A subset of sensory substitution (SS) devices translate images into sounds in real time using a portable computer, camera, and headphones. Perceptual constancy is the key to understanding both functional and phenomenological aspects of perception with SS. In particular, constancies enable object externalization, which is critical to the performance of daily tasks such as obstacle avoidance and locating dropped objects. In order to improve daily task performance by the blind, and determine if constancies can be learned with SS, we trained blind (N = 4) and sighted (N =10) individuals on length and orientation constancy tasks for 8 days at about 1 hour per day with an auditory SS device. We found that blind and sighted performance at the constancy tasks significantly improved, and attained constancy performance that was above chance. Furthermore, dynamic interactions with stimuli were critical to constancy learning with the SS device. In particular, improved task learning significantly correlated with the number of spontaneous left-right head-tilting movements while learning length constancy. The improvement from previous head-tilting trials even transferred to a no-head-tilt condition. Therefore, not only can SS learning be improved by encouraging head movement while learning, but head movement may also play an important role in learning constancies in the sighted. In addition, the learning of constancies by the blind and sighted with SS provides evidence that SS may be able to restore vision-like functionality to the blind in daily tasks.