İlköğretim matematik öğretmeni adaylarının matematiksel tümevarımın versiyonlarına yönelik beceri ve güçlükleri

Öz

Bu çalışmada ilköğretim matematik öğretmeni adaylarının matematiksel tümevarımın farklı versiyonlarına yönelik beceri ve güçlüklerinin ortaya çıkarılması amaçlanmıştır. Tümevarımın; zayıf, genişletilmiş zayıf, güçlü ve genişletilmiş güçlü tümevarım yöntemi olmak üzere dört versiyonuna odaklanılmıştır. Nitel araştırma yaklaşımı ile tasarlanan çalışma bir durum çalışması örneğidir. Araştırmanın çalışma grubunu 2023-2024 eğitim-öğretim yılı güz döneminde Türkiye’deki bir devlet üniversitesinin ilköğretim matematik öğretmenliği bölümünde öğrenimlerine devam eden ikinci sınıf öğrencileri oluşturmaktadır. Veriler araştırmacılar tarafından geliştirilen Matematiksel Tümevarım Versiyonları Beceri Formu yardımıyla toplanmıştır. Formdan elde edilen veriler betimsel analizle çözümlenmiştir. Çalışma sonucunda öğretmen adaylarının çoğunun zayıf tümevarım dışındaki tümevarım versiyonlarında başarısız oldukları, bu başarısızlığın zayıf tümevarımdan genişletilmiş güçlü tümevarıma doğru gittikçe arttığı tespit edilmiştir. Araştırmanın diğer ilgi çekici bir sonucu da öğretmen adayları zayıf ve genişletilmiş zayıf tümevarım yönteminde çoğunlukla tümevarım adımını oluşturmakta güçlük yaşarken güçlü ve genişletilmiş güçlü tümevarım yönteminde ise daha bu adıma geçemeden tümevarım hipotezlerini yazma aşamasında güçlük yaşadıkları ve bu yüzden ispatları tamamlayamadıkları saptanmıştır. Sonuçlar öğretmen yetiştirme bağlamında tartışılmış ve önerilerde bulunulmuştur.

Anahtar Kelimeler

• İspat
• matematik eğitimi
• öğretmen yetiştirme
• tümevarım
• tümevarım versiyonları

Prospective primary school mathematics teachers’ skills and difficulties towards versions of mathematical induction

Abstract

This study aimed to reveal the skills and difficulties of prospective primary school mathematics teachers towards different versions of mathematical induction. We focus on four induction versions: weak, extended weak, strong, and extended strong induction. The study designed with a qualitative research approach is a case study. The study group consisted of second-year students studying in the Department of Elementary School Mathematics Teacher Education at a state university in Türkiye in the fall semester of the 2023-2024 academic year. The data of the study were collected with the help of the Mathematical Induction Versions Skill Form developed by the researchers. The data obtained from the form were analyzed by descriptive analysis. As a result of the study, it was found that most of the pre-service teachers were unsuccessful in induction versions other than weak induction, and this failure increased from weak induction to extended strong induction. In weak and extended weak induction, the students mostly had difficulty in forming the induction step, whereas in strong and extended strong induction, the students had difficulty in writing induction hypotheses. The results were discussed in the context of teacher training and suggestions were made.

Keywords

• Proof
• mathematics education
• teacher training
• induction
• versions of induction

Kaynakça

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