In this paper I argue my opposition to the consensus which has dominated the literature that young children view shapes as a whole and pay no attention to shape structure and that geometrical thinking can be described through a hierarchical model formed by levels. This consensus is linked to van Hiele's weok by van Hiele-based research. In the light of some paradoxes I have identified in van Hiele's theory, and the discussion concerning the implications of describing thinking through hierarchies, I argue in favor of an alternative interpretation of the van Hiele model that moves away from the idea of levels.