Studies on spatial frameworks suggest that the way we locate objects in imagined environments is influenced by the physical and functional properties of the world and our body. The present study provides evidence that such an influence also characterizes imagined navigation. In Experiment 1, participants followed spatial directions to construct an imagined path, while either keeping constant or updating their orientation at each step. A pattern of step times diagnostic of spatial frameworks was obtained in the updated-orientation but not in the constant-orientation condition. In Experiment 2, participants performed the updated-orientation condition with two levels of external support for the reference frame being used. Step times conformed to the predictions of spatial frameworks in both conditions. Both experiments also provided support that the processes involved in imagined navigation exhibit the operator-operand dynamics of other mental skills previously documented in the mental arithmetic domain. These results reinforce Piaget's (1954) notion that spatial displacements and integer arithmetic share a set of structural characteristics