Middle School Students' Mathematical Generalization Abilities with the use of Different Representations

Year 2017, Volume: 8 Issue: 1, 103 - 129, 31.03.2017

Sibel Yeşildere-imre , Hatice Akkoç , Burcu Nur Baştürk-şahin

https://doi.org/10.16949/turkbilmat.303220

Abstract

The purpose of this
research is to examine the forms of thinking and generalization types of
students during the generalization of the patterns presented with different
representations. It is aimed to examine the generalizations used by the
students through the theoretical framework, to determine the forms of thinking
that prevent them from making algebraic generalization and to determine the use
of different representations of the students. For this purpose, case survey
research is used in the research. Participants were selected by purposeful
sampling method. The study was conducted with 92 students studying in the
sixth, seventh and eighth grades. Descriptive and content analysis were used to
analyze the data. Data analysis has shown that students tended to have
arithmetic generalizations rather than algebraic generalizations. Students have
difficulties in making algebraic generalizations using pictorial patterns. They
have transformed visual patterns into number patterns and have not been able to
make effective use of pictorial patterns.

Keywords

Generalization, algebraic generalization, representations

Ortaokul Öğrencilerinin Farklı Temsil Biçimlerini Kullanarak Matematiksel Genelleme Yapma Becerileri

Abstract

Bu araştırmada farklı temsil biçimleriyle
sunulan örüntüleri genellemede öğrencilerin düşünme şekillerini ve genelleme
yapma türlerini incelemek amaçlanmaktadır. Öğrencilerin kullandıkları genelleme
türlerinin kuramsal çerçeve bağlamında incelenmesi, cebirsel genelleme yapmaya
engel olan düşünme şekillerinin belirlenmesi ve öğrencilerin farklı temsil
biçimlerini genelleme yapma yönünde kullanma şekillerinin saptanması
hedeflenmektedir. Bu bağlamda araştırmada örnek olay tarama modeli
kullanılmıştır. Katılımcılar amaçlı örnekleme yöntemi ile seçilmiştir. Çalışma
altıncı, yedinci ve sekizinci sınıfta okuyan 92 öğrenciyle
gerçekleştirilmiştir. Elde edilen veriye betimsel ve içerik analizi
uygulanmıştır. Veri analizi öğrencilerin cebirsel genelleme yerine aritmetik
genelleme eğilimlerinin olduğunu göstermiştir. Öğrenciler şekil örüntülerini
kullanarak cebirsel genelleme yapmada güçlük çekmişlerdir. Şekil örüntülerini
sayı örüntüsüne dönüştürmüşler ve şekil örüntüsünden etkili şekilde
yararlanamamışlardır.

Keywords

Genelleme, cebirsel genelleme, temsiller

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