Türk ve Amerikan Matematik Ders Kitaplarının Hareket ve Eşleştirme Yaklaşımları Bağlamında Karşılaştırılması: Yansıma Dönüşümü Örneği

Year 2025, Issue: 63, 764 - 795, 27.03.2025

Kübra İler , Murat Akarsu , Mehmet Fatih Öçal

https://doi.org/10.53444/deubefd.1565403

Abstract

Bu çalışma, Türkiye ve Amerika Birleşik Devletleri'ndeki lise matematik ders kitaplarının yansıma dönüşümünü nasıl ele aldığını, hareket ve eşleme perspektiflerine odaklanarak incelemektedir. Ders kitapları, öğrencilerin matematiksel kavramları anlamasında önemli bir rol oynamaktadır. Farklı perspektifler göz önünde bulundurulduğunda, hareket perspektifi, eşit uzaklık ve diklik gibi temel özelliklere vurgu yapmadan, şekillerin simetri ekseni boyunca yansıtılmasını içerir ve bu durum kavram yanılgılarına yol açabilir. Öte yandan, eşleme perspektifi bu temel özellikleri korur ve tüm noktaların düzlemde yansıtılmasına odaklanır. Çalışmada, her iki ülkeden iki ders kitabı, simetri dönüşümünün tanımları, simetri ekseninin ele alınışı ve simetri tanım kümesi yaklaşımları açısından doküman incelemesi yöntemiyle analiz edilmiştir. Türk ders kitapları büyük ölçüde hareket perspektifini benimserken, eşleme perspektifine daha az yer vermektedir. Buna karşılık, Amerika Birleşik Devletleri ders kitapları daha çeşitli bir yaklaşım sergilemekte; birinin eşleme, diğerinin ise hareket perspektifine odaklandığı görülmektedir. Türk ders kitapları, örnekler ve etkinlikler yoluyla genellikle hareket perspektifini pekiştirirken, Amerika Birleşik Devletleri ders kitapları her iki perspektifi daha dengeli bir şekilde sunmaktadır. Çalışmanın bulguları, Türk ders kitaplarının öğrenciler ve öğretmenler arasında hareket perspektifinin tercih edilmesine katkıda bulunabileceğini göstermektedir. Amerika Birleşik Devletleri ders kitapları ise öğrencilerin her iki perspektifle de etkileşimde bulunmasına daha fazla olanak tanımaktadır. Sonuç olarak, her iki perspektifi de içeren öğretim materyallerinin, öğrencilerin yansıma ve simetri dönüşümlerine ilişkin kavramsal anlayışlarını geliştirebileceği ortaya konmuştur.

Keywords

Matematik ders kitapları, yansıma dönüşümü, hareket perspektifi, eşleştirme perspektifi, doküman incelemesi

A Comparison of Turkish and American Mathematics Textbooks in the Context of Motion and Mapping Perspectives: The Case of Reflection Transformation

Abstract

This study examines how high school mathematics textbooks from Türkiye and the United States address the concept of reflection transformation, focusing on two perspectives: motion and mapping. Textbooks play a crucial role in shaping students' understanding of mathematical concepts. When considering different perspectives, the motion perspective involves reflecting shapes across a symmetry axis without emphasizing key properties such as equal distance and perpendicularity, which can lead to misunderstandings. In contrast, the mapping perspective stresses reflecting all points on the plane while preserving these essential properties. The study analyzes two textbooks from each country, assessing their definitions of symmetry transformation, treatment of the symmetry axis, and approach to the domain of symmetry using a documentary analysis method. Turkish textbooks largely adopt the motion perspective, placing little emphasis on the mapping perspective. In contrast, U.S. textbooks display a more diverse approach, with one focusing on the mapping perspective and the other on the motion perspective. Turkish textbooks tend to reinforce the motion perspective through examples and activities, while U.S. textbooks present a more balanced view of both perspectives. The findings suggest that Turkish textbooks may contribute to a preference for the motion perspective among students and teachers. U.S. textbooks, however, offer more opportunities for students to engage with both perspectives. The study concludes that integrating both perspectives in teaching materials could enhance students' conceptual understanding of reflection and symmetry transformations

Keywords

Mathematics textbooks, reflection transformation, motion perspective, mapping perspective, documentary analysis

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