Evolving from Counting to Functional Reasoning: Middle School Students’ Strategies for Pattern Generalization

Abstract

This study aims to examine the generalization strategies employed by middle school students in linear pattern tasks according to their grade levels. The research was conducted using a two-phase qualitative design, consisting of written worksheet implementations with a total of 30 students from grades 5, 6, 7, and 8, and individual interviews with 11 students representing varying levels of academic achievement. The data were analyzed using descriptive analysis based on the framework of generalization strategies defined by Lannin (2005). The findings indicate that 5th and 6th grade students predominantly used counting, drawing, iterative, and contextual strategies, whereas 7th and 8th grade students primarily relied on contextual and functional (linear) strategies. Notably, students in higher grades developed more systematic approaches toward constructing functional rules. These findings suggest that pattern-based activities should be supported with differentiated instructional strategies across grade levels to foster the development of algebraic thinking.

Keywords

• Algebraic thinking
• Linear patterns
• Generalization strategies
• Middle school students

YAKINDAN UZAĞA, SAYMADAN FONKSİYONA: ORTAOKUL ÖĞRENCİLERİNİN GENELLEME STRATEJİLERİNİN EVRİMİ

Abstract

Bu çalışma, ortaokul öğrencilerinin lineer örüntü görevlerinde kullandıkları genelleme stratejilerini sınıf düzeylerine göre incelemeyi amaçlamaktadır. Araştırma, 5, 6, 7 ve 8. sınıf düzeylerinde öğrenim gören toplam 30 öğrenciyle gerçekleştirilen çalışma kağıdı uygulamaları ve farklı başarı düzeylerine sahip 11 öğrenciyle yapılan bireysel görüşmelerden oluşan iki aşamalı bir nitel tasarım ile yürütülmüştür. Veriler, Lannin (2005) tarafından tanımlanan genelleme stratejileri çerçevesinde betimsel analiz yöntemiyle değerlendirilmiştir. Bulgular, 5. ve 6. sınıf öğrencilerinin genellikle sayma, çizme, yinelemeli ve içeriksel stratejileri tercih ettiğini; 7. ve 8. sınıf öğrencilerinin ise içeriksel ve doğrusal stratejileri ağırlıklı olarak kullandığını göstermektedir. Özellikle üst sınıf düzeylerinde öğrencilerin fonksiyonel kurallar oluşturmaya yönelik daha sistematik yaklaşımlar geliştirdiği gözlenmiştir. Bu bulgular, cebirsel düşünmenin gelişimi açısından örüntü temelli etkinliklerin farklı sınıf düzeylerinde farklılaşan öğretim stratejileriyle desteklenmesi gerektiğini ortaya koymaktadır.

Keywords

• Cebirsel düşünme
• lineer örüntüler
• genelleme stratejileri

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