Argümantatif akıl yürütme ve genelleme arasındaki ilişkinin matematiksel yazılar temelinde incelenmesi

Öz

Bu çalışma, dördüncü sınıf öğrencilerinin matematiksel yazılarında argümantatif akıl yürütme ile genelleme arasındaki ilişkiyi incelemektedir. Araştırma, 289 katılımcı ile yürütülmüş olup, öğrencilere bir çözüm stratejisinin geçerliliğini değerlendirmeleri ve fikirlerini ifade etmeleri gereken bir yazma görevi verilmiştir. Bu görevde ayrıca, sunulan örneklerde kullanılan yöntem veya stratejilerin diğer problemlere uygulanabilirliğinin de belirlenmesi istenmiştir. Öğrencilerin %37,7'si matematik yazılarında argümantatif akıl yürütme becerisi sergilerken, %56'sı stratejileri farklı bağlamlara genelleyebilmiştir. Bulgular, argümantatif akıl yürütme ile genelleme arasında orta düzeyde pozitif ve istatistiksel olarak anlamlı bir korelasyon olduğunu ortaya koymuştur. Bu da bir bilişsel becerideki gelişmenin diğerini olumlu yönde etkileyebileceğini ve genel matematik yazma yeteneğini destekleyebileceğini düşündürmektedir. Çalışma, hem akıl yürütme hem de genelleme becerilerini aynı anda ele alan öğretim stratejilerinin önemini vurgulamaktadır. Bu bilişsel süreçleri gözlemlemek ve incelemek zor olsa da, araştırma, öğrenci yazıları temelinde bu iki süreçlerin birbirleriyle bağlantılı olduğunu ortaya koyarak literatüre katkıda bulunmaktadır.

Anahtar Kelimeler

• argümantatif akıl yürütme
• genelleme
• matematiksel yazma

Investigating the relationship between argumentative reasoning and generalization in fourth-grade mathematical writing

Abstract

This study explores the relationship between argumentative reasoning and generalization in mathematical writing among fourth-grade students. Conducted with 289 participants, the research involved a writing task where students were required to understand and articulate the validity of a given solution strategy. Additionally, they needed to determine whether the methods or strategies used in the provided examples could be applied to other problems. Analysis of the students’ work revealed that 37.7% demonstrated argumentative reasoning, while 56% successfully generalized strategies to different contexts. Statistical analysis indicated a moderately positive and significant correlation between argumentative reasoning and generalization. These findings suggest that students who are able to reason argumentatively are more likely to generalize problem-solving strategies, highlighting the interconnection between these cognitive skills. The study underscores the importance of instructional approaches that simultaneously foster reasoning and generalization abilities, as enhancing one skill may positively influence the other, thereby supporting the development of effective mathematical writing. These results contribute to the literature by providing evidence of these processes in young learners.

Keywords

• argumentative reasoning
• generalization
• mathematical writing

Kaynakça

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