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İSPAT’IN ÖNEMİ VE İSPAT KONUSUNDAKİ ÖĞRETMEN YETERLİKLERİNİN İNCELENMESİ

THE IMPORTANCE OF PROOF AND THE ANALYSIS OF TEACHERS' PROFICIENCIES IN THIS DOMAIN

Journal Name:

  • Turkish Studies

Publication Year:

  • 2017
DOI: 
http://dx.doi.org/10.7827/TurkishStudies.11589

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
Proof is an effective way of doing mathematics and, it comprises high quality of reasoning. In addition to its major role in validating a mathematical argument proof supports the teaching-learning processes in many different ways. Above all, proof promotes critical and creative thinking. It serves as a means to explore relationships between mathematical notions and, thus, fosters the development of students’ conceptual understanding. Proof creates environments in which students synthesise their prior knowledge and use them through deductive chains of reasoning to discover a new one. However, previous studies indicated that both pre-service and in-service teachers posses a limited understanding of this notion. In this respect, most commonly cited limitation is that many teachers tend to accept specific examples and empirically-based arguments as a valid proof. The purpose of this paper is to review the literature on proof and proving. We illustrate logical principles of mathematical proof and explain salient aspects of proof techniques, such as proof by mathematical induction. Then, we provide a comprehensive review concerning the teachers’ conceptions as to the role of proof and their subject-matter understanding of this notion. The paper concludes with a brief summary that brings recommendations to improve teachers’ understanding of proof and proving.
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Abstract (Original Language): 
İspatlar formel mantığın ve akıl yürütmenin etkili kullanıldığı uygulamalardır. Bu nedenle, verilen bir teoremin doğruluğunu kanıtlamanın ötesinde öğrenme-öğretme süreçlerini etkin kılma adına çok sayıda işlevinden bahsetmek mümkündür. En temelde ispatların eleştirel ve yaratıcı düşüncenin gelişimini desteklediği bilinmektedir. Bilgiler arası ilişkilerin açığa çıkarılmasındaki rolü nedeniyle öğrencilerin kavramsal bilgi edinmelerine imkân tanıdığı da bir gerçektir. İspat sürecinde geçmiş bilgiler sentezlenerek kullanılır ve yapılan çıkarsamalarla yeni bilgilere ulaşılır ki bu özelliğinden ötürü öğrencilere matematiksel bilgileri kendilerinin keşfetmeleri için uygun ortamlar sunduğu söylenebilir. Ayrıca, matematiksel dil ve terminolojinin aktif olarak kullanıldığı ispat süreçleri bireyler arasında kavram temelli tartışmaların ve fikir alış-verişlerinin yapılması için ortamlar sunar. Ancak, yapılan çalışmalar öğretmen adaylarının ve matematik öğretmenlerinin ispat bilgilerinin sınırlı olduğunu göstermektedir. Bu bağlamda kaydedilen en temel sıkıntı özel örnekler ve uygulama etkinlikleri üzerinden yapılan izahları ispat olarak kabul ettikleri hususudur. Ayrıca, ispat konusunda yaşanan sorunların farklı ispat yöntemlerinin mantıksal temelleriyle alakalı olduğu ve sayılar teorisi, cebir ve geometri gibi farklı alanları kapsadığı söylenebilir. Literatür taramasından oluşan bu yazıda genel olarak matematik öğretiminde ispatın rolü ve önemi konusu işlenmektedir. Bu çerçevede, ispatın matematiksel manasının yanı sıra okul matematiği kapsamında kullanılan farklı ispat yöntemlerinin mantıksal temelleri örnekler üzerinden açıklanmaktadır. Ayrıca, öğretmen adaylarının ve öğretmenlerin ispat algılarını ve bu alandaki bilgilerini inceleyen çalışmaların geniş bir özeti sunulmaktadır. Bu çalışmaların ortaya koyduğu bulgular tartışılmakta, ortaya çıkan sonuçlar ışığında öğretmen adaylarının ve öğretmenlerin ispat konusundaki yeterliklerini artırmak için getirilen önerilerle yazı sonlandırılmaktadır.
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  • Turkish

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İspat’ın Önemi ve İspat Konusundaki Öğretmen Yeterliklerinin İncelenmesi 39
Turkish Studies
International Periodical for the Languages, Literature and History of Turkish or Turkic
Volume 12/14
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40 İbrahim BAYAZIT
Turkish Studies
International Periodical for the Languages, Literature and History of Turkish or Turkic
Volume 12/14
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