenler (cinsiyet, akademik başarı vb.) açısından incelenmesi amaçlanmıştır. Araştırmada ilişkisel tarama modeli kullanılmıştır. Çalışma grubunu, İstanbul ili Zeytinburnu ilçesinde bulunan bir devlet ortaokulunun farklı sınıf seviyelerinde öğrenim görmekte olan 466 öğrenci oluşturmaktadır. Veriler, “Demografik Bilgi Formu (DBF)” ve “Matematiksel Anlama Düzeylerini Belirleme Ölçeği (MADBÖ)” ile elde edilmiştir. Araştırma sonuçlarına göre; erkek öğrencilerin matematiksel anlamalarının kız öğrencilere göre daha düşük olduğu belirlenmiştir. Ayrıca ortaokul öğrencilerinin matematiksel anlamalarının sınıf seviyelerine, akademik başarılarına, okul dışı matematik dersine yardımcı ders alıp almama durumlarına ve anne-baba eğitim düzeylerine göre anlamlı bir şekilde farklılaştığı ortaya çıkmıştır.
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REFERENCES

References: 

Amit, M., & Fried, M. N. (2002). High-stake assessment as a tool for promoting mathematical literacy
and the democratization of mathematics education. Journal of Mathematical Behaviour, 21, 499-514.
The Analysis Of Middle School Students’ Mathematical Understanding... 1433
July 2017 Vol:25 No:4 Kastamonu Education Journal
Aydın, F. (2009). İşbirlikli öğrenme yönteminin 10. sınıf coğrafya dersinde başarıya, tutuma ve motivasyona
etkileri (Yayınlanmış doktora tezi). Gazi Üniversitesi Eğitim Bilimleri Enstitüsü: Ankara.
Bal, A. P. (2006). İlköğretim beşinci sınıf öğrencilerinin matematiksel kavrama ve işlem becerileri
arasındaki farkın bazı değişkenler açısından değerlendirilmesi. Çukurova Üniversitesi Eğitim
Fakültesi Dergisi, 3(32), 13-23
Ball, D. L. (1990a). The mathematical understandings that prospective teachers bring to teacher
education. The Elementary School Journal, 90(4), 449–466.
Ball, D. L. (1990b). Prospective elementary and secondary teachers’ understanding of division.
Journal for Research in Mathematics Education, 21(2), 132–144.
Brown, T. A. (2006). Confirmatory factor analysis for applied research. NY: Guilford Publications, Inc.
Brownell, W. A. (1945). Psychological considerations in the learning and teaching of arithmetic.
In W. D. Reeve (Eds.), The teaching of arithmetic, Tenth yearbook of the National Council of
Teachers of Mathematics (pp. 1-31). New York: Teachers College, Columbia University.
Brownell, W. A., & Sims, V. M. (1946). The nature of understanding. In J. F. Weaver & J. Killpatrick (Eds.)
The place of meaning in mathematics instruction: Selected theoertical papers of William A. Brownell
(Studies in Mathematics, 21, 161-179). Stanford University: School Mathematics Study Group.
Büyüköztürk, Ş. (2012). Sosyal bilimler için veri analizi el kitabı. Ankara: Pegem Akademi
Büyüköztürk, Ş., Çokluk, Ö. ve Köklü, N. (2010). Sosyal bilimler için istatistik. Ankara: Pegem Akademi.
Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz, Ş. ve Demirel, F. (2011). Bilimsel
araştırma yöntemleri. Ankara: Pegem Akademi.
Byers, V., & Erlwanger, S. (1985). Memory in mathematical understanding. Educational Studies in
Mathematics, 16, 259-281.
Byers, V., & Herscovics, N. (1977). Understanding school mathematics. Mathematics Teaching, 81, 24-27.
Cavey, L. O. (2002). Growth in the mathematical understanding while learning how to teach: A
theoretical perspective. Proceedings of the Annual Meeting (of the) North American Chapter of
the International Group for the Psychology of Mathematics Education. Athens, GA.
Davis, E. J. (1978). A model for understanding in mathematics. Arithmetic Teacher, 26(1), 13-17.
Dursun, Ş. ve Peker, M. (2003). İlköğretim altıncı sınıf öğrencilerinin matematik dersinde
karşılaştıkları sorunlar. Cumhuriyet Üniversitesi Sosyal Bilimler Dergisi, 27(1), 135-142.
Herscovics, N., & Bergerson, J. (1988). An extended model of understanding. Proceedings of the
Annual Meeting of the North American Chapter of the International Group for the Psychology
of Mathematics Education (pp.15-22). Dekalb, IL: Northern Illinois University.
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In Grouws, D. A. (Eds.)
Handbook of Research on MathematicsT eaching and Learning (pp. 65-97). NewY ork: Macmillan.
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis:
Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. doi:
10.1080/10705519909540118
Kaba, Y., ve Şengül, S. (2015). Ortaokul öğrencilerinin matematiksel anlamaları ile matematiğe yönelik
tutumları arasındaki ilişki. Eğitim ve Bilim, 40(180), 103-123. doi: 10.15390/EB.2015.4355
Karasar, N. (2002). Bilimsel araştırma yöntemi. Ankara: Nobel Yayıncılık.
Kastberg, S. E. (2002). Understanding mathematical concepts: The case of the logarithmic function.
(Unpublished doctoral dissertation). The University of Georgia. Georgia: Athens.
Kaya, A., Bozaslan, H. ve Genç, G. (2012). Üniversite öğrencilerinin anne-baba tutumlarının
problem çözme becerilerine, sosyal kaygı düzeylerine ve akademik başarılarına etkisi. Dicle
Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 18, 208-225.
1434 Sare ŞENGÜL, Yasemin KABA, Fatma ERDOĞAN...
Temmuz 2017 Cilt:25 No:4 Kastamonu Eğitim Dergisi
Kline, R. B. (2005). Principles and practice of structural equation modeling. NY: Guilford Publications, Inc.
Martin, L. C. (2008). Folding back and the dynamical growth of mathematical understanding:
Elaborating the Pirie-Kieren theory. The Journal of Mathematical Behavior, 27, 64-85. doi:
10.1016/j.jmathb.2008.04.001
Meel, D. E. (2003). Models and theories of mathematical understanding: Comparing Pirie and Kieren’s
model of the growth mathematical understanding and APOS theory. Journal of Mathematical
Education, 12, 132-174.
OMDÖP (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: Milli
Eğitim Bakanlığı, Talim Terbiye Kurulu Başkanlığı.
Patton, M. Q. (1990). Qualitative evaluation and research methods. London: Sage Publications.
Pirie, S. E. B., & Kieren, T. E. (1989). A recursive theory of mathematical understanding. For the
Learning of Mathematics, 9(3), 7-11.
Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it
and how can we represent it? Educational Studies in Mathematics, 26(2/3), 165-190.
Polya, G. (1945). How to solve it. Priceton, NJ: Priceton University Press.
Ravid, R. (1994). Practical statistics for educators. New York: University Press in America.
Schroeder, T. L. (1987). Student’s understanding of mathematics: A review and synthesis of some
recent research. In J. Bergerson, N. Herscovics, & C. Kieran (Eds.), Psychology of Mathematics
Education XI, 3, 332-338. Montreal: PME.
Sierpinska, A. (1990). Some remarks on understanding in mathematics. For the Learning of Mathematics,
10(3), 24-41.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching,
77, 20-26.
Skemp, R. R. (1982). Symbolic understanding. Mathematics Teaching, 99, 59-61.
Smith, K. B. (1996). Guided discovery, visualization, and technology applied to the new curriculum for
secondary mathematics. Journal of Computers in Mathematics and Science Teaching, 15(4), 383-399.
Smith, M. S. (2000). Redefining success in mathematics teaching and learning. Mathematics Teaching
in the Middle School, 5(6), 378- 386.
Sümer, N. (2000). Yapısal eşitlik modelleri. Türk Psikoloji Yazıları, 3(6), 49-74.
Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division
of fractions. Journal for Research in Mathematics Education, 31(1), 5–25. doi: 10.2307/749817
Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem
posing. Teaching and Teacher Education, 25(1), 166–175. doi: 10.1016/j.tate.2008.08.003
Van Engen, H. (1949). An analysis of meaning in arithmetic. Elementary School Journal, 49(6), 321-329.
von Glasersfeld, E. (1987). Learning as a constructive activity. In C. Janvier (Eds.), Problems of
representation in the learning and teaching of mathematics (pp. 3-18). Hillsdale, NJ: Erlbaum.
Wertheimer, M. (1959). Productive thinking. New York: Harper & Row.

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