Lise Öğrencilerinin ve Öğretmenlerinin Görsel İspat ile İlgili Deneyimleri

Öz

İspat, matematiğin ve matematik eğitiminin ana bileşenlerinden biridir. Buna rağmen öğrenciler ve öğretmenler her düzeyde ispat öğreniminde ve öğretiminde güçlük yaşamaktadırlar. Bu bağlamda düşünüldüğünde öğrencilere kullanabilecekleri alternatif ispat yöntemlerinin sunulması ile hem zengin öğrenme ortamları oluşturmuş olacak hem de bir ispatı yapmak için başvurulabilecek alternatif yollar sunulmasıyla öğrenciye farklı bakış açıları kazandırılmış olacaktır. Görsel ispatlar ispat öğretiminde alternatif bir yöntemdir. Bu çalışmada görsel ispat etkinliklerinde yer alan lise öğrencileri ve öğretmenlerinin deneyimlerine dönük görüşleri alınmıştır. Çalışmanın modeli durum çalışmasıdır. Katılımcılar 9. sınıfta öğrenim gören ve uygulama sırasında görsel ispatlar ile deneyim yaşayan dört öğrenci ve onların öğretmenleridir. Öğretmen görsel ispat deneyimi yaşayan öğrencilerin sonraki derslerde formüllerin nereden geldiğini merak ettiklerini başka bir deyişle sorgulamaya başladıklarını, derse ilgilerinin arttığını ve formüllerin akıllarında daha çok kaldığını belirtmiştir. Öğrenciler ise görsel ispat etkinliklerini eğlenceli bulduklarını, ispatı anladıkları zaman mutlu olduklarını buna karşın anlamadıkları zaman mutsuz olduklarını belirtmişlerdir.

Anahtar Kelimeler

• İspat
• ispat öğretimi
• ispat yöntemleri
• sözsüz ispat
• görsel ispat

High School Students’ and Their Teacher’s Experiences with Visual Proofs

Abstract

Proof is one of the main components of both mathematics and mathematics education. However, students and teachers at every level have difficulties in proof and proof teaching. Presenting alternative proof methods to students will not only provide a rich learning environment but also allow the students to have different perspectives by providing alternative ways they can apply for constructing a proof. The visual proofs are one of the alternative proof methods. The visual proofs are seen as valuable tools for mathematics education; it is planned to investigate the views of high school students and their teacher about visual proof. Case study method is used in the study. Participants of the study consisted of four high school students who were nineth-graders and their teacher. The teacher said that after the visual proof activities, the students started to wonder where the formulas came from, in other words, they started questioning, their interest levels increased, and the formulas were kept in their minds more. The high school students stated that they found the visual proof activities enjoyable, and they were happy when they understood the visual proofs and unhappy when they could not understand them.

Keywords

• Proof
• proof teaching
• proof methods
• proof without words
• visual proof

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