Matematik Öğretmen Adaylarının Lineer Kongrüanslara İlişkin Soyutlamayı İndirgeme Eğilimleri

Year 2014, Issue: 10, 59 - 72, 23.07.2016

Ş Can Şenay , Ahmet Ş Özdemir

Abstract

Matematik öğretmen adaylarının lisans eğitimi süresince alan bilgilerinin şekillenmesinde önemli rolü olan derslerden birisi de Sayılar Teorisi dersidir. Bu çalışmada, matematik öğretmen adaylarının, Sayılar Teorisi dersi kapsamında verilen lineer kongrüanslar ile ilgili algılayışları, Hazzan’ın (1999) geliştirdiği soyutlamanın indirgenmesi teorisi çerçevesinde incelenmiştir. Soyutlamanın indirgenmesi düşüncesi öğrencilerin, kavramların derste verildiği soyutlama seviyesinden daha düşük seviyedeki bir soyutlamayla çalışma eğilimlerine dayanmaktadır. Araştırmamızda, ilköğretim ve ortaöğretim matematik eğitimi bölümlerinde okuyan öğretmen adaylarından oluşan bir çalışma grubuna sorulan üç tane lineer kongrüans denkleminin çözümüne yönelik yazılı cevaplar, betimsel analiz ve içerik analizi yöntemleri ile incelenmiştir. Elde edilen bulgulardan, öğretmen adaylarının birçoğunun, denklemlerin çözümünün varlığı için gerekli şartları belirten teoremleri kullanmadan veya yanlış kullanarak çözüme ulaşmaya çalıştıkları görülmüştür. Bu durum, soyutlama seviyesinin indirgendiğinin bir göstergesidir

Keywords

Soyutlamanın indirgenmesi, lineer kongrüanslar

Pre-Service Mathematics Teachers’ Tendencies of Reducing Abstraction about Linear Congruence

Abstract

Number theory is one of the courses that play an important role in forming the content knowledge of the pre-service mathematics teachers during their undergraduate education. In this research, the conception of the pre-service mathematics teachers about linear congruence which is given in the number theory course is examined through the framework of the theory of reducing abstraction. The theme of reducing abstraction is based on students’ tendencies to work on a lower level of abstraction than the one in which concepts are introduced in class. The answers of a study group to the questions related with linear congruence are analyzed with the methods of content and descriptive analysis. From the obtained findings, it was observed that many of the pre-service teachers try to solve the equations without using the theorems about the existence of the solutions of a linear congruence or they misused them. This situation is an indication that the level of abstraction is reduced

Keywords

Reducing abstraction, linear congruence

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