Mathematically, the process of enumeration is fundamental to arithmetic. Psychologically, it is a sensorimotor chain controlled at every stage by a shifting perceptual organization. Enumeration requires a chant ("1, 2, 3 . . ."), a shifting indicator response (pointing), and a perceptual grouping of objects into those already counted and those still ahead. The arrangement of the objects has, theoretically, an important effect on the speed and accuracy of enumeration. Further analysis shows that the serial chain of behavior, required for counting a fairly large set of objects, must be divided into parts, and the objects grouped into corresponding subsets. 3 experiments show the relationship between arrangement of objects and counting.