İspat Sürecinden Yansımalar: Öğretmen Adaylarının İleri-Geri Tekniğini Kullanma Durumlarının İncelenmesi

Abstract

Çalışmanın amacı, matematik öğretmen adaylarının ispatlama sürecindeki zihinsel eylemlerini ileri-geri tekniği aracılığıyla resmedebilmektir. Bu amaçla akademik başarı düzeyi iyi, orta ve düşük olarak belirlenen üç matematik öğretmeni adayıyla geometri ve cebir alanından toplam iki soru üzerinden klinik mülakatlar gerçekleştirilmiştir. Öğretmen adaylarının ispat süreci analiz edilerek ileri-geri yöndeki zihinsel eylem haritaları oluşturulmuş ve bu haritaların ispatı tamamlamadaki rolü tartışılmıştır. Araştırma sonucunda öğretmen adaylarının akademik başarı düzeyi ve sorunun alanı fark etmeksizin ispat sürecinde ileri-geri hamlelerini bilinçli olmasa da yoğun bir şekilde gerçekleştirdiği belirlenmiştir. Adayların akademik başarısı arttıkça ispat sürecindeki ileri ve geri hamle sayılarının arttığı belirlenmiştir. Bu bakımdan öğretim üyelerinin ispat yaparken bu teknik aracılığıyla düşüncelerini sesli olarak ifade etmeleri, öğretmen adayları için ispatı yaratıcı bir inşa sürecine dönüştürme imkânı sunabilir.

Keywords

• ispat
• ileri-geri tekniği
• öğretmen adayı
• matematik öğretmen adayı

The Analysis of the Employment of the Forward-Backward Technique by Mathematics Pre-service Teachers

Abstract

The study aims to depict the mental actions of mathematics pre-service teachers during the process of proof, with the employment of the forward-backward method. Clinical interviews were conducted with three pre-service mathematics teachers, whose academic achievements were good, moderate and low, based on one geometry and one algebra questions. Mental maps for the forward-backward technique were developed based on the analysis of the proof processes adopted by each pre-service teacher, and the role of these maps in the achievement of the proof was discussed. The results demonstrated that three pre-service teachers intensively employed the forward-backward technique in proof, albeit not always consciously, regardless of their academic achievement levels and the field of the question. It was determined that the number of forward-backward steps increased with the increase in academic achievements of the pre-service teachers. Since the technique allows the faculty members to express their ideas verbally, this could provide the opportunity to turn proof into a creative construction process for the pre-service teachers.

Keywords

• proof
• forward-backward technique
• pre-service mathematics teacher

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