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

Yıl 2017, Cilt: 25 Sayı: 4, 1421 - 1434, 15.07.2017

Öz

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. 

Kaynakça

  • 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.
  • 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 theoretical 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 Mathematics Teaching and Learning (pp. 65-97). New York: 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.
  • 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.

Ortaokul Öğrencilerinin Matematiksel Anlamalarının Farklı Değişkenler Açısından İncelenmesi

Yıl 2017, Cilt: 25 Sayı: 4, 1421 - 1434, 15.07.2017

Öz

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. 

Kaynakça

  • 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.
  • 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 theoretical 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 Mathematics Teaching and Learning (pp. 65-97). New York: 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.
  • 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.
Toplam 44 adet kaynakça vardır.

Ayrıntılar

Konular Eğitim Üzerine Çalışmalar
Bölüm Derleme Makale
Yazarlar

Sare Şengül Bu kişi benim

Yasemin Kaba Bu kişi benim

Fatma Erdoğan Bu kişi benim

Yayımlanma Tarihi 15 Temmuz 2017
Kabul Tarihi 11 Ekim 2016
Yayımlandığı Sayı Yıl 2017 Cilt: 25 Sayı: 4

Kaynak Göster

APA Şengül, S., Kaba, Y., & Erdoğan, F. (2017). The Analysis Of Middle School Students’ Mathematical Understanding In Terms Of Different Variables. Kastamonu Eğitim Dergisi, 25(4), 1421-1434. https://doi.org/10.24106/kefdergi.332486