Examining Students’ Mathematical Understanding of Patterns by Pirie-Kieren Model

Abstract

The purpose of this study is to investigate students’ mathematical understanding of patterns. Three 7th grade students who enrolled in a public school solved the questions regarding the patterns. Semi-structured interviews were conducted with them about their solutions. The data were analyzed by using the Pirie-Kieren theory of mathematical understanding. The findings of this study revealed that students’ mathematical understanding varied between first six levels from primitive knowing to observing and their mathematical understanding mostly occurred between Image Making and Formalising layers. In terms of theory, students were able to pass the first and second “Don’t Need” boundaries but they could not progress their understanding over the third “Don’t Need” boundary. The results also illustrated that all of the students had knowledge about the patterns. In order to find the general rule of the pattern, they mostly endeavored to determine a formula and check its correctness by writing initial three steps.

Keywords

• mathematical understanding
• Pirie-Kieren model
• patterns
• middle school students

Öğrencilerin Örüntülere İlişkin Matematiksel Anlamalarının Pirie-Kieren Modeli ile İncelenmesi

Abstract

Bu çalışmanın amacı öğrencilerin örüntülere ilişkin matematiksel anlamalarını araştırmaktır. Bir devlet okulunda öğrenim gören üç yedinci sınıf öğrencisi çalışmaya katılmış ve örüntülerle ilgili soruları çözmüştür. Bu öğrencilerle çözümlerine yönelik yarı yapılandırılmış görüşmeler gerçekleştirilmiştir. Veriler Pirie-Kieren teorisi kullanılarak analiz edilmiştir. Elde edilen bulgular, öğrencilerin matematiksel anlamalarının ön bilgiden gözlem yapmaya kadar ilk altı düzey arasında çeşitlilik gösterdiğini ve genellikle imaj oluşturma ile formülleştirme aşamalarında gerçekleştiğini ortaya koymaktadır. Teoriye göre, öğrencilerin ilk ve ikinci ihtiyaç duyulmayan sınırların ilerisine gidebildikleri fakat üçüncü sınırı geçemedikleri görülmüştür. Sonuçlar öğrencilerin örüntülere ilişkin bilgilerinin olduğunu ve örüntünün genel formülünü bulmak için çoğunlukla bir kural belirlemeye ve bunun doğrulunu ilk üç terim için kontrol etmeye çalıştıklarını göstermektedir.

Keywords

• matematiksel anlama
• Pirie-Kieren model
• örüntüler
• ortaokul öğrencileri

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