Ortaokul Öğrencilerinin Dik Dairesel Silindire İlişkin Geometrik Akıl Yürütmeleri

Abstract

Bu çalışma, sekizinci sınıf öğrencilerinin dik dairesel silindire ilişkin geometrik akıl yürütmelerini, Fischbein’ın Şekilsel Kavram Teorisi çerçevesinde şekilsel ve kavramsal yönler arasındaki etkileşime odaklanarak incelemektedir. Durum çalışması olarak desenlenen araştırmaya devlet ortaokullarında öğrenim gören 25 öğrenci katılmış; veriler Geometrik Cisimlere İlişkin Akıl Yürütme Değerlendirme Aracı ve yarı yapılandırılmış görüşmelerle toplanmıştır. Bu araç, silindiri tanıma, tanımlama ve açınımını oluşturmaya yönelik görevler içermekte; görüşmeler ise öğrencilerin akıl yürütme süreçlerine ilişkin daha derinlemesine bilgi sağlamaktadır. Nitel analiz, geometrik akıl yürütmenin ağırlıklı olarak şekilsel olduğunu ortaya koymuştur. On altı öğrenci (%64) şeklin kavramı yönettiği, kavramsal özelliklerden çok görsel ipuçlarına dayanan şekil baskın bir akıl yürütme sergilerken, yalnızca dört öğrencinin (%16) şekilsel temsilleri kavramsal anlamayla bütünleştiren potansiyel uyumlu bir akıl yürütmeye sahip olduğu belirlenmiştir. Beş öğrencinin (%20) verileri sınıflandırma için yetersiz bulunmuştur. Hiçbir öğrenci tam uyumlu akıl yürütme sergilememiştir. Şekil baskın öğrenciler silindiri doğru tanımlamakta, sınıflandırmalarını gerekçelendirmekte ve kavramsal açıdan doğru çizimler yapmakta zorlanmış, çoğunlukla nesnenin görünüşüne dayalı ya da işlemsel açıklamalara başvurmuştur. Potansiyel uyumlu öğrenciler tanıma ve gerekçelendirme görevlerinde daha başarılı olmakla birlikte uzamsal akıl yürütmede sınırlılıklar göstermiştir. Önceki çalışmalardan farklı olarak öğrencilerin prototip şekillere daha az bağlı kaldığı görülmüştür. Bu durum, öğrencilerin şekilsel temsillerinin esnek olduğunu, ancak bu esnekliğin kavramsal anlamayla tam olarak bütünleşmediğini göstermektedir. İki boyutlu şekillere ilişkin alanyazından ayrışan bu bulgunun, öğrencilerin gündelik yaşamda silindir biçimli nesnelerle sıkça karşılaşmasından kaynaklanabileceği düşünülmektedir. Bulgular, ortaokul öğrencilerinin geometrik akıl yürütmesinin ağırlıklı olarak algısal kontrol altında kaldığını ve kavramsal anlamanın kendiliğinden gelişmediğini göstermektedir. Öğretime yönelik çıkarımlar arasında, görsel temsilleri kavramsal akıl yürütmenin yerine geçecek biçimde değil onu destekleyecek biçimde bütünleştiren ve geometrik nesnelerin kritik özelliklerini açıkça vurgulayan öğrenme ortamlarının tasarlanması yer almaktadır. Somut materyallerin ve dinamik görselleştirmelerin rehberlik eşliğinde kullanılması, şekilsel ve kavramsal yönler arasındaki uyumu destekleyerek öğrencilerin üç boyutlu geometride doğru akıl yürütme becerilerini geliştirebilir.

Keywords

• Geometrik akıl yürütme
• Şekilsel Kavram Teorisi
• Bilişsel perspektif
• Dik dairesel silindir
• Ortaokul

Supporting Institution

Çalışma herhangi bir kurum ya da kuruluş tarafından desteklenmemiştir

Ethical Statement

Bu çalışma, Pamukkale Üniversitesi Sosyal ve Beşeri Bilimleri Bilimsel Araştırma ve Yayın Etiği Kurulunun onayıyla yürütülmüştür (karar no: 15-3; 17.08.2021 tarihli ve E-93803232-622.02-89178 sayılı yazı).

Middle School Students’ Geometric Reasoning About the Right Circular Cylinder

Abstract

This study investigates eighth-grade students’ geometric reasoning regarding right circular cylinders, focusing on the interaction between figural and conceptual components within Fischbein’s Figural Concept Theory. Twenty-five students from public middle schools participated in a case study using the Reasoning Assessment Instrument (RAI) and semi-structured interviews. The RAI included tasks on recognizing, defining, and constructing cylinder developments, while interviews provided deeper insights into students’ reasoning processes. Qualitative analysis revealed that geometric reasoning was predominantly figural. Sixteen students (64%) were figure-dominant, relying primarily on visual cues rather than conceptual properties, while only four students (16%) demonstrated potentially harmonic reasoning, integrating figural images with conceptual understanding. Five students (20%) provided insufficient data for classification. None exhibited fully harmonic reasoning. Figure-dominant students struggled to define cylinders correctly, justify classifications, and produce conceptually accurate drawings, often relying on image-based or procedural explanations. Potentially harmonic students performed better in recognition and justification tasks but still showed limitations in spatial reasoning. Notably, prototypical reasoning was less pronounced than in prior studies, suggesting flexible figural representations without full conceptual integration. This deviation from traditional literature on 2D shapes could be attributed to students' frequent daily-life exposure to 3D cylindrical objects, which potentially enhances the flexibility of their figural representations. These findings highlight that middle school students’ geometric reasoning remains predominantly under perceptual control and does not spontaneously develop conceptual understanding. Instructional implications include designing learning environments that explicitly emphasize critical properties of geometric objects while integrating visual representations to support, rather than replace, conceptual reasoning. Guided use of manipulatives and dynamic visualizations may foster harmony between figural and conceptual components, enhancing students’ ability to reason accurately about three-dimensional geometry.

Keywords

• Geometric reasoning
• cognitive perspective
• right circular cylinder
• middle school
• Figural Concept Theory

Supporting Institution

This study received no support from any institution or organization.

Ethical Statement

This study was conducted with the approval of the Pamukkale University Social and Human Sciences Research and Publication Ethics Committee, dated August 17, 2021, and numbered E-93803232-622.02-89178.

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