Öğretmen Adaylarının Orantısal Olan ve Olmayan İlişkileri Belirleyebilme ve Temsil Edebilmelerinin Problem İçerikleri Açısından İncelenmesi

Bu çalışmada, 46 ortaokul matematik öğretmen adayının çözüm yöntemleri, orantısal olan ve olmayan ilişkileri belirleyebilmeleri ve temsil edebilmeleri problem içerikleri bağlamında incelenmiştir. Öğretmen adaylarına iki adet sorudan (Bisiklet ve Mum) oluşan bir kağıt-kalem testi verilmiştir. Adayların kağıt-kalem testine verdikleri cevaplar içerik analizi yöntemi kullanılarak analiz edilmiştir. Analizler sonucunda sekiz öğretmen adayı ile yarı yapılandırılmış görüşmeler gerçekleştirilmiştir. Elde edilen bulgular, öğretmen adaylarının çözüm yöntemlerinin ve orantısal olan ve olmayan ilişkileri belirleyebilmelerinin ve temsil edebilmelerinin problem içeriklerinden etkilendiğini göstermiştir. Alan yazında belirtilenin aksine, öğretmen adayları ters orantılı ilişkiyi belirleme ve temsil etme konusunda doğru orantılı ilişkiyi belirleme ve temsil etmeye göre daha başarılı olmuşlardır. Öte yandan, adaylar en çok orantısal olmayan ilişkinin belirlenmesi ve temsil edilmesinde zorlanmışlardır. Derinlemesine inceleme gerektiren problemler daha gelişmiş çözüm yöntemlerinin ortaya çıkmasını sağlayıp, öğretmen adaylarının ezbere hesaplamaları kullanmaktan kaçınmasına yardımcı oldu.

Anahtar Kelimeler:

matematiksel temsiller, orantısal akıl yürütme, orantısal ilişkiler, öğretmen adayları, problem içeriği

Investigating Preservice Teachers’ Determination and Representation of Proportional and Nonproportional Relationships in Terms of Problem Contexts

This study investigated 46 preservice middle school mathematics teachers’ solution strategies and determination and representation of proportional and nonproportional relationships in terms of problem contexts. The preservice teachers were given a paper-pencil test with two mathematical tasks (Bicycle and Candle). The preservice teachers’ responses were analyzed using a content analysis method. Based on the analysis, semi-structured interviews were conducted with eight preservice teachers. The findings indicated that the preservice teachers’ solution strategies and determination and representation of relationships were affected by the problem contexts. The preservice teachers were better at determining and representing inversely proportional relationship than directly proportional relationship, which was quite opposite of the findings usually cited in the literature. Determining and representing nonproportional relationship appeared to be the most challenging task for them. Problems that required in-depth examinations elicited the use of more sophisticated solution strategies and helped the preservice teachers to avoid using rote computations.

Keywords:

mathematical representations, preservice teachers, problem context, proportional reasoning, proportional relationships,

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Author (2018). International Journal of Science and Mathematics Education.
Author (2019). International Journal of Science and Mathematics Education.
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