A Phenomenographic Investigation of Middle School Pre-service Mathematics Teachers' Conceptions of Proof

Year 2021, Volume: 15 Issue: 1, 118 - 143, 27.06.2021

Yasemin Yılmaz Akkurt Selda Yıldırım

https://doi.org/10.17522/balikesirnef.939068

Abstract

The capability of pre-service teachers to teach mathematical reasoning depends on the quality of their proof conceptions. This qualitative study focuses proof conceptions of middle school pre-service mathematics teachers. To this end, this study employed a phenomenographic approach to identify the variation in pre-service teachers’ experience of proof. Analysis of semi-structured interviews revealed five qualitatively different categories: proof is (a) a way of problem-solving, (b) a means for understanding, (c) explaining thinking in a convincing way, d) validating conjectures using logical arguments, and (e) a means for discovery of mathematics. This study contributes to the pedagogical knowledge about a framework of proof conceptions. Results may be used to promote the quality of the mathematics teacher preparation programs.

Keywords

phenomenography, pre-service teachers, proof conception

Ortaokul Matematik Öğretmen Adaylarının İspat Kavramlarının Fenomenografik Bir İncelemesi

Abstract

Öğretmen adaylarının matematiksel akıl yürütmeyi öğretme yetenekleri sahip oldukları ispat kavramlarının kalitesine bağlıdır. Bu nitel çalışma, ortaokul matematik öğretmen adaylarının ispat kavramlarına odaklanmaktadır. Bu amaçla, bu çalışma öğretmen adaylarının ispat deneyimlerindeki farklılıkları belirlemek için fenomenografik bir yaklaşım kullanmıştır. Yarı yapılandırılmış görüşmelerin analizi, niteliksel olarak farklı beş kategori ortaya çıkarmıştır. Buna göre, ispat (a) bir problem çözme yoludur, (b) anlamanın bir aracıdır, (c) düşünmeyi ikna edici bir şekilde açıklamaktır, d) mantıksal argümanlar kullanarak varsayımları doğrulamaktır ve (e) matematiğin keşfi için bir araçtır. Bu çalışma, ispat kavramlarıyla ilgili pedagojik bilgiye katkıda bulunmaktadır. Sonuçlar, matematik öğretmeni hazırlık programlarının kalitesini artırmak için kullanılabilir.

Keywords

fenomenografi, ispat kavramı, öğretmen adayı

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