Students’ understanding of axial and central symmetry

Abstract

The paper focuses on students’ understanding of the concepts of axial and central symmetries in a plane. Attention is paid to whether students of various ages identify a non-model of an axially symmetrical figure, know that a line segment has two axes of symmetry and a circle has an infinite number of symmetry axes, and are able to construct an image of a given figure in central symmetry. The results presented here were obtained by a quantitative analysis of tests given to nearly 1,500 Czech students, including pre-service mathematics teachers. The paper presents the statistics of the students’ answers, discusses the students’ thought processes and presents some of the students’ original solutions. The data obtained are also analysed with regard to gender differences and to the type of school that students attend. The results show that students have two principal misconceptions: that a rhomboid is an axially symmetrical figure and that a line segment has just one axis of symmetry. Moreover, many of the tested students confused axial and central symmetry. Finally, the possible causes of these errors are considered and recommendations for preventing these errors are given.

Heuristic Strategies: Achieving Influence Motivation with Success to Design Industrial Products in Projects from the Department of Architectural Education and Design

“…Further, knowledge level represented whether the students had the intellectual skill levels in systematic thinking with the high opportunity to be graduated in the future [33]. Thus, it is based on systematic thinking with clear steps aiding for the design product students to design and make industrial products with responding to the customer requirement in high effectiveness, especially for the students who may lack clear systematic thinking [34][35].…”