Matematik Öğretmeni Adaylarının Geometrik İspatlarda İspat Yazma Becerilerinin İncelenmesi: Van Hiele Modeli

Öz

Bu çalışmanın amacı, van Hiele modeline dayalı öğretim etkinliklerinde matematik öğretmeni adaylarının ispat yazma becerilerindeki gelişimlerinin incelenmesidir. Çalışma, ilköğretim matematik öğretmenliği programı birinci sınıfında öğrenim görmekte olan on öğretmen adayıyla gerçekleştirilmiştir. Çalışmada, van Hiele modelinin öğretmen adaylarının ispat yazma becerilerindeki etkiliğinin ortaya konulması amaçlandığından nitel araştırma yöntemlerinden öğretim deneyi deseni benimsenmiştir. Bu amaçla nitel veri toplama araçları (bireysel görüşmeler, öğretmen adaylarının çalışma kağıtları ve araştırmacı alan notları) veri toplanması için kullanılmıştır. Öğretmen adaylarının ispat yazma becerilerinin gelişimleri van Hiele modelinde yer alan öğretim aşamaları ve düzeyleri kapsamında ele alınmıştır. Çalışma sonucunda, VH modelinde öğretmen adaylarının ispat yazma becerilerinin gelişimsel bir süreç ile desteklendiği ve ispat yazmada van Hiele-4 düzeyine erişebildikleri görülmüştür. Matematik öğretmen adaylarının gelişimsel olarak desteklenmesinde ise van Hiele modelinde yer alan bilgi ve sorgulama, rehberlik etme/destekleyici yönlendirme, açıklama/yorumlama, serbest yönlendirme ve entegrasyon öğretim ortamı unsurları etkili olduğu sonucuna ulaşılmıştır. Bu sonuçlar doğrultusunda matematik öğretmen adaylarının geometri öğrenimlerinde van Hiele geometrik düşünme gelişimlerini destekleyici önerilerde bulunulmuştur.

Anahtar Kelimeler

• van Hiele modeli
• ispat yazma
• öğretim deneyi
• matematik öğretmeni adayı

Examining Proof Writing Skills of Pre-Service Mathematics Teachers' in Geometric Proofs: Van Hiele Model

Abstract

The aim of this study is to examine the development of pre-service mathematics teachers' proof-writing skills in teaching activities based on the van Hiele model. The study was carried out with 10 pre-service mathematics teachers studying in the first year of the primary school mathematics teaching programme. In the study, teaching experiment design, one of the qualitative research methods, was adopted since it was aimed to reveal the effectiveness of the van Hiele model on pre-service mathematics teachers' proof-writing skills. For this purpose, qualitative data collection tools (personal interviews, pre-service teachers' worksheets, and researcher field notes) were used to collect data. The development of pre-service mathematics teachers' proof-writing skills was discussed within the scope of teaching stages and levels in the van Hiele model. As a result of the study, it was seen that the pre-service mathematics teachers' proof-writing skills were supported by a developmental process in the van Hiele model, and they were able to reach the van Hiele-4 level in proof-writing. It was concluded that knowledge and inquiry, guidance/directed orientation, explicitation/interpretation, free guidance and integration, which are the components of the teaching environment in the van Hiele model, are effective in supporting the pre-service mathematics teachers developmentally. In line with these results, suggestions were made to support the development of van Hiele geometric thinking in geometry learning of pre-service mathematics teachers.

Keywords

• van Hiele model
• proof-writing
• teaching experiment
• pre-service mathematics teacher

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