Analyzing the Structures of Figural Patterns Produced by Middle School Students Based on Number Patterns

Abstract

Pattern is one of the most important topics of mathematics education in all grades. Some researchers asserted that pattern is the heart and soul of mathematics. Many skills and mathematical knowledge of students can be developed through pattern activities. In this study analyzing the structures of figural patterns/situations produced by middle school students based on number patterns was investigated. In total, 474 middle school students (254 were girls and 220 were boys) attended to study. Data were collected from a pattern task including linear and quadratic (non-linear) number patterns, in which participants were asked to generate figural patterns based on those number patterns. The obtained data were analysed at two levels. The results of the study indicated that participants created 18 linear forms and 33 non-linear forms for linear number pattern and 13 linear forms and 20 non-linear forms for quadratic number pattern. During the study participants preferred to use same geometrical shapes such as circles, triangles and squares, etc. while creating figural patterns. Moreover, participants  created many more figural patterns for the 3,5,7,9,11,… number pattern than for the 2,6,12,20,30,… number pattern. Some of the participants had problems while generating figural patterns such as producing non pattern forms, no answer, creating an irrelevant pattern and extending number patterns. 

Keywords

• Number pattern,figural pattern,linear pattern,quadratic pattern,pattern structures

Ortaokul Öğrencilerinin Sayı Örüntülerine Dayalı Olarak Oluşturdukları Şekil Örüntülerinin Yapılarının Analiz Edilmesi

Abstract

Örüntü matematik eğitiminde her düzeyde en önemli konulardan biridir. Bazı araştırmacılar örüntünün matematiğin kalbi ve ruhu olduğunu belirtmektedirler. Öğrencilerin bir çok becerisi ve matematiksel bilgisi örüntü etkinlikleri ile geliştirilebilir. Bu çalışmada öğrencilerin sayı örüntülerine bağlı olarak oluşturdukları şekil örüntülerinin yapıları analiz edilmiştir. Çalışmaya toplam 474 ortaokul öğrencisi (254 kız ve 220 erkek) katılmıştır. Çalışmanın verileri lineer ve lineer olmayan sayı örüntülerinin bulunduğu örüntü görevi ile toplanmıştır. Araştırmadan elde edilen veriler iki düzeyde analiz edilmiştir. Araştırmadan elde edilen sonuçlara bakıldığında katılımcıların 18 lineer yapı ve 33 lineer olmayan yapı lineer sayı örüntüsü için, 13 lineer yapı ve 20 lineer olmayan yapı quadratik örüntüler için üretmişlerdir. Örüntü oluşturma sırasında katılımcılar daire, üçgen ve kare gibi geometrik şekiller kullanmayı tercih etmişlerdir. Ayrıca, katılımcıların 3, 5, 7, 9, 11,..  sayı örüntüsü için oluşturdukları şekiller, 2, 6, 12, 20, 30,..sayı örüntüsü için oluşturdukları şekillerden daha fazladır.  Katılımcılardan bazıları şekil örüntüsü oluştururken örüntü olmayan yapılar oluşturma, yanıt verememe, ilgisiz örüntü oluşturma ve örüntüyü devam ettirme gibi sorunlar yaşamışlardır. 

Keywords

• Sayı örüntüsü,şekil örüntüsü,lineer örüntü,lineer olmayan örüntü,örüntü yapıları

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