The paper deals with the well-known problem of teleoperating a robotic arm along six degrees of freedom. The prevailing and most effective approach to this problem involves a direct position-to-position mapping, imposing robotic end-effector movements that mirrors those of the user. In the particular case where the robot stands near the operator, there are alternatives to this approach. Drawing inspiration from head pointers utilized in the 1980s, originally designed to enable drawing with limited head motions for tetraplegic individuals, we propose a "virtual wand" mapping. It employs a virtual rigid linkage between the hand and the robot's end-effector. With this approach, rotations produce amplified translations through a lever arm, creating a "rotation-to-position" coupling. This approach expands the translation workspace at the expense of a reduced rotation space. We compare the virtual wand approach to the one-to-one position mapping through the realization of 6-DoF reaching tasks. Results indicate that the two different mappings perform comparably well, are equally well-received by users, and exhibit similar motor control behaviors. Nevertheless, the virtual wand mapping is anticipated to outperform in tasks characterized by large translations and minimal effector rotations, whereas direct mapping is expected to demonstrate advantages in large rotations with minimal translations. These results pave the way for new interactions and interfaces, particularly in disability assistance utilizing head movements (instead of hands). Leveraging body parts with substantial rotations could enable the accomplishment of tasks previously deemed infeasible with standard direct coupling interfaces.