Primary school students' structure and levels of abilities in transformational geometry

The aim of this study was twofold: 1) to investigate the components that synthesize primary school students’ transformational geometry ability, and 2) to describe levels of abilities in transformational geometry. A test aiming to measure abilities in geometric transformations (translations, reflections and rotations) was administered to 166 primary school students of the fourth, fifth and sixth grade. Confirmatory factor analyses indicated the existence of four distinct factors of ability for each of the three geometric transformations, suggesting that they have similar structure. Furthermore, RASCH measurement methodology was used to create a hierarchy of these tasks. The scale was interpreted as a progression of five levels of abilities in transformational geometry: wholistic image, motion of an object, mapping of an object, mapping of the plane, and self-regulated mapping of the plane. Students’ development of understanding is interpreted in light of the theoretical framework of geometrical paradigms and geometric work space (GWS).