Sensorimotor learning can change the tuning of neurons in motor-related brain areas and rotate their preferred directions (PDs). These PD rotations are commonly interpreted as reflecting motor command changes; however, cortical neurons that display PD rotations also contribute to sensorimotor learning. Sensorimotor learning should, therefore, alter not only motor commands but also the tuning of neurons responsible for this learning, and thus impact subsequent learning ability. Here, we investigate this possibility with computational modeling and by directly measuring adaptive responses during sensorimotor learning in humans. Modeling shows that the PD rotations induced by sensorimotor learning, predict specific anisotropic changes in PD distributions that in turn predict a specific spatial pattern of changes in learning ability. Remarkably, experiments in humans then reveal large, systematic changes in learning ability in a spatial pattern that precisely reflects these model-predicted changes. We find that this pattern defies conventional wisdom and implements Newton's method, a learning rule where the step size is inversely proportional rather than proportional to the learning gradient's amplitude, limiting overshooting in the adaptive response. Our findings indicate that PD rotation provides a mechanism whereby the motor system can simultaneously learn how to move and learn how to learn.