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

Year 2020, Volume: 14 Issue: 1, 629 - 660, 30.06.2020

Muhammet Arıcan

https://doi.org/10.17522/balikesirnef.683225

Cited By: 1

Abstract

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

Supporting Institution

This study was supported by the Ahi Evran University Scientific Research Projects Coordination Unit.

Project Number

EGT.A4.18.014

Thanks

I would like to thank Dr. Wim Van Dooren and Dr. Lieven Verschaffel for their valuable feedback on earlier drafts of this paper. I also thank to TÜBİTAK- Directorate of Science Fellowships and Grant Programmes (BİDEB) for their support with providing me a research funding to stay in KU Leuven during which I was able to write this paper.

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

Abstract

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.

Keywords

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

Project Number

EGT.A4.18.014

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