ORTAOKUL MATEMATİK ÖĞRETMENLERİNİN UZMANLIK ALAN BİLGİLERİNİN MATEMATİKSEL HATALAR BAĞLAMINDA İNCELENMESİ

Abstract

EXAMINATION OF MIDDLE SCHOOL MATHEMATICS TEACHERS' SPECIALIZED CONTENT KNOWLEDGE WITH RESPECT TO MATHEMATICAL ERRORS

In this study, a secondary school teacher's specialized content knowledge in the linear equations with one unknown for 7th grade students have been examined with respect to mathematical errors made in class. Teachers' duties and responsibilities regarding mathematics within the conceptual framework of "Mathematical Knowledge for Teaching" (MKT) developed by Ball, Thames and Phelps (2008) is adopted in the examination of mathematics teachers' specialized content knowledge (SCK). Information was obtained about teachers' specialized content knowledge by way of observing the duties in question in classroom environment. In the meantime, the researcher noted the mathematical errors the teacher made in classes. Conducting detailed analysis by focusing on a middle school mathematics teacher, knowledge used in teaching the concept of equation and the errors made by the teacher during class were examined. The study was carried out using special case study design, one of several qualitative study methods. The middle school mathematics teacher who agreed to participate in the study was interviewed on the specialized content knowledge component of the MKT model. 8 class hours of teaching process of the teacher was observed, and video recorded. Once the teaching processes were completed, another general interview was made with the mathematics teacher. A descriptive analysis and content analysis were performed on the obtained data. In conclusion, the mathematics teacher was found to lack a sufficient level of specialized content knowledge. In particular, missing information provided and errors made by the teacher during lecturing adversely affected the learning process.

Keywords: mathematical knowledge for teaching, specialized content knowledge, mathematics teacher, equation concept

Öz

Bu çalışmada, bir ortaokul matematik öğretmeninin 7. Sınıf birinci dereceden bir bilinmeyenli denklemler konusuna ilişkin uzmanlık alan bilgisi, derste ortaya çıkan matematiksel hatalar bağlamında incelenmiştir. Matematik öğretmeninin uzmanlık alan bilgisinin (UAB) incelenmesinde, Ball, Thames ve Phelps (2008) tarafından geliştirilen, “Öğretmek İçin Matematik Bilgisi” (ÖMB) kuramsal çerçevesindeki, öğretmenin matematik ile ilişkili görev ve sorumluluklarından yararlanılmıştır. Söz konusu görevlerin sınıf ortamında gözlemlenmesiyle öğretmenin uzmanlık alan bilgisine dair bilgiler edinilmiştir. Bu süreçte öğretmenin derslerinde yapmış olduğu matematiksel hatalar araştırmacı tarafından not edilmiştir. Bir ortaokul matematik öğretmeni özelinde detaylı incelemeler yapılarak, denklem kavramı öğretiminde kullanılan bilgiler araştırırılmış ve öğretmenin derste yaptığı matematiksel hatalar incelenmiştir. Araştırma nitel araştırma yöntemlerinden biri olan özel durum çalışması deseninden yararlanılarak yürütülmüştür. Çalışmaya gönüllü olarak katılmayı kabul eden ortaokul matematik öğretmeniyle ÖMB modelinin uzmanlık alan bilgisi bileşenine ilişkin bir görüşme yapılmıştır. Sonrasında matematik öğretmeninin 8 ders saatlik öğretim süreci gözlenmiş ve video kamera ile kaydedilmiştir. Öğretim süreçlerinin tamamlanmasının ardından matematik öğretmeni ile genel bir görüşme daha yapılmıştır. Elde edilen verilere betimsel ve içerik analizi uygulanmıştır. Araştırma sonucunda, matematik öğretmeninin uzmanlık alan bilgisinin yeterli düzeyde olmadığı sonucuna ulaşılmıştır. Öğretmenin özellikle konu anlatımı sırasında verdiği eksik ilgiler ve yapmış olduğu hatalar öğrenme sürecini olumsuz etkilemiştir.

Anahtar Sözcükler: öğretmek için matematik bilgisi, uzmanlık alan bilgisi, matematik öğretmeni, denklem kavramı

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