Ortaokul Yedinci Sınıf Öğrencilerinin Kesirlerle Çıkarma İşlemine Kurdukları Problemlerin Analizi

The purpose of the study was to determine potential errors, which might be experienced by seventh grade middle school students related to the problems posed by them about the subtraction operation with fractions. The study was conducted with 143 students studying at six middle schools existing in Erzurum. Problem posing test composed of four items about the subtraction operation with fractions was used as a data collection tool. The answers given by the students were classified in accordance with the categories of problem, not a problem and empty. Then, the errors in the answers within the category of problem were analyzed. Twelve errors were determined in the problems posed by the students. Moreover, students made more errors in posing problems about the subtraction operations with fractions which the minuend and subtrahend fractions are mixed fractions.Araştırmada, ortaokul yedinci sınıf öğrencilerinin kesirlerle çıkarma işlemine yönelik kurdukları problemlerde karşılaşabilecekleri olası hataların belirlenmesi amaçlanmıştır. Bunun yanında araştırmada kesirlerle toplama işleminden farklı olarak sadece kesirlerle çıkarma işleminde görülen hata türlerinin de belirlenmesi hedeflenmiştir. Araştırma, Erzurum merkezdeki altı ortaokulun yedinci sınıflarında öğrenim gören 143 öğrenci ile yapılmıştır. Kesirlerle çıkarma işlemine yönelik dört maddeden oluşan Problem Kurma Testi, veri toplama aracı olarak kullanılmıştır. Öğrenciler tarafından verilen yanıtlar problem, problem değil ve boş kategorilerine göre sınıflandırılmıştır. Bu tür bir sınıflandırmadan sonra problem kategorisinde yer alan yanıtlarda karşılaşılan hataların analizi yapılmıştır. Öğrencilerin kurdukları problemlerde 12 hata türü tespit edilmiştir. Bunun yanında eksilen ve çıkan kesir sayılarının tamsayılı kesir olduğu işlemlerde öğrencilerin daha fazla hata yaptıkları da tespit edilmiştir

Transfer of Mathematical Knowledge: Series

The aim of this study is to explain students’ ability to transfer their knowledge about mathematical series to the problems that they encounter. The data of the study were obtained by using two different tests, namely “Problem Solving Test (PST)” and “Series Character Identification Test (SCT)” which were developed by the researchers. The study was conducted to third- grade students from department of elementary school mathematics education in the 2009-2010 academic year. In view of the analysis of the data, it was observed that the students experienced no difficulty in the SCT which required procedural knowledge. They experienced difficulty in the PST which required skill to transfer their knowledge about the series to the circumstances that they encounter. According to these results, it was determined that the students experienced difficulty in transforming real life problems to series and interpreting these problems