Students' understanding of the core concept of function
Başlık çevirisi mevcut değil.
- Tez No: 400298
- Danışmanlar: PROF. DAVİD TALL
- Tez Türü: Doktora
- Konular: Eğitim ve Öğretim, Matematik, Education and Training, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2003
- Dil: İngilizce
- Üniversite: University of Warwick
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Matematik Eğitimi Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 298
Özet
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Özet (Çeviri)
This thesis is concerned with students? understanding of the core concept of functionwhich cannot be represented by what is commonly called the multiple representations offunctions. The function topic is taught to be the central idea of the whole of mathematics.In that sense, it is a model of mathematical simplicity. At the same time it has a richnessand has mathematical complexity. Because of this nature, for students it is so difficult tograsp. The complexity of the function concept reveals itself as cognitive complications forweak students. This thesis investigates why the function concept is so difficult for students.In the Turkish context, students in high school are introduced to a colloquial definition andare presented with four different aspects of functions, set-correspondence diagrams, sets ofordered pairs, graphs and expressions. The coherency in recognizing these different aspectsof functions by focusing on the definitional properties is considered as an indication of anunderstanding of the core concept of function. Focusing on a sample of a hundred andfourteen students, their responses in the questionnaires are considered to select ninestudents for individual interviews. The responses from these nine students in the interviewsare categorized as they deal with different aspects of functions. The data indicates thatthere is a spectrum of performance of students. In this spectrum, responses range from theresponses which handle the flexibility of the mathematical simplicity and complexity to theresponses which are cognitively complicated. Successful students could focus on thedefinitional properties by using the colloquial definition for all different aspects offunctions. Less successful students could use the colloquial definition for only setcorrespondencediagrams and sets of ordered pairs and gave complicated responses for thegraphs and expressions. Weaker students could not focus on the definitional properties forany aspect of functions.
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