Matematik Öğretmen Adaylarının Şekil Örüntülerini Genelleme Süreçleri

Bu araştırmanın amacı matematik öğretmen adaylarının örüntüleri genelleme süreçlerini incelemek ve bu süreçte model kullanımında tercih ettikleri görsel kalıpları belirlemektir. 145 ilköğretim matematik öğretmen adayına lineer olan ve lineer olmayan şekil örüntülerini genellemeye yönelik dört tane açık uçlu problem yöneltilmiştir. Öğretmen adaylarının problemlere verdikleri yanıtlar, örüntüyü genelleme süreçleri ve şekil örüntülerini bu süreçte nasıl kullandıkları analiz edilmiştir. Cebirsel genelleme sürecinin analizinde Radford (2006) tarafından ortaya konulan kuramsal çerçeve kullanılmıştır. Veriler analiz edildiğinde öğretmen adaylarının genelleme sürecinde lineer şekil örüntülerinden lineer olmayanlara göre daha çok yararlandıkları belirlenmiştir. Ayrıca, öğretmen adaylarının şekil örüntüsünü nümerik olarak belirterek genelleme yapmaya yatkın oldukları görülmüştür. Bunun yanı sıra verilen örüntüdeki ortak özelliği belirleme bağlamında genelleme yapmaya yardımcı olacak seçimlerde bulunmadıkları, sadece bir sonraki terimi bulmayı sağlayacak şekilde ortak bir özellik araştırdıkları gözlemlenmiştir.

Anahtar Kelimeler:

Örüntü, model kullanma, genelleme

Pre-Service Mathematics Teachersâ Generalization Processes of Visual Patterns

The aim of this study is to investigate pre-service mathematics teachersâ generalization processes and models used in these processes. 145 elementary pre-service mathematics teachers were asked four openended problems which requires to generalize linear and non-linear pictorial patterns. Pre-service teachers' written responses were analyzed to investigate their generalization processes and how they used pictorial models in these processes. Radfordâs (2006) framework is used for the analysis. The analysis of data indicated that pre-service teachers used pictorial models more effectively for linear patterns when compared to non-linear patterns. It was also found that they tend to represent pictorial patterns numerically first and then generalize the numerical pattern. In addition to that it was observed that the way they discovered the commonalities among the terms of the patterns were not helpful in generalization process since they looked for commonalities by focusing on the consecutive terms of the patterns.

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