Examining of Secondary School Students’ Transition to Algebra in the context of Making Properties in Natural Number System Visible via Generalization

Abstract

The purpose of this study is to examine secondary school students’ transition from arithmetic to algebra in the context of making properties in natural number system visible via generalization. The cross-sectional study, which is one of the developmental research methods, was used in this study. Open-ended written tests were applied to 285 secondary school students from different grades (5th-8th Grades), and 24 students were interviewed clinically. Three questions and additional other questions were prepared to collect the data for this study in which the transition from arithmetic to algebra was investigated; and the data were assessed according to the characterization table prepared. In addition, the changes and developments in the transition process of the students of different grades from arithmetic to algebra data have been investigated with the clinical interview. As a conclusion, it has been observed that as the educational level of the students increase, the transition from arithmetic to algebra changed and developed in a positive manner in the context of generalization of the properties of the natural number system; however, this change and development has been realized at a little rate. There is not a clear differentiation between the 5th and 6th and between the 6th and 7th graders; and the most distinctive change and development among the educational levels has been observed between the 7th and 8th Graders.

Keywords

• Transition to algebra,Commutative,associative and distributive properties,Natural number system,Generalization,Secondary school students

Doğal Sayı Sistemindeki Özellikleri Genelleme Yoluyla Görünür Kılma Bağlamında Ortaokul Öğrencilerinin Cebire Geçişlerinin İncelenmesi

Öz

Bu çalışmanın amacı, doğal sayı sistemindeki bazı özellikleri genelleme yoluyla görünür kılma bağlamında farklı öğrenim seviyesindeki ortaokul öğrencilerinin aritmetikten cebire geçişlerini incelemektir. Gelişimci araştırmaların bir türü olan enlemesine çalışmanın kullanıldığı bu çalışmada, farklı öğrenim seviyelerindeki 285 ortaokul (5-8.sınıf) öğrencisine açık-uçlu yazılı sınavlar uygulanmış, 24 öğrenciyle ise klinik mülakatlar yürütülmüştür. Veri toplamak amacıyla aritmetikten cebire geçişin inceleneceği bu iki konuyu içeren 3 soru ile ek sorular hazırlanmış ve elde edilen veriler hazırlanan karakterizasyon tablosuna göre değerlendirilmiştir. Ayrıca elde edilen klinik mülakat verileriyle farklı öğrenim seviyelerindeki ortaokul öğrencilerin aritmetikten cebire geçiş sürecindeki değişim ve gelişimleri incelenmiştir. Sonuç olarak öğrencilerin öğrenim seviyesi arttıkça doğal sayı sistemi ile ilgili özellikleri genelleme bağlamında aritmetikten cebire geçişin olumlu yönde değiştiği ve geliştiği görülmüş, ancak bu değişim ve gelişim çok az olmuştur. Özellikle 5 ile 6 ve 6 ile 7.sınıf öğrencileri arasında çok belirgin bir farklılaşma olmamakla birlikte, öğrenim seviyeleri arasındaki en belirgin değişim ve gelişim 7 ile 8.sınıf öğrencileri arasında gerçekleşmiştir.

Anahtar Kelimeler

• Cebire geçiş,Değişme,birleşme ve dağılma özellikleri,Doğal sayı sistemi,Genelleme,Ortaokul öğrencileri

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