Reasoning and Proof in 5th Grade Mathematics Textbooks Aligned with The Century of Türkiye Education Model

Abstract

Developing mathematical reasoning, justifying and proving ideas are considered important skills in contemporary mathematics education. As fundamental resources in teaching and learning processes, textbooks play a key role in developing these types of skills. This study aims to systematically examine all content in fifth grade mathematics textbooks, prepared as part of the new curriculum created within the scope of The Century of Türkiye Education Model from the perspective of reasoning, justification, and proof. The research was designed as a qualitative study to examine how reasoning is incorporated in the mathematics textbook consisting of two books at the fifth-grade level. The data was analyzed using descriptive analysis method, which enabled the identification of the elements in the textbook, its thematic emphases, and the extent to which proof, reasoning, and justification are utilized. The findings showed that mathematical reasoning, justification, and proof were included in the fifth-grade textbook content, although the depth and distribution varied depending on the subject. Additionally, while proofs were more prominent in some themes in the fifth-grade textbook, they were limited in others. The study reveals the extent to which tasks that offer direct proof opportunities and require deductive thinking are addressed in textbooks, to implement the vision of mathematical thinking envisioned by The Century of Türkiye Education Model.

Keywords

• Textbook
• Justification
• Proof
• Mathematics
• Reasoning

Türkiye Yüzyılı Maarif Modeli’ne Yönelik Geliştirilen Beşinci Sınıf Matematik Ders Kitaplarında Muhakeme ve İspat

Abstract

Matematiksel akıl yürütmenin geliştirilmesi, fikirleri gerekçelendirme ve ispat, çağdaş matematik eğitiminde önemli becerilerden sayılmaktadır. Öğretim ve öğrenme süreçlerinde temel birer kaynak olarak ders kitapları bu tür becerilerin geliştirilmesinde kilit bir rol oynamaktadır. Bu çalışma, Türkiye Yüzyılı Maarif Modeli kapsamında oluşturulan öğretim programının bir parçası olarak hazırlanan beşinci sınıf matematik ders kitaplarındaki tüm içeriğin muhakeme, gerekçelendirme ve ispat perspektifinden sistematik olarak incelenmesini amaçlamaktadır. Araştırma beşinci sınıf düzeyindeki iki kitaptan oluşan matematik ders kitabında muhakemenin nasıl yer aldığını incelemek için nitel bir araştırma yöntemi olarak tasarlanmıştır. Veriler; kitaptaki unsurları, tematik vurguları ile ispat, muhakeme ve gerekçelendirmenin kullanım düzeylerini belirlemeye olanak tanıyan betimsel analiz yöntemiyle analiz edilmiştir. Bulgular, derinliği ve dağılımı konuya göre değişmekle birlikte beşinci sınıf ders kitabında matematiksel muhakeme, gerekçelendirme ve ispatın ders kitabı içeriğinde yer aldığını göstermiştir. Ayrıca beşinci sınıf ders kitabında ispat, bazı temalarda daha fazla yer alırken bazı temalarda sınırlı düzeyde yer almıştır. Çalışma, Türkiye Yüzyılı Maarif Modeli’nin öngördüğü matematiksel düşünme vizyonunun hayata geçirilebilmesi için ders kitaplarına doğrudan ispat yapma fırsatları sunan ve akıl yürütmeyi gerektiren görevlerin ele alınma düzeyini ortaya koymaktadır.

Keywords

• Ders kitabı
• Gerekçelendirme
• İspat
• Matematik
• Muhakeme

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