Matematik Öğretmeni Adaylarının Tümdengelimsel Akıl Yürütme Yoluyla İspat Anlayışları

Year 2024, Issue: 62, 362 - 404, 23.09.2024

Emine Gaye Çontay

https://doi.org/10.9779/pauefd.1359924

Abstract

Bu çalışmanın amacı matematik öğretmeni adaylarının tümdengelimsel akıl yürütme yoluyla ispat yapma becerilerini, ispat yöntemlerine ilişkin bilgilerini ve ispat yöntemlerini kullanma becerilerini ispat şemalarıyla ilişkilendirerek “ispat anlayışları” bağlamında ortaya koymaktır. Çalışma bir devlet üniversitesinde son sınıfta öğrenim gören 44 öğretmen adayı ile gerçekleştirilmiştir. Çalışmada öğretmen adaylarının ispat anlayışlarını ortaya koyması amacıyla iki farklı ölçme aracı geliştirilmiş ve uygulanmıştır. Çalışmanın bulguları öğretmen adaylarının büyük bölümünün ispat becerilerinin zayıf olduğunu, ispat yaparken kullandıkları yöntemlerden habersiz biçimde önermede yer alan değişkene değerler vererek ispatı yapılandırdıklarını, çoğunlukla deneysel ispat şeması göstergeleri ile hareket ettiklerini ortaya koymuştur. Öğretmen adayları ispat yöntemlerine ilişkin bilgileri açısından değerlendirildiklerinde, en çok aksine örnek verme ile ispat yöntemine ilişkin bilgiye sahip oldukları görülmüştür. Öğretmen adaylarının analitik dönüşümsel ispat şemasına ilişkin göstergelerle hareket ettikleri tek ispat sorusu ise durumlarla ispat yöntemi ile çözülebilecek ispat sorusudur. Analitik ispat şeması göstergeleriyle ispatlarını yapılandıran öğretmen adaylarından hiçbirinin, kullandıkları ispat yöntemini bilmedikleri belirlenmiştir. Dolayısıyla bu çalışmaya katılan matematik öğretmeni adaylarının ispat anlayışları yetersiz bulunmuştur.

Keywords

matematik öğretmeni adayı, ispat becerisi, ispat öğretimi, ispat şeması, ispat yöntem bilgisi

Ethical Statement

Bu araştırma, Pamukkale Üniversitesi Sosyal ve Beşeri Bilimleri Araştırma ve Yayın Etiği Kurulunun 0909//2020 tarihli 68282350/2018/G07 sayılı kararı ile alınan izinle yürütülmüştür.

Supporting Institution

Pamukkale Üniversitesi BAP Birimi

Project Number

2019BSP017

Preservice Mathematics Teachers’ Understanding of Proof Through Deductive Reasoning

Abstract

The aim of the study is to investigate preservice mathematics teachers' skills in proving through deductive reasoning, their knowledge of proof methods, and their ability to use proof methods in the context of their "understanding of proof" by associating them with proof schemes. The study was conducted with 44 preservice teachers studying in their final year at a state university. Two different assessment instruments were developed and applied. The findings of the study revealed that the majority of preservice teachers had weak proof skills that they structured the proof by giving values to the and that they frequently acted with experimental proof scheme indicators. When preservice teachers were evaluated in terms of their knowledge of proof methods, they had the knowledge about the method of counterexample. The only proof question in which preservice teachers acted with indicators related to the analytical transformational proof scheme was that could be solved by using the method of “proof cases.” It was identified that none of the preservice teachers who structured their proofs with analytical proof scheme indicators knew the proof method they used. Consequently, the proof understanding of the preservice mathematics teachers who participated in this study was found insufficient.

Keywords

Preservice mathematics teachers, Proof ability, Proof education, Proof scheme, Knowledge of the proof method

Project Number

2019BSP017

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