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Examining in-Service and Pre-Service Mathematics Teachers’ Instructional Explanations in the Context of Mathematical Models

Yıl 2024, Cilt: 20 Sayı: 2, 175 - 198, 22.08.2024
https://doi.org/10.17860/mersinefd.1443293

Öz

The aim of this research is to examine the instructional explanations of mathematics teachers and pre-service teachers about dividing by fractions in the context of mathematical models. Within the scope of the research, the case study survey method was used. The participants of the research consist of two mathematics teachers working in different public schools in the same city and two senior students studying in the Primary Mathematics Teaching program of a state university. In this research, eight open-ended questions and semi-structured interviews were used as data collection tools. The mathematical models used by the participants in the study were evaluated in two different dimensions. These are mathematical and pedagogical dimensions. The mathematical dimension includes the features of the models, whereas the pedagogical dimension includes their levels of usage. As a result of the research, it was seen that although the instructional explanations and models used by the participants were generally mathematically correct and valid, they did not always reflect the mathematical situation to which they were related in all aspects, and in the pedagogical dimension, they were generally suitable for the conceptual and problem-solving level. The lowest performance in the pedagogical dimension belongs to the epistemic level. As a result of the research, it was also concluded that the instructional explanations and models used by the teachers were more compatible with the indicators in the mathematical and pedagogical dimensions compared to the pre-service teachers. The findings were discussed in relation to the literature and some suggestions were made in line with the results.

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Matematik Öğretmenleri ile Öğretmen Adaylarının Öğretimsel Açıklamalarının Matematiksel Modeller Bağlamında İncelenmesi

Yıl 2024, Cilt: 20 Sayı: 2, 175 - 198, 22.08.2024
https://doi.org/10.17860/mersinefd.1443293

Öz

Bu araştırmanın amacı matematik öğretmenleri ile öğretmen adaylarının kesirlerle bölmeye yönelik öğretimsel açıklamalarının matematiksel modeller bağlamında incelenmesidir. Araştırma kapsamında durum çalışması tarama araştırması yönteminden yararlanılmıştır. Araştırmanın katılımcılarını aynı ilde yer alan farklı devlet okullarında görev yapmakta olan 2 matematik öğretmeni ile bir devlet üniversitesinin İlköğretim Matematik Öğretmenliği programında öğrenim görmekte olan 2 son sınıf öğrencisi oluşturmaktadır. Bu araştırmada veri toplama aracı olarak araştırmacılar tarafından oluşturulan sekiz adet açık uçlu soru ile yarı yapılandırılmış görüşmeler kullanılmıştır. Araştırma kapsamında yer alan katılımcıların öğretimsel açıklamalarında kullandıkları matematiksel modeller iki farklı boyutta değerlendirilmiştir. Bunlar matematiksel ve pedagojik boyutlardır. Matematiksel boyutta kullanılan modellerin özelliklerine, pedagojik boyutta ise kullanım düzeylerine yer verilmiştir. Araştırma sonucunda katılımcıların kullandıkları öğretimsel açıklama ve modellerin matematiksel olarak genelde doğru ve geçerli olmakla birlikte ilişkili oldukları matematiksel durumu tüm yönleriyle her zaman yansıtmadığı, pedagojik boyutta ise genel olarak kavramsal düzeye ve problem çözme düzeyine uygun olduğu görülmüştür. Pedagojik boyutta en düşük performans ise epistemik düzeye aittir. Araştırma sonucunda ayrıca öğretmenlerin kullandıkları öğretimsel açıklama ve modellerin, öğretmen adaylarına nazaran matematiksel ve pedagojik boyutlarda yer alan göstergelerle daha uyumlu olduğu sonucu elde edilmiştir. Elde edilen bulgular alan yazınla ilişkili olarak tartışılmış ve sonuçlar doğrultusunda bazı önerilerde bulunulmuştur.

Kaynakça

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  • Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. https://doi.org/10.1080/07370000802177235
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  • Kocaoğlu, T., & Yenilmez, K. (2010). Beşinci sınıf öğrencilerinin kesir problemlerinde yaptıkları hatalar ve kavram yanılgıları. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 14, 71-85. https://dergipark.org.tr/en/download/article-file/787095
  • Lachner, A., & Nückles, M. (2015). Bothered by abstractness or engaged by cohesion? Experts’ explanations enhance novices’ deep learning. Journal of Experimental Psychology: Applied, 21(1), 101-115. https://doi.org/10.1037/xap0000038
  • Lamon, S. (1996). The development of unitizing: Its role in children’s partitioning strategies. Journal for Research in Mathematics Education, 27, 170-193. https://doi.org/10.5951/jresematheduc.27.2.0170
  • Lee, J. E., & Lee, M. Y. (2023). How elementary prospective teachers use three fraction models: their perceptions and difficulties. Journal of Mathematics Teacher Education, 26(4), 455-480. https://doi.org/10.1007/s10857-022-09537-4
  • Leinhardt, G. (2001). Instructional explanations: A commonplace for teaching and location for contrast. V. Richardson (Ed.), Handbook for research on teaching (4th Edition). American Educational Research Association.
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  • Lo, J. J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15, 481-500. https://doi.org/10.1007/s10857-012-9221-4
  • Ma, L. (1999). Knowing and teaching elementary mathematics. Lawrence Erlbaum Associates.
  • Macit, E. (2019). 6. sınıf öğrencilerinin kesirler konusundaki imajlarının kavram yanılgıları ve başarıları ile ilişkisinin incelenmesi (Tez No: 610998). [Doktora tezi, İnönü Üniversitesi].
  • Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources, and development of pedagogical content knowledge for science teaching. In Examining pedagogical content knowledge: The construct and its implications for science education (pp. 95-132). Springer Netherlands.
  • Martin, J. R. (1970). Explaining, understanding, and teaching. McGraw-Hill.
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  • Milli Eğitim Bakanlığı [MEB] (2018). Matematik dersi öğretim programları (ilkokul ve ortaokul 1., 2., 3., 4.,5.,6., 7. ve 8. sınıflar). MEB.
  • Monte-Sano, C. (2011). Beyond reading comprehension and summary: Learning to read and write in history by focusing on evidence, perspective, and interpretation. Curriculum Inquiry, 41(2), 212-249. https://doi.org/10.1111/j.1467-873X.2011.00547.x
  • National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. NCTM.
  • Nemirovsky, R. (1994). On ways of symbolizing: The case of Laura and the velocity sign. The Journal of Mathematical Behavior, 13(4), 389-422. https://doi.org/10.1016/0732-3123(94)90002-7
  • Niss, M. (1987). Applications and modelling in the mathematics curriculum—state and trends. International Journal of Mathematical Education in Science and Technology, 18(4), 487-505. https://doi.org/10.1080/0020739870180401
  • Olkun, S., & Toluk-Uçar, Z. (2012). İlköğretimde etkinlik temelli matematik öğretimi. Eğiten Kitap.
  • Özer, A. (2020). Ortaokul 6. sınıf kesirler konusunun görselleştirme ile öğretiminin akademik başarıya etkisinin incelenmesi (Tez No: 616475). [Yüksek lisans tezi, Kırıkkale Üniversitesi].
  • Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in Science Education, 38, 261-284. https://doi.org/10.1007/s11165-007-9049-6
  • Parmar, R. (2003). Understanding the concept of “division”: assessment considerations. Exceptionality, 11(3), 177-189. http://dx.doi.org/10.1207/S15327035EX1103_05
  • Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri (M. Bütün ve S. B. Demir, çev.). Pegem Akademi.
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  • Rey, G. D., & Fischer, A. (2013). The expertise reversal effect concerning instructional explanations. Instructional Science, 41(2), 407-429. https://doi.org/10.1007/s11251-012-9237-2
  • Rosli, R., Han, S., Capraro, R. M., & Capraro, M. M. (2013). Exploring preservice teachers' computational and representational knowledge of content and teaching fractions. Research in Mathematical Education, 17(4), 221-241. http://dx.doi.org/10.7468/jksmed.2013.17.4.221
  • Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.
  • Şahin, Ö., Gökkurt, B., & Soylu, Y. (2013, Nisan). Matematik öğretmeni adaylarının kesirlerle ilgili pedagojik alan bilgilerinin öğrenci hataları bağlamında incelenmesi. 4th International Conference on New Trends in Education and Their Implications konferansında sunulan sözlü bildiri, Antalya. https://www.demo.emuder.com/icontedemo/wp-content/uploads/2024/02/4._iconte_bildiri_ozetleriii-2013.pdf
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  • Seçir, S. (2017). İlköğretim matematik öğretmen adaylarının kesirlerle çarpma ve bölme işlemlerine ilişkin özelleştirilmiş alan bilgilerinin gelişiminin incelenmesi (Tez No: 461458). [Doktora tezi, Gazi Üniversitesi].
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  • Turan, Y. (2023). Ortaokul matematik öğretmenlerinin farklı kesir şemaları bağlamında model kullanmaya yönelik pedagojik tercihlerinin incelenmesi (Tez No: 863226). [Yüksek lisans tezi, Ordu Üniversitesi].
  • Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally. Fifth edition. Allyn & Bacon.
  • Watson, J., Beswick, K., & Brown, N. (2006). Teachers’ knowledge of their students as learners and how to intervene. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, pp. 551-558). Sydney: MERGA.
  • Wittwer, J., & Renkl, A. (2008). Why instructional explanations often do not work: A framework for understanding the effectiveness of instructional explanations. Educational Psychologist, 43(1), 49-64. https://doi.org/10.1080/00461520701756420
  • Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96, 101–111. https://doi.org/10.1007/s10649-017-9760-9
  • Yavuz Mumcu, H. (2018). Kesir işlemlerinde matematiksel modellerin kullanımı: Bir durum çalışması. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 12 (1), 122-151.
  • Yin, R. K. (2017). Case study research and applications: Design and methods. Sage Publications.
  • Zbiek, R. M. (1998). Prospective teachers’ use of computing tools to develop and validate function as mathematical models. Journal for Research in Mathematics Education, 29(2), 184–201. https://doi.org/10.5951/jresematheduc.29.2.0184
  • Zembat, İ. Ö. (2007). Sorun aynı-kavramlar; kitle aynı-öğretmen adayları. İlköğretim Online, 6(2), 305-312. https://dergipark.org.tr/en/download/article-file/91015
Toplam 91 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Matematik Eğitimi
Bölüm Makaleler
Yazarlar

Emine Aktaş 0000-0001-5530-8887

Hayal Yavuz Mumcu 0000-0002-6720-509X

Yayımlanma Tarihi 22 Ağustos 2024
Gönderilme Tarihi 27 Şubat 2024
Kabul Tarihi 24 Haziran 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 20 Sayı: 2

Kaynak Göster

APA Aktaş, E., & Yavuz Mumcu, H. (2024). Matematik Öğretmenleri ile Öğretmen Adaylarının Öğretimsel Açıklamalarının Matematiksel Modeller Bağlamında İncelenmesi. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 20(2), 175-198. https://doi.org/10.17860/mersinefd.1443293

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