Ortaokul Öğrencilerinin Üslü İfadeler Konusunda Modelleme Yeterliklerinin İncelenmesi: Sarmal Kitaplık Problemi

Abstract

Bu çalışmanın amacı, eğitimsel modelleme perspektifi benimsenerek üslü ifadeler konusunda bir matematiksel modelleme etkinliğinin tasarlanması ve bu etkinlik aracılığı ile ortaokul öğrencilerinin matematiksel modelleme yeterliklerinin belirlenmesidir. Bu kapsamda araştırmacılar tarafından üslü ifadeler kazanımlarını içeren bir matematiksel modelleme etkinliği tasarlanmıştır. Bu etkinlik, ortaokulda öğrenim öğren 35 öğrenciye uygulanmış ve süreçteki çözümlerini nedenleri ile birlikte ifade etmeleri istenmiştir. Betimsel analiz yöntemi ile analiz edilen veriler bilişsel perpektif çerçevesinde oluşturulmuş “Modelleme Yeterlikleri Değerlendirme Rubriği” aracılığı ile değerlendirilerek öğrencilerin matematiksel modelleme yeterliklerindeki seviyeleri belirlenmiştir. Çalışmanın sonucunda öğrencilerin genellikle zorluk yaşadıkları üslü ifadeler konusunda matematiksel modelleme etkinliğinde görüntülenen süreçler Blum ve Leiss'in (2007) döngüsel modellemesiyle tutarlı olarak gözlemlenmiştir. Genellikle modelleme basamaklarında başarılı olan öğrencilerin yorumlama ve doğrulama basamaklarında düşük performans gösterdikleri belirlenmiştir. Bu süreç bağlamında öğretim programındaki kazanımları içeren matematiksel modelleme etkinliklerinin kullanımı ve uygulama çeşitliliğinin arttırılmasına ihtiyaç duyulduğu tespit edilmiştir.

Keywords

• Matematiksel modelleme
• eğitimsel modelleme perspektifi
• üslü ifadeler
• modelleme yeterlikleri

Examination of Secondary School Students' Modelling Competencies on Exponential Expressions: The Spiral Bookshelf

Abstract

The aim of this study is to design a mathematical modelling activity on exponential expressions by adopting an educational modelling perspective and to determine the mathematical modelling competencies of secondary school students through this activity. In this context, a mathematical modelling activity including exponential expression gains was designed by the researchers. This activity was applied to 35 secondary school students and they were asked to express their solutions in the process with their reasons. The data analyzed with the descriptive analysis method were evaluated through the “Modelling Competencies Evaluation Rubric” created within the framework of cognitive perspective, and the students' levels of mathematical modeling competencies were determined. As a result of the study, the processes displayed in the mathematical modelling activity for exponential expressions, which students generally have difficulty with, were observed to be consistent with the cyclic modelling of Blum and Leiss (2007). It was determined that the students who were successful in the modeling steps generally showed poor performance in the interpretation and validation steps. In the context of this process, it has been determined that there is a need to increase the use and application diversity of mathematical modelling activities that include the gains in the curriculum.

Keywords

• Mathematical modelling
• educational modelling perspective
• exponential expressions
• modelling competencies

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