Lise Öğrencilerinin İkinci Dereceden Denklemleri Çözme Başarıları

Bu çalışmanın amacı onuncu sınıf öğrencilerinin ikinci dereceden denklemleri çözme başarılarını incelemek, tam kareye tamamlama, çarpanlara ayırma, ikinci dereceden denklem formülü olmak üzere farklı çözüm yollarını kullanma eğilimlerini araştırmak ve öğrenciler tarafından yapılan hataları belirlemektir. Çalışmanın örneklemini Türkiye’nin kuzeyinde yer alan bir lisede öğrenim gören 50 onuncu sınıf öğrencisi oluşturmaktadır. Veriler ikinci dereceden denklemlere yönelik 9 sorunun örneklemdeki bütün öğrencilere uygulanmasıyla elde edilmiştir. İçerik analizi yapılarak veriler analiz edilmiş, yüzde ve frekans değerleri verilerek tanımlayıcı istatistiksel bilgi sunulmuştur. Bunun yanı sıra, öğrencilerin cevaplarından alıntılar yapılarak hata türleri gösterilmiştir. Bulgular, öğrencilerin ikinci dereceden denklemleri çözmekte zorlandıklarını ve çözerken çeşitli hatalar yaptıklarını göstermektedir. Öğrencilerin ikinci dereceden denklemleri çözerken yaptıkları hatalar cebirsel ifadeler, kesirler, negatif sayılar, ikinci dereceden denklem çözme kuralları, hesaplama ve cebirsel sadeleştirme gibi konuları tam öğrenememesine dayalı zayıflığından kaynaklanmaktadır. Ayrıca, öğrencilerin genellikle ikinci dereceden denklemleri çarpanlara ayırma yöntemiyle çözme eğiliminde oldukları sonucuna ulaşılmıştır.

Anahtar Kelimeler:

Cebir, ikinci dereceden denklemler, çözüm yolları

High School Students’ Achievement Of Solving Quadratic Equations

The purpose of the present study was to investigate tenth grade students` achievement of solving quadratic equations, to examine their tendency of using different solution ways which are completing the square, factorization and quadratic formula and to determine the errors made by students. 50 tenth grade students of a high school in northern part of Turkey constituted the sample of the study. In data collection, 9 open-ended questions related to quadratic equations was carried out all students in the sample. Data were analyzed through content analysis and also descriptive statistics: percentage and frequency were presented. Besides, the errors made by students were showed by quoting from their answers. The findings showed that most of the students have difficulty in solving quadratic equations and make various errors. The students’ errors in solving quadratic equation were tend to be due to their weaknesses in mastering topics such as algebra, fractions, negative numbers, the rules of quadratic equations` solution methods, calculation and algebraic simplification. In addition to this, the findings revealed that students were usually in tendency to use factorization in order to solve quadratic equations.

Keywords:

Algebra, quadratic equations, solution ways,

PDF

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