Öğrencilerin Silindirin Hacmi Konusunda Geliştirdikleri Matematiksel Fikirler: Sınıf İçi Argümantasyon Modeli

Öz

Bu çalışmanın amacı, silindirin hacmi konusu kapsamında sekizinci sınıf öğrencilerinin geliştirdikleri matematiksel fikirleri saptamak ve bunun için uygulanan içeriğin etkililiğini sekizinci sınıf matematik dersinde test etmektir. Bu bağlamda, bir varsayıma dayalı öğrenme yörüngesinin rehberliği ile bir öğretim dizisi kullanılmıştır. Konu olarak silindirin hacmi belirlenmiştir. Süreç iki hafta boyunca devam etmiştir. Sınıf içi argümantasyon, dinamik geometri yazılımı ve günlük yaşam örnekleri sınıf etkinliklerini desteklemiştir. Verilerin analizi için Krummheuer’in (2015) argümantasyon modeli kullanılmıştır. Analiz sonucunda dört matematiksel fikir elde edilmiştir; (a) hacim üçüncü boyut ile ilgilidir, (b) hacim bir cismin içini doldurmaktır, (c) hacim hesabı yükseklik, genişlik ve uzunluk kavramlarını içerir, (d) hacim taban alanı ile yüksekliğin çarpımıdır.

Anahtar Kelimeler

• matematiksel fikirler
• argümantasyon
• silindir
• tasarım tabanlı çalışma
• varsayıma dayalı öğrenme yörüngesi

Mathematical Ideas Developed by Students on Volume of Cylinder: A Classroom Argumentation Model

Öz

The aim of this study is to determine the mathematical ideas developed by eighth-grade students in the context of the volume of the cylinder and to test the effectiveness of the applied content in the eighth-grade mathematics course. In this context, an instructional sequence with the guidance of a hypothetical learning trajectory was used. The volume of the cylinder was the subject. The process continued for two weeks. Classroom argumentations, dynamic geometry software, and daily life examples supported instructional activities. The argumentation model of Krummheuer (2015) was used to analyze classroom argumentations. The analysis of the data collected from the study yielded four mathematical ideas; (a) the volume is related to the third dimension; (b) the volume is to fill the solid; (c) the volume calculation includes the concepts of height, width, and length; (d) volume equals to the multiplication of base area and height.

Anahtar Kelimeler

• mathematical ideas
• argumantation
• cylinder
• design-based study
• Hypothetical learning trajectory

Kaynakça

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