A rolling walker comprises a frame, a seat supported by that frame, and a backrest supported by the frame. By one approach the backrest is configured to selectively move between a first position that provides back support for a person sitting in the seat facing in a forward direction and a second position that provides back support for a person sitting in the seat facing in a rearward direction. If desired, this backrest can be comprised of a material (such as a memory foam material) that biases the backrest towards that first position when the backrest is in the first position and that biases the backrest towards the second position when the backrest is in the second position.