Conceptual Analysis of Derivative as a Rate of Change and Analysis of the Mathematics Textbooks

Abstract

In this study, initially, we provided a conceptual analysis for the rate of change interpretation of derivative from the quantitative reasoning perspective. Then, based upon the principles drawn from the quantitative reasoning perspective, the 12th-grade Turkish mathematics textbooks were analyzed, specifically focusing on the derivative topic, using the document analysis research method. The findigs indicated that mathematics textbooks are insufficient in terms of the diversity of real-life contexts. Even, the derivative as a rate of change concept is generally introduced limited with the kinematic contexts. Units of the quantities are properly used in the real-life contexts that appeared in the textbooks, however, the discussions and interpretations on the derivative concept by using the units of the quantities are not deep enough. Moreover, the covariation and relative-size ideas that are accepted to be prominent for the understanding of the rate of change are not sufficiently emphasized in all of the textbooks. The weak points in the Turkish mathematics textbooks that need to be enriched related to the concept of the derivative as a rate of change were emphasized. In the light of the findings, we also discussed the aspects that need to be developed in the textbooks provided with some samples of the real-life interpretations of the derivative as a rate of change and as relative size.

Keywords

• Covariation
• derivative
• mathematics textbooks
• quantitative reasoning
• rate of change

Türevin Değişim Oranı (Hızı) Yorumunun Kavramsal Analizi ve Matematik Ders Kitaplarının İncelenmesi

Abstract

Bu çalışmada türevin değişim oranı yorumunun anlamına yönelik kavramsal analizi nicel muhakeme teorik çerçevesinden detaylı olarak açıklanmaktadır. Daha sonra, nicel muhakeme çerçevesinden elde edilen temel prensipler doğrultusunda Türkiye’de okutulan lise ders kitaplarında türev kavramın nasıl ele alındığı nitel araştırma yöntemlerinden doküman inceleme yöntemiyle analiz edilmiştir. Elde edilen bulgular, incelenen ders kitaplarında türev kavramının anlamının tartışıldığı gerçek hayat bağlam çeşitliliğinin yetersiz olduğu ve hatta kinematik bağlamıyla sınırlı olduğunu göstermektedir. Kullanılan farklı gerçek hayat bağlamlarında birimlerin doğru kullanıldığı fakat kullanılan niceliklerin birimleri ile türevin anlamı üzerine derinlemesine yorumlamaların yeterli olmadığı görülmektedir. İncelenen her üç ders kitabında da türev kavramı ve değişim oranı yorumunun doğru anlaşılması bakımından önemli görülen kovaryasyon ve nispi büyüklük fikirlerinin de yeterince vurgulanmadığı görülmüştür. Ayrıca, türev kavramına yönelik olarak ders kitaplarında güçlendirilmesi gereken yönler vurgulanmıştır. Elde edilen bulgular ışığında, türev kavramının öğretimine yönelik ders kitaplarında yer verilmesi gereken bağlam örnekleri ile bunların nispi büyüklük olarak yorumlaması ile ilgili tartışmalar yapılmıştır.

Keywords

• Değişim oranı (hızı)
• Kovaryasyon
• Matematik ders kitabı
• Nicel muhakeme
• Türev

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