thesis: Children of pre-school age are entering stage of structural change of thinking. The way how they grasp solving mathematical tasks reflects whether these changes have already started. This work surveys visible intellectual outputs in the group of 20 children who passed set of experimental tasks at arithmetic learning environments "Stepping" and "Bus". Children were subsequently subjected to pedagogical diagnostics and results of this investigation and carried experiments were trade off. From comparison it can be concluded that results of both surveys correspond enough to facilitate the application of selected mathematical tasks as pedagogical diagnostic tools.