Üniversite Öğrencilerinin Analiz Dersi Kapsamında Matematiksel Kanıtlama Süreçleri: Örnek Olay Çalışması

Bu çalışmanın amacı öğrencilerin kanıtla ilgili görüşlerini belirlemek ve kanıtlama süreçlerini incelemektir. Nitel olarak desenlenen bu çalışma bir durum çalışmasıdır. Çalışmaya ikisi kız biri erkek üç öğrenci katılmış, hepsi matematik öğretmenliği birinci sınıf öğrencileridir. Katılımcılar, Analize Giriş II dersi kapsamında düşük, orta ve yüksek başarı gösteren öğrenciler olarak çalışmaya seçilmişlerdir. Veriler, ders gözlemleri, öğrencilerle yapılan görüşmeler ve görüşmede sorulan ifadeyi kanıtladıkları kâğıtlardan oluşmaktadır. Verilere içerik analizi uygulanmış ve görüşmeler Nvivo 7 programında kodlanmıştır. Çalışmada öğrencilerin sahip oldukları kanıt şemaları ve kanıt yapma yaklaşımları belirlenmiş, farklı başarı seviyesindeki öğrencilerin kanıt şemaları ve kanıt yapma yaklaşımlarının arasında nasıl bir bilişsel örüntü olduğu araştırılmıştır.

Undergraduate Students' Mathematical Proof Processes in a Calculus Course: A Case Study

This qualitative case study is designed to determine students’ views on and processes of constructing proofs. The participants were two females and one male freshman students in a mathematics teacher training program. The participants were selected representing their proficiency level in Intro to Analysis II as low, medium and high achievers. Data were gathered through classroom observations, structured interviews and papers where students reflected their proof processes. The data were analyzed through content analysis by using a qualitative analysis software program, Nvivo 7. The findings describe students’ proof schemes and approaches, as well as display the patterns in showing the relationship between proof schemes and approaches.

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