Abstract
The goal of this study is to illuminate the mechanism of birth and development of geometrical schema in a pupil's mind. Three manipulative learning environments in which pupils build their ideas about geometrical objects, relationships between them and inside of them, situations and processes are presented.
The innovative nature of the presented approach to teaching geometry will be highlighted by its presentation on the background of description of historical development in geometry and in teaching geometry at schools in past 100 years. The new conception presents the results of our longitudinal research.