Teleoperation-i.e., controlling a robot with human motion-proves promising in enabling a humanoid robot to move as dynamically as a human. But how to map human motion to a humanoid robot matters because a human and a humanoid robot rarely have identical topologies and dimensions. This work presents an experimental study that utilizes reaction tests to compare joint space and task space mappings for dynamic teleoperation of an anthropomorphic robotic arm that possesses human-level dynamic motion capabilities. The experimental results suggest that the robot achieved similar and, in some cases, human-level dynamic performances with both mappings for the six participating human subjects. All subjects became proficient at teleoperating the robot with both mappings after practice, despite that the subjects and the robot differed in size and link length ratio and that the teleoperation required the subjects to move unintuitively. Yet, most subjects developed their teleoperation proficiencies more quickly with task space mapping than with joint space mapping after similar amounts of practice. This study also indicates the potential values of three-dimensional task space mapping, a teleoperation training simulator, and force feedback to the human pilot for intuitive and dynamic teleoperation of a humanoid robot's arms.