Matematik Öğretmen Adaylarının Kesirlerde Bölme İşlemi Konusunda Problem Kurma ve Kavramsal Açıklama Becerilerinin Değerlendirilmesi

Öz

Kesirler, öğrencilerin matematiğin soyut yapısına geçişindeki ilk önemli adımlardan biri olarak görülmektedir. Ancak öğretmen adayları ve öğretmenler, kesirlerde bölme işlemini kavramsal olarak anlamakta ve bunu gerçek yaşam bağlamlarıyla ilişkilendirmekte güçlük çekmektedir. Araştırmalar öğretmen ve öğretmen adaylarının kesirler konusundaki kavrayışlarını derinlemesine incelemek amacıyla matematiksel problem kurma çalışmalarının faydalı olabileceği göstermektedir. Bu araştırmanın amacı matematik öğretmen adaylarının kesirlerde bölme işlemiyle ilgili problem kurma becerilerini incelemek, bu süreçte yaptıkları hataları belirlemek ve kurdukları problemleri kavramsal düzeyde nasıl açıkladıklarını analiz etmektir. Bir devlet üniversitesinde İlköğretim Matematik Öğretmenliği programının üçüncü sınıfında öğrenim gören 53 öğretmen adayı bu araştırmanın katılımcılarını oluşturmaktadır. Bu araştırmada öğrencilerden bir kesri bir tam sayıya, bir tam sayıyı bir kesre ve bir kesri bir diğer kesre bölmelerini gerektiren problemler kurmaları ve kurdukları bu problemin çözümünü anlatmaları istenmiştir. Problemi doğru kuramayan ve gönüllü olan altı öğretmen adayı ile görüşme gerçekleştirilmiştir. Araştırmanın bulguları, matematik öğretmen adaylarının kesirlerde bölme işlemiyle ilgili problem kurma becerilerinde çeşitli zorluklar yaşadıklarını ve kavramsal anlamda eksikliklere sahip olduklarını göstermektedir. Öğretmen adayları en çok bir kesri başka bir kesre bölmeyi gerektiren işleme ilişkin problem kurmada zorluk yaşamaktadır. Bulgular, öğretmen adaylarının matematiksel anlayışlarını teşhis ve değerlendirmede problem kurma görevlerinin yararlılığını vurgulamaktadır.

Anahtar Kelimeler

• Kesirlerde bölme işlemi
• problem kurma
• öğretmen adayları.

Evaluation of Mathematics Teacher Candidates' Problem Posing and Conceptual Explanation Skills on Division of Fractions

Öz

Fractions are seen as one of the first important stages in students' transition to the abstract structure of mathematics. However, pre-service teachers and teachers have difficulty in conceptually understanding the division of fractions and relating it to real life contexts. Research has shown that mathematical problem posing activities can be useful in order to examine teachers' and pre-service teachers' comprehension of fractions in depth. The purpose of this study was to examine pre-service mathematics teachers' problem posing skills related to division of fractions, to identify the errors they made in this process, and to analyze how they explained the problems they posed at the conceptual level. The participants of this study were 53 pre-service mathematics teachers studying in the third year of the Primary Mathematics Teacher Education program at a state university. Students were asked to pose problems that required them to divide a fraction by a whole number, a whole number by a fraction, and a fraction by another fraction, and to explain the solution of the problem they posed. Interviews were conducted with six pre-service mathematics teachers who could not construct the problem correctly and volunteered. The findings of the study show that pre-service mathematics teachers have various difficulties and conceptual deficiencies in their problem posing skills related to division of fractions. The pre-service mathematics teachers had the most difficulties in constructing problems related to the operation that requires dividing one fraction by another fraction. The findings emphasize the usefulness of problem posing tasks in diagnosing and assessing pre-service teachers' mathematical understanding.

Anahtar Kelimeler

• Division of fractions
• problem posing
• pre-service teachers.

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