Nejla YÜRÜK, Hasan Hüseyin UĞURLU, Hilal GÜLKILIK

Öğrencilerin Düzlem Dönüşümlerine Ait Kavramsal Anlamalarının Geliştirdikleri İç Temsiller Kapsamında İncelenmesi

Matematik eğitiminin başlıca amacı, öğrencilere matematiği anlayarak öğrenecekleri ortamlar sunmaktır. Araştırmalar, bu ortamların matematiksel kavramların çoklu temsillerini içerecek şekilde düzenlenmesi gerektiğine işaret etmektedir. Bu çalışmanın amacı, 10. sınıf öğrencilerinin çoklu temsillerle zenginleştirilmiş öğrenme ortamlarında, düzlem dönüşümlerine yönelik kavramsal anlamalarını geliştirdikleri iç temsiller kapsamında belirlemektir. Bu amaç gereği öteleme, dönme, yansıma ve homoteti dönüşümlerinin çoklu temsilleriyle çalışan dört 10. sınıf öğrencisiyle, söz konusu dönüşümlere yönelik görev temelli yarı yapılandırılmış birebir görüşmeler gerçekleştirilmiştir. Bulgular, öğrencilerin matematiksel kavramların çoklu temsilleri olan sözel, görsel, cebirsel temsiller ve manipülatiflerle geçirdikleri deneyimlerin kavramsal anlamalarına yön verdiğini göstermektedir. Öğrenciler bu temsilleri kullanarak, kavramlara yönelik uygun iç temsiller geliştirebildikleri ölçüde sağlam bir kavramsal anlama inşa edebilmektedir.

Investigating Students' Conceptual Understanding about Plane Transformations within the Scope of Internal Representations

The main goal of mathematics education is to provide environments in which students learn mathematics with understanding. Research studies indicate that these environments should be arranged to contain multiple representations of mathematical concepts. This study aims to identify 10th grade students' conceptual understanding about plane transformations in terms of internal representations that they developed in a learning environment enriched with multiple representations. For this purpose, one to one task-based semi-structured interviews were conducted with four 10th grade students who gained experience with multiple representations of translation, rotation, reflection and dilation. The results revealed that students' mathematical understanding developed through the experiences they had with standard external representations of mathematical concepts such as verbal, visual, algebraic representations and manipulatives. Students developed a deeper conceptual understanding of mathematical ideas to the extent that they can build appropriate internal representations of these external representations.

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