Examination of Prospective Mathematics Teachers' Concept Images of Prism and Cylinder in the Scope of Their Definitions, Drawings, and Grouping Skills

Yıl 2023, Cilt: 42 Sayı: 1, 33 - 96, 30.06.2023

Feyza Aliustaoğlu

https://doi.org/10.7822/omuefd.1197895

Öz

In this study, it was aimed to reveal the concept images of prospective mathematics teachers (known hereafter as PMTs) about prisms and cylinders. For this purpose, PMTs’ definitions of these geometric objects, their different drawings, and the way they grouped the given geometric objects were examined. The research was conducted based on the case study model. The study group of the research consisted of 45 prospective teachers studying at the first grade level in the Department of Primary Education Mathematics Teaching at the Faculty of Education of a state university in the north of Turkey. Firstly, the geometric objects test, which includes the skills of defining, drawing, and grouping cylinders and prisms, was applied to the PMTs. Then interviews were conducted with 6 prospective teachers. The analysis of the data was carried out based on the content analysis technique. The descriptive analysis technique was used in the analysis of the interview data. The results obtained from the research were presented under the headings of the PMTs’ definitions, drawings and grouping styles. As a result of the research, it was found that the PMTs’ definitions of cylinder and prism were not fully sufficient and they had difficulty in distinguishing the critical features. Concept images are based on prototype examples-usually in the form of right objects with a circular region base for a cylinder and a polygon base for a prism. It was seen that the concept images of the PMTs were more dominant than the concept definitions. In addition, it was determined that they made mistakes in using the mathematical language and that there were deficiencies in the content knowledge about the subject. When considering the hierarchical relationship between the cylinder and the prism, it was concluded that the PMTs generally thought of these objects as discrete sets, but had different ideas. Various suggestions were made based on the results obtained from the research.

Anahtar Kelimeler

Cylinder, Concept image, Mathematics education, Prism, Prospective mathematics teachers

Matematik Öğretmen Adaylarının Prizma ve Silindire Yönelik Kavram İmajlarının Tanımları, Çizimleri ve Gruplandırma Becerileri Kapsamında İncelenmesi

Öz

Bu araştırmada ilköğretim matematik öğretmen adaylarının prizma ve silindire yönelik kavram imajlarını ortaya çıkarmak amaçlanmıştır. Bu amaç doğrultusunda öğretmen adaylarının bu geometrik cisimlere yönelik tanımları, farklı çizimleri ve verilen geometrik cisimleri gruplandırma biçimleri incelenmiştir. Araştırma durum çalışması modeline dayalı olarak yürütülmüştür. Araştırmanın çalışma grubunu Türkiye’nin kuzeyinde bulunan bir devlet üniversitesinin Eğitim Fakültesi İlköğretim Matematik Öğretmenliği Bölümünde birinci sınıf düzeyinde öğrenim gören 45 öğretmen adayı oluşturmaktadır. Öncelikle uygun örnekleme yöntemi kullanılarak belirlenen öğretmen adaylarına silindir ve prizmaya yönelik tanımlama, çizim yapma ve gruplama becerilerini içeren geometrik cisimler bilgi testi uygulanmıştır. Ardından maksimum çeşitlilik örneklemesi yöntemine dayalı olarak öğretmen adaylarının verdikleri cevapların incelenmesi sonucunda 6 öğretmen adayı ile görüşmeler gerçekleştirilmiştir. Verilerin analizi içerik analizi tekniğine dayalı olarak gerçekleştirilmiştir. Görüşme verilerinin analizinde ise betimsel analiz tekniği kullanılmıştır. Araştırmadan elde edilen sonuçlar öğretmen adaylarının tanımları, çizimleri ve gruplandırma biçimleri başlıkları altında sunulmuştur. Araştırma sonucunda öğretmen adaylarının silindir ve prizma tanımlarının tam olarak yeterli olmadığı, bu geometrik cisimlere yönelik kritik özellikleri ayırt etmekte güçlük yaşadıkları bulunmuştur. Kavram imajları genellikle silindir için dairesel tabanlı ve prizma için çokgen tabanlı ve dik cisimler şeklindedir. Çizimlerinde genellikle prototip algıya dayalı çizim yapmışlar, gruplandırmada da prototip örnekleri ayırt etmekte zorlanmamışlar ancak prototip olmayan örnekleri ayırt etmekte zorlanmışlardır. Öğretmen adaylarının kavram imajlarının kavram tanımlarına göre daha baskın olduğu görülmüştür. Ayrıca matematiksel dili kullanmada hatalar yaptıkları ve konu ile ilgili alan bilgilerinde de eksikler olduğu tespit edilmiştir. Silindir ve prizma arasındaki hiyerarşik ilişki düşündüğünde öğretmen adaylarının genellikle bu cisimleri ayrık kümeler olarak düşünmekle birlikte farklı fikirlere sahip olduğu sonucuna ulaşılmıştır. Araştırmadan elde edilen sonuçlara dayalı olarak çeşitli öneriler getirilmiştir.

Anahtar Kelimeler

Kavram imajı, Matematik eğitimi, Matematik öğretmen adayları, Prizma, Silindir

Kaynakça

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