A study on the plane figures of elementary school in the view of transformation geometry

Abstract

One of the main purposes of geometry learning is the classification of shapes. Thus the activity of classifying shapes from a geometric symmetry (invariant) point of view has sufficient educational significance from Klein's point of view. The concept of translation, line symmetry, and rotational symmetry is introduced as part of activities to raise spatial sense in the current elementary school mathematics curriculum. The above three transformations are basic activities in the concept of congruence. But the current mathematics curriculum tends to deal with three basic concepts and congruence regardless of whether they are related. In fact, three activities and congruent concepts for developing spatial senses was introduced in different the grade-band for each other. In this paper, we shall classify triangles and quadrilaterals from the viewpoint of a symmetry breaking