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…

Presents a framework for differentiating between five levels of extension of knowledge: basic features, forms, rules, application, and elaboration. Comparison of the extent of knowledge use exhibited by (n=14) Year-11 Australian students on a range of plane geometry problems found that high-achieving students exhibited greater extension of…