Understanding of Eight Grade Students about Transformation Geometry: Perspectives on Students’ Mistakes

Abstract

People need the idea of transformation geometry in order to understand the nature and environment they live in. The teachers should provide learning environments towards perceptual understanding in symmetry training and development practice skills of the students. In order to make up such a learning environment, teachers should have information about the mathematical structure of the concept of symmetry, the difficulties the students encounter while learning, misconceptions and the causes. Therefore, the challenges and the common mistakes the 8 th grade middle school students encounter about the transformation geometry was analysed in the study. The study was conducted using mixed method designs with 125 8 th grade students. At the end of the study, it was observed that the students understood that the translation transformation is a movement of replacement, but they had difficulty in the topics such as the direction of the transformation and the position of the shape within the transformation. A misconception was developed for the reflection by confusing the similarity with the congruence property of the shapes. It was detected that the students had difficulty in identifying the equation of the axis of symmetry for the images of the shapes under reflection, confused the rule that the points intersecting with the symmetry of the shape within the reflection should intersect with the image under transformation and they made mistakes since they couldn't explore the relationship between symmetry axis in regular polygons and sides. They had problems in finding and practicing the angle of rotation about rotational transformation and also. In the study, learning environments were recommended towards overcoming these challenges for teachers and coursebook writers and improving conceptual information and the skill to practice these concepts.

Students’ understanding of axial and central symmetry

“…Thanks to this, and also from interviews from the pre-test, we know that the symmetry axis of the rhomboid is most often considered a horizontal median (those who answered "1" axis of symmetry), both medians (those who answered "2" axes of symmetry), or medians and diagonals (those who answered "4" axes of symmetry). Answer "2" was generally one of the most frequent incorrect answers, as in other research (Aktaş and Ünlü, 2017;Son, 2006). Leikin, Berman and Zaslavsky (2000) also encountered medians as the axes of symmetry of a rhomboid.…”

“…Here we can observe a misconception: 'a rhombus is an axially symmetrical figure.' Even worse results in research into the same problem were obtained by Aktaş and Ünlü (2017), who found that only 6.4% of respondents described a rhomboid as an axially asymmetrical figure.…”

“…The results suggest that rotation is the most difficult of them; axial symmetry is the easiest (Ada and Kurtuluş, 2010;Hollebrands, 2004;Xistouri and Pitta-Pantazi, 2011). Several studies have highlighted frequent misconceptions such as: confusing axial and central symmetries (Son, 2006;Jagoda, 2008); problems with constructing a mirror image in axial symmetry with an oblique axis of symmetry (Jagoda, 2008); problems with finding the axis of symmetry correctly (Hacısalihoğlu-Karadeniz et al, 2015;Kaplan and Öztürk, 2014); and incorrect identification of a figure that is not axially symmetrical as an axially symmetrical one, e.g., a rhomboid (Son, 2006;Aktaş and Ünlü, 2017;Hacısalihoğlu-Karadeniz et al, 2015;Leikin, Berman and Zaslavsky, 2000). Aktaş and Ünlü (2017), Herendiné-Kónya (2008) and Hollebrands (2004) pointed out the problems that students of different ages have with constructing a simple planar figure in central symmetry.…”

Dönüşüm Geometrisi Alt Öğrenme Alanındaki Program Değişikliğinin Uygunluğunun Öğretmenler Açısından İncelenmesi

“…Alanyazında sadece öğrencilerin değil öğretmen ve öğretmen adaylarının dönüşümler konusunda bilgi düzeylerinin yetersiz olduğunu belirten çalışmalar da (Ada & Kurtuluş, 2010;Al-Khateeb, 2016;Aktaş & Ünlü, 2017;Desmond, 1997;Gürbüz & Durmuş, 2009;Hacısalihoğlu-Karadeniz, Baran, Bozkuş & Gündüz, 2015;Harper, 2002;Kambilombilo & Sakala, 2015;Law, 1991;Mbusi, 2016;Son, 2006;Turgut, Yenilmez & Anapa, 2014) -Dönmede şekil üzerindeki her bir noktanın bir nokta etrafında belirli bir açıyla saat veya tersi yönünde dönüşüme tabi olduğunu ve şekil ile görüntüsünün eş olduğunu keşfeder.…”

“…Dönme hareketi programdan tamamen çıkarılarak yansıma ve öteleme hareketlerine yönelik kazanımlara ise sadece 8.sınıf düzeyinde yer verilmiştir. Ortaokul öğrencilerinin dönüşüm geometrisini öğrenmede zorluklar yaşadığını ve kavramları zihinlerinde yapılandırmakta güçlük çektiğini ortaya koyan bazı araştırmaların (Aktaş &Ünlü, 2017;Clements & Burns, 2000;Glass, 2001;İlaslan, 2013;Kaplan & Öztürk, 2014;Yanık, 2014) sonuçları dikkate alındığında, 2018 programında dönüşüm geometrisine daha az yoğunlukta ve güçlük düzeyi azaltılarak yer verilmesi yerinde bir karar olarak düşünülebilir. Mashingaidze (2012)' göre dönüşüm geometrisi matematik müfredatının biraz zor ve soyut kabul edilebilecek konuları arasındadır.…”