This study explores young children's abstraction of the rules underlying a robot's emergent behavior. The study was conducted individually with six kindergarten children, along five sessions that included description and construction tasks, ordered by increasing difficulty. We developed and used a robotic control interface, structured as independent concurrent rules. To capture the children's changing knowledge representations, we have employed a framework that underscores the differences in generality between "episodes," a unique sequence of events, "scripts," which include repeating temporal patterns, triggered by an environmental condition and "rules," atemporal associations between local environmental conditions and the robot's actions. Our data unravels the progression through which rules are constructed. From an episode that focuses on the robot's actions, noticing repeated sequences triggered by occasional environmental conditions emerges into scripts. Once both actions and conditions are attributed with similar importance, noticing the co-variance of environmental conditions with robot actions is made possible, bolstering abstraction of atemporal rules. In addition, we have supported the children's reasoning by helping them attend to relevant features, and compared their spontaneous and supported descriptions. We elaborate on the role of function and mechanism as invariants, and the support of "concrete-abstractions" in the interaction between cognitive schemas and object-embedded abstract schemas, for the children's evolving explanations of the robot's behavior.