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İlköğretim Matematik Öğretmenliği Öğrencilerinin Sürekli Fonksiyonlarla İlgili İspatlama ve Ters Örnek Oluşturma Performansları

Proofing and Counter-exampling Performances of Students in the Elementary Mathematics Education Department for Continuous Functions

Journal Name:

  • Middle Eastern & African Journal of Educational Research

Publication Year:

  • 2014

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In advanced mathematical thinking, proof and counterexample are very important to indicate why a proposition is true or false and whether such proposition exists or not. It is important for students to learn counter-exampling and proofing within function domains because functions are frequently mentioned and used within many mathematics courses. Recent studies have revealed that students have difficulty in mathematical proofs. Most of these studies have focused on the potentiality of proofing and counter-exampling within the domains of functions. The aim of this study is to measure proofing and counter-exampling skills of students and to determine their mathematical perceptions. The findings show that participants experience problems in proofing and counter-exampling, and in the light of these findings, it is assumed that it is necessary to exemplify proofs and counterexamples carefully in learning and teaching process. Furthermore, to prove a theorem or to set a counterexample may contribute to the formation of a teaching draft within the advanced mathematics and curriculum analysis courses.
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Abstract (Original Language): 
Üst düzey matematiksel düşünmede, ispat yapma ve ters örnek verme bir önermenin niçin doğru veya yanlış olduğunu ve böyle bir önermenin olup olmadığını göstermek için çok önemli yere sahiptir. Öğrenciler birçok matematik dersinde sürekli fonksiyonlarla karşılaştıklarından fonksiyonların tanım bölgelerinde ispatları ve ters örnekleri öğrenmeleri önemlidir. Son zamanlarda, yapılan çalışmalar matematiksel ispatlarda öğrencilerin zorlandıklarını ortaya koymuştur. Bu araştırma çalışmalarının birçoğu lisans düzeyinde sürekli fonksiyonların tanım bölgelerinde ispat ve ters örneklerin üretilebileceği üzerine odaklanmıştır. Yaptığımız bu çalışmanın amacı da, öğrencilerin ispat ve ters örnek üretme yeteneklerini ve matematiksel algılarını belirlemektir. Bu çalışmanın bulguları, katılımcıların ispat ve ters örnek yazmada zorluk yaşadıklarını, öğrenme ve öğretmede ispat ve ters örnek verirken daha dikkatli olunması gerektiğini düşündürmektedir. Daha da önemlisi, bir teoremin ispatını yapmak veya ters örnek kurmak müfredat analizi ve ileri matematik derslerinde öğretim tasarımı oluşturma düşüncesini geliştirebilir.
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