Ortaokul Öğrencileri Kanıt Yapabilir mi?

Year 2021, Volume: 11 Issue: 2, 852 - 880, 01.07.2021

Tuğba Yulet Yılmaz , Nilüfer Köse

https://doi.org/10.18039/ajesi.923938

Abstract

Öğrencilerin muhakeme becerilerinin gelişiminin desteklemesi için küçük yaşlardan itibaren matematiksel kanıtla tanışmaları ve bu süreçteki eylemleri gerçekleştirmeleri oldukça gerekli ve önemli olmakla birlikte bu durum “küçük yaştaki öğrenciler kanıt yapabilir mi?” sorusunu akla getirmektedir. Bu soru doğrultusunda bu çalışmanın amacı ortaokul öğrencilerinin verilen problem ve önermeleri kanıtlama sürecindeki muhakemelerini incelemektir. Bu amaçla 2019-2020 eğitim öğretim yılında, bir devlet ortaokulunda öğrenim gören yedinci sınıf öğrencileri katılımcı olarak seçilmiştir. Nitel araştırma yaklaşımının benimsendiği bu çalışmada veriler açık uçlu görevler aracılığıyla toplanmıştır. Çalışma bulguları görevleri anlamayan öğrencilerin görevi yanıtsız bıraktıklarını, tekrar yazdıklarını, görevdeki verileri eksik, hatalı kullandıklarını ya da verilerin dışına çıktıklarını, bazen de görevdeki önermenin öncülünü anlamadıklarını ortaya koymuştur. Görevleri anlayan öğrencilerin muhakemeleri incelendiğinde, doğrudan kanıt yapmayı gerektiren sayı görevlerinde genel olarak deneysel doğrulama yaptıkları belirlenmiştir. Doğrudan kanıt yapmayı gerektiren geometri görevlerinde ise çoğunlukla bir dörtgenin kapsadığı dörtgeni aksine örnek vererek hatalı gerekçelendirme, prototip çizim üzerinde sembolle gerekçelendirme ya da hatalı çizime dayalı gerekçelendirme yaptıkları, bazı öğrencilerin ise tümdengelimsel muhakeme yaptığı belirlenmiştir. Aksine örnek vererek kanıt yapmaları gereken görevlerde bazı öğrencilerin ön bilgi eksikliğinden kaynaklı mantıksal olmayan gerekçelendirmeler yaptıkları, bununla birlikte pek çok öğrencinin tümdengelimsel muhakeme yaptığı görülmüştür. Bu çalışmada genel olarak öğrencilerin kanıtlama sürecinde argüman üretmede zorlandıkları, çoğunlukla özel durumlar kullanarak genelleme yapma eğiliminde oldukları ve önceki öğrenmelerini dönüşüm yapmadan kullandıkları söylenebilir.

Keywords

deneysel doğrulama, matematik eğitimi, matematiksel kanıt, tümdengelimsel muhakeme

Can Middle School Students Make Proof?

Abstract

In order to support the development of reasoning skills, it is very necessary and important for students to meet mathematical proof from an early age and to carry out actions in this process, and this is why "can young students make proof?" brings to mind the question. In line with this question, the purpose of this study is to examine the reasoning of middle school students in the process of proving the given problems and propositions. For this purpose, in the 2019-2020 academic year, seventh-grade students studying at a state middle school were selected as participants. In this study, in which qualitative research approach was adopted, the data were collected through open-ended tasks. The study findings revealed that students who did not understand the tasks left the task unanswered, rewrote it, used the data in task incompletely, incorrectly or went outside the data and sometimes did not understand the premise of the proposition in the task. When the reasoning of the students who understood the tasks was examined, it was determined that they generally made empirical verification in number tasks that require direct proof. In geometry tasks that require direct proof, it was determined that they mostly made incorrect justification by giving an example as opposed to another quadrilateral covered by a quadrilateral, justification with symbols on the prototype drawing, or justification based on incorrect drawing, and some students make deductive reasoning. In tasks in which they need to give counterexamples, was observed that some students made non-logical justifications caused by a lack of prior knowledge in the tasks, while many students made deductive reasoning. In this study, it can be said that students in general have difficulty making arguments in the proving process, often tend to generalize using special situations and use their previous learnings without transformation.

Keywords

deductive reasoning, empirical verification, mathematics education, mathematical proof

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