Proof Characteristics of Primary School Mathematics Teacher Candidates in The Algebra and Geometry Domains

Öz

The aim of this study is to reveal the characteristics of the proofs made by primary school mathematics teacher candidates in the domains of algebra and geometry. In this context, the focus was on the proof structures and schemes of the proofs made by prospective teachers in the domains of algebra and geometry. The study group consists of 29 teacher candidates studying in the fourth grade of the primary mathematics teaching department of a state university in Türkiye. The research data were collected through the Algebra-Geometry Proof Form. The form included two open-ended questions that prospective teachers had to prove in the domains of algebra and geometry. These proofs were analyzed with the help of descriptive analysis. The analysis results of the proof structures revealed that teacher candidates were mostly able to produce inductive and structural-intuitive proofs in proofs in both algebra and geometry, and that they could produce valid proofs in a very limited number of deductive structures in both domains. The analysis of proof schemes revealed that pre-service teachers mostly used inductive and non-referential symbolic proof schemes in proofs in the domain of algebra, and that they mostly used inductive and perceptual proof schemes in proofs in the domain of geometry. These results revealed that prospective teachers were unsuccessful in making proofs in both algebra and geometry. When the structural unity situations between the proofs in the domains of algebra and geometry were examined, it was determined that there was no structural continuity between the proofs in these two domains, there was mostly structural distance, and this was followed by spontaneous continuity.

Anahtar Kelimeler

• Algebra
• Geometry
• Primary school mathematics teacher candidate
• Proof
• Proof characteristics

İlköğretim Matematik Öğretmeni Adaylarının Cebir ve Geometri Alanlarındaki İspat Özellikleri

Öz

Bu çalışmanın amacı ilköğretim matematik öğretmeni adaylarının cebir ve geometri alanında yaptıkları ispatların özelliklerini ortaya çıkarmaktır. Bu bağlamda öğretmen adaylarının cebir ve geometri alanında yaptıkları ispatların; ispat yapılarına ve şemalarına odaklanılmıştır. Araştırmanın çalışma grubunu Türkiye’deki bir devlet üniversitesinin ilköğretim matematik öğretmenliği bölümü dördüncü sınıfında öğrenim gören 29 öğretmen adayı oluşturmaktadır. Araştırmanın verileri Cebir-Geometri İspat Formu aracılığı ile toplanmıştır. Formda öğretmen adaylarının cebir ve geometri alanından ispat yapmaları gereken iki açık uçlu soru yer almıştır. Bu ispatların çözümlenmesinde betimsel analiz kullanılmıştır. İspat yapılarının analiz sonuçları ilköğretim matematik öğretmen adaylarının hem cebir hem de geometri alanındaki ispatlarda çoğunlukla tümevarımsal ve yapısal-sezgisel yapıda ispat üretebildiklerini, her iki alanda da çok sınırlı sayıda tümdengelimsel yapıda geçerli ispat üretebildiklerini ortaya koymuştur. İspat şemalarının analizi öğretmen adaylarının cebir alanındaki ispatlarda çoğunlukla tümevarımsal ve referanssız-sembolik ispat şemalarını kullandıklarını, geometri alanındaki ispatlarda ise çoğunlukla tümevarımsal ve algısal ispat şemalarını kullandıklarını ortaya çıkarmıştır. Bu sonuçlar öğretmen adaylarının hem cebir hem de geometri alanında ispat yapmada başarısız olduklarını gözler önüne sermiştir. Cebir ve geometri alanlarındaki ispatlar arasındaki yapısal bütünlük durumları incelendiğinde bu iki alandaki ispatlar arasında yapısal sürekliliğin olmadığı, çoğunlukla yapısal mesafenin olduğu bunu da spantone sürekliliklerin takip ettiği belirlenmiştir.

Anahtar Kelimeler

• Cebir
• Geometri
• İlköğretim matematik öğretmen adayı
• İspat
• İspat özellikleri

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