Both terms in the title of this paper are probably suspect. The mathematician, versed in a subject with hundreds of years of noble tradition, tends to be suspicious of a paper on psychology; the teacher of mathematics, immersed daily in psychological relationships with ordinary children, tends to be suspicious of a paper on mathematical ability. The discussion promises to be unsatisfactory, to the one because psychology lacks mathematical precision, to the other because mathematical ability seems to present no urgent psychological problems. The teacher-mathematician may then be pardoned if he reacts sceptically to our title with the petition, “Psychology, if there be a science of psychology, help me to cope with mathematical disability.” But these suspicions are not well founded. Not only is psychology, as we shall see, becoming increasingly mathematical, but also, if we interpret our terms as mathematicians should, disability is seen to be merely the negative aspect of ability. As such, it will not be excluded from our discussion.