Pre-service Teachers' Mind Maps on Rational Numbers: Pirie-Kieren Theory

Year 2024, Volume: 53 Issue: 241, 133 - 164, 01.02.2024

Sare Şengül , Büşra Kıral Demir

https://doi.org/10.37669/milliegitim.1141497

Abstract

The aim of this study is to examine the mathematical understanding levels of secondary school mathematics teacher candidates regarding the concept of rational numbers according to the Pirie-Kieren theory. The research was carried out with three pre-service teachers studying in a university in Istanbul's primary school mathematics teaching program. The pre-service teachers were selected from among volunteer pre-service teachers with a high and good level of academic achievement and high communication skills who took the courses "Basics of Mathematics", "Secondary School Mathematics Curriculum", and "Teaching Numbers". The research was designed according to the case study pattern. The data were collected through a rational numbers concept test consisting of four open-ended questions on the concept of rational numbers developed by the researchers and semi-structured interviews. The obtained data were analyzed according to the Pirie-Kieren comprehension layers. The study determined that pre-service teachers were mostly in the "image creation" layer. Considering the process together with the semi-structured interview results, it was determined that the pre-service teachers tried to construct their knowledge by folding back and forth between the layers of "having the image", "noticing the feature", and "abstraction". In addition, pre-service teachers' mind maps were created according to the Pirie-Kieren theoretical model, and the results were discussed. According to the results obtained, suggestions have been developed for researchers in this field.

Keywords

Pirie-Kieren theory, conceptual understanding, rational numbers, pre-service teacher

Öğretmen Adaylarının Rasyonel Sayılara İlişkin Zihin Haritaları: Pirie-Kieren Teorisi

Abstract

Bu araştırmanın amacı, ortaokul matematik öğretmeni adaylarının, rasyonel sayılar kavramına ilişkin matematiksel anlama düzeylerinin Pirie-Kieren teorisine göre incelenmesidir. Araştırma, İstanbul ilindeki bir üniversitenin ilköğretim matematik öğretmenliği programında öğrenim görmekte olan üç öğretmen adayı ile yürütülmüştür. Öğretmen adayları “Matematiğin Temelleri”, “Ortaokul Matematik Öğretim Programları” ve “Sayıların Öğretimi” derslerini almış, akademik başarıları yüksek ve iyi düzeyde olan iletişim becerileri yüksek, gönüllü öğretmen adayları arasından seçilmiştir. Araştırma, durum çalışması desenine göre tasarlanmıştır. Veriler, araştırmacılar tarafından geliştirilmiş rasyonel sayılar kavramına ilişkin dört açık uçlu sorudan oluşan rasyonel sayılar kavram testi ve yarı-yapılandırılmış görüşmelerle toplanmıştır. Elde edilen veriler, Pirie-Kieren anlama katmanlarına göre analiz edilmiştir. Araştırmada öğretmen adaylarının ağırlıklı olarak “görüntü oluşturma” katmanında bulundukları belirlenmiştir. Yarı-yapılandırılmış görüşme sonuçları ile beraber süreç göz önüne alındığında ise öğretmen adaylarının “görüntüye sahip olma”, “özelliği fark etme” ve “soyutlama” katmanları arasında ileri geri katlamalar yaparak bilgilerini yapılandırma çabası gösterdikleri tespit edilmiştir. Ayrıca, öğretmen adaylarının Pirie-Kieren teorik modeline göre zihin haritaları oluşturularak sonuçlar tartışılmıştır. Elde edilen sonuçlara göre bu alandaki araştırmacılar için öneriler geliştirilmiştir.

Keywords

Pirie-Kieren teorisi, kavramsal anlama, rasyonel sayılar, öğretmen adayı

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