Representing and using numerical information

Issues of mental representation are central to cognitive psychology and indeed to psychology in general. This article synthesizes recent theoretical and empirical research concerning cognitive representations in one specific domain, that of numbers. First, several forms of cognitive numerical representation are defined, and the roles the various forms may play in numerical processing are considered. Then, two current representational issues that have generated some controversy are examined: In what form are arithmetic table facts (e.g., 4 x 7 = 28) stored in memory, and what forms of representation are involved in converting numerals from one form to another (as in reading 604 aloud as "six hundred four")? In the course of the discussion the major current theories of numerical cognition are described, with emphasis on how they differ in their assumptions about numerical representations and how these differences are reflected in the positions taken on various specific issues.