Matematik Öğretmeni Adaylarının Logaritmik Fonksiyon Kavramına Yönelik Anlayışlarının İncelenmesi

Öz

Günümüzde üstel ve logaritmik fonksiyonlar; büyüme, azalma, değişim ve ölçeklendirme süreçlerinin modellenmesi açısından hem gerçek yaşamda hem de matematik öğretim programlarında önemli bir yere sahiptir. Logaritmik fonksiyon, ortaöğretim ve lisans düzeyindeki programlarda temel kavramlar arasında bulunmasına rağmen öğrenciler ve öğretmen adayları tarafından kavramsal açıdan güçlük yaşanan konular arasında gösterilmektedir. Öğretmen adaylarının ileride bu konuyu sınıf ortamında öğretme sorumluluğunu üstlenecek olmaları, logaritmik fonksiyona ilişkin anlayışlarının incelenmesini önemli kılmaktadır. Çalışmanın amacı, matematik öğretmeni adaylarının logaritmik fonksiyon kavramına yönelik anlayışlarını incelemektir. Araştırmanın katılımcılarını, 2024-2025 eğitim öğretim yılı bahar döneminde bir devlet üniversitesinde öğrenim gören beş ortaöğretim matematik öğretmeni adayı oluşturmaktadır. Çalışma, nitel araştırma yöntemlerinden durum çalışması deseniyle yürütülmüştür. Veri toplama aracı olarak araştırmacı tarafından geliştirilen ve dört açık uçlu sorudan oluşan bir görüşme formu kullanılmıştır. Sorular, “logaritmik fonksiyonun tanımı ve özellikleri”, “logaritmik fonksiyonun grafikleri ve özellikleri” ve “logaritmik fonksiyon ile gerçek yaşam ilişkisi” olmak üzere üç kategori altında toplanmıştır. Veriler yarı yapılandırılmış görüşmeler yoluyla toplanmış, içerik analiziyle çözümlenmiş ve öğretmen adaylarının ifadeleri alt kategoriler ve kodlar altında sınıflandırılmıştır. Bulgular, öğretmen adaylarının logaritmik fonksiyonun tanım koşullarını doğru ve tutarlı biçimde ifade etmekte zorlandıklarını, logaritmik fonksiyonların grafiklerini genellikle artan bir yapı olarak yorumladıklarını ve gerçek yaşam bağlamlarını ağırlıklı olarak deprem ölçeği örneğiyle sınırlı tuttuklarını göstermektedir. Elde edilen bulgular doğrultusunda, öğretmen adaylarının logaritmik fonksiyon kavramına ilişkin anlayışlarını geliştirmeye yönelik öğrenme ortamlarının tasarlanması önerilmektedir.

Anahtar Kelimeler

• Matematik eğitimi
• logaritmik fonksiyonlar
• kavramsal anlayış
• matematik öğretmeni adayları.

An Investigation of Pre-service Mathematics Teachers’ Understanding of the Concept of the Logarithmic Function

Öz

Exponential and logarithmic functions occupy an important place in both real-world modelling and mathematics curricula, as they are used to represent processes such as growth, decay, change, and scaling. Although the concept of the logarithmic function is a fundamental topic in secondary and undergraduate programmes, it is frequently reported as an area in which students and pre-service teachers experience conceptual difficulties. Given that pre-service teachers will eventually assume responsibility for teaching this topic, examining their understanding of the concept of the logarithmic function is particularly important. This qualitative study aims to investigate pre-service mathematics teachers’ understanding of the concept of the logarithmic function. The participants were five pre-service secondary mathematics teachers enrolled at a public university during the spring semester of the 2024-2025 academic year. The study was conducted as a case study. Data were collected through a researcher-developed interview form consisting of four open-ended questions under three categories: (i) the definition and properties of logarithmic functions, (ii) graphs of logarithmic functions and related features, and (iii) connections between logarithmic functions and real-world contexts. Semi-structured interviews were conducted, and the data were analysed using content analysis by coding participants’ statements into subcategories. The findings indicated that participants had difficulty expressing the defining conditions of logarithmic functions accurately and consistently, tended to interpret logarithmic graphs mainly as increasing, and associated real-world contexts largely with the earthquake magnitude scale. In line with these findings, learning environments should be designed to enhance pre-service teachers’ understanding of the concept of the logarithmic function.

Anahtar Kelimeler

• Mathematics education
• logarithmic functions
• conceptual understanding
• pre-service mathematics teachers.

Kaynakça

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