The effects of practice on the discrimination of direction of motion in briefly presented noisy dynamic random dot patterns are investigated in several forced-choice psychophysical tasks. We found that the percentage of correct responses on any specific task increases linearly with repetition of trials within roughly 200 trials from about chance to a performance of 90% or better. The level of performance remained constant or improved over several days, and in most instances it did not transfer when stimulus parameters changed. We used a modified Radial Basis Function (RBF) representation to model the psychophysical tasks. The performance of the model is functionally similar to the psychophysical results. We propose a Hebbian learning algorithm which deactivates the inputs from neurons responding to motion noise in the stimulus. Our computational model suggests that to solve this task in biological systems, neurons (perhaps in MT) improve their performance by 'learning to ignore' noise in the image.