ABSTRACT
R. N. Shepard, D. W. Kilpatrick, and J. P. Cunningham applied multidimensional scaling to responses and found for a variety of notational systems that people’s sense of number was tied closely to the representational conventions underlying a notation. Coding schemes are representational conventions; research with special application to studies of mental arithmetic has been carried out on two schemes especially: one on language in the context of bilingual skills, and the other on forms of notational convention. On the hypothesis that the mental operations reflect the means of representation, time to verify the equations would vary with their form. In neither case, however, do the special skills underlying the mental operations controlling the behavior transfer; each skill is learned as an individual. There is something about notations and formal systems that seems to be unnatural, some aspects of mental manipulation that come with difficulty even to intellectually sophisticated people.
