Fonksiyon Kavramının Anlaşılması: Tanımsal Özellikler ve Çoğul Temsiller

Bu çalışma matematiğin önemli kavramlarından fonksiyon kavramının lise 3 öğrencileri tarafından anlaşılmasını inceler. Bunu yaparken, kuramsal çatı fonksiyonların çoğul temsilleri ile fonksiyon tanımının kullanımı arasındaki ilişkiyi temel alır. Amaç öğrencilerin küme eşlemesi diyagramları, sıralı ikili kümeleri, grafikler ve denklemler gibi çoğul temsiller hakkında yorum yaparken tanımsal özellikleri kullanabilme becerilerini ortaya çıkarmaktır. Çalışmanın örneklemini 9 lise 3 öğrencisi oluşturmaktadır. Bu 9 öğrenci, Matematik, Türkçe – Matematik ve Sosyal gruplarından olmak üzere 114 lise 3 öğrencisine dağıtılan anketlerin sonuçlarına göre teorik örnekleme yöntemi ile seçilmiştir. Temel olarak niteliksel olan bu çalışmanın verileri bu 9 lise 3 öğrencisi ile yapılan yarı-yapılandırılmış mülakatlardan elde edilmiştir. Mülakatlarda öğrencilerden çeşitli temsillerin fonksiyon olup olmadığı hakkında yüksek sesle düşünmeleri ve verilen sabit bir fonksiyonu diğer temsillere dönüştürmeleri istenmiştir. Mülakatların çözümlenmesi göstermiştir ki öğrencilerin farklı temsiller için tanımsal özellikleri kullanımları da farklılık göstermektedir. Dahası, tanımsal özellikleri bütün temsiller için kullanan öğrenciler temsiller arası dönüşümleri de daha başarılı bir şekilde yapmışlardır.

Understanding the Function Concept: Definitional Properties and Multiple Representations

This study investigates grade 11 students’ understanding of the function concept. To do that, the theoretical framework is based on the relationship between multiple representations and the use of the definition of function. The aim is to reveal students’ ability to use the definition as they comment on the multiple representa-tions of functions such as set correspondence diagrams, sets of ordered pairs, graphs and expressions. The sample of the study is 9 students in grade 11 in two schools in Adana, Turkey. These 9 students were selected among 114 grade 11 students in three different subjects groups (Mathematics, Turkish and Mathematics and Social subjects) on the basis of the results from the questionnaires. This study is mainly qualitative and the main data is obtained from the semi-structured interviews with the 9 students. In these interviews, students were asked to decide whether the given representations are functions or not and they were also asked to transform a constant function to its other representations. The analysis of the in-terviews indicates that students’ responses differ in the use of the definitional properties for various representations. Furthermore, students who can use the definitional properties for all representations can do transformations from one representation to the other more successfully.

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