8. Sınıf Öğrencilerinin Kanıt Şemalarının Matematiksel Bilgi Açısından İncelenmesi

Year 2025, Volume: 27 Issue: 1, 13 - 40, 03.03.2025

Burhan Karakaya , Ahmet Cihangir

https://doi.org/10.32709/akusosbil.1248468

Abstract

Sekizinci sınıf öğrencilerinin kanıt şemalarının matematiksel bilginin türü açısından incelendiği bu araştırmanın modeli durum çalışması olarak belirlenmiştir. Çalışma grubunu, 2020-2021 yılında Afyonkarahisar merkez ilçesinde bulunan iki okulda öğrenim gören 36 sekizinci sınıf öğrencisi arasından ölçüt örneklemesi yöntemiyle seçilen 6 öğrenci oluşturmaktadır. Elde edilen verilerin analizinde, betimsel yöntem kullanılmıştır. KİBS' ten edilen verilere göre; kavramsal bilgiye sahip öğrencilerin denklem çözme performanslarının daha yüksek olduğu ve öğrencilerin çoğunun kavramsal bilgiye sahip olamadıkları belirlenmiştir. Yarı Yapılandırılmış Mülakatlar sonucunda öğrencilerin denklemler çözümlerini kanıtlamakta yetersiz kaldıkları ve gerekçe olarak otoriter kanıt şemalarını kullandıkları görülmüştür. Sonuç olarak öğrencilerin denklemlerde eşitlik bilgisine kavramsal olarak sahip olsalar da bu bilgilerini ispat yaparken kullanamadıkları belirlenmiştir. Öğrencilerin kavramsal bilgilerini geliştirmek ve matematiksel olarak geçerli kanıt yapabilmelerini sağlamak için problem çözümünde buldukları sonuçların ve yaptıkları işlemlerin nedenleri üzerine tartışmaları sağlanabilir.

Keywords

Kanıt şemaları, matematiksel eşitlik, eşitlik sembolü, kavramsal bilgi, işlemsel bilgi, mathematical equation, equality symbol

Examining Proof Schemes of 8th Grade in Terms of Mathematical Knowledge

Abstract

The model of this research, in which the proof schemes of eighth grade students were examined in terms of the type of mathematical knowledge, was determined as a case study. The study group consists of 6 students selected by criterion sampling method among 36 eighth grade students studying in two schools in Afyonkarahisar central district in 2020-2021. In the analysis of the obtained data, descriptive method was used. According to the data obtained from KİBS; It has been determined that the equation solving performance of students with conceptual knowledge is higher and most of the students do not have conceptual knowledge. As a result of the Semi-Structured Interviews, it was seen that the students were insufficient in proving the solutions of the equations and they used authoritative proof schemes as a justification. As a result, it was determined that although the students had the knowledge of equality in equations conceptually, they could not use this knowledge while making proofs. In order to improve the conceptual knowledge of the students and to enable them to make mathematically valid proofs, it can be ensured that they discuss the results they found in problem solving and the reasons for the operations they performed.

Keywords

Proof schemes, equality symbol, mathematical equality, equlity symbol, conceptual knowledge, procedural knowledge

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