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

Yıl 2017, Cilt: 13 Sayı: 1, 65 - 79, 16.04.2017

Çiğdem Kılıç

https://doi.org/10.17860/mersinefd.305756

Öz

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. 

Anahtar Kelimeler

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

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

Öz

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. 

Anahtar Kelimeler

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

Kaynakça

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