A student who is a perceptual counter can count items that he or she can perceive (see, hear or touch). A perceptual counter will demonstrate the one-to-one principle, generating terms in the sequence of number words as needed and matching one number word to one item, without skipping or double-counting items. A student who is at the perceptual counting stage needs to perceive the items to solve number problems.
In a thorough analysis of how children develop counting skills, Gelman and Gallistel (1978) described four basic logical principals that must be satisfied if an activity is to be classified as counting. These principles may be summarised as:
- establishing a one-to-one correspondence between the things to be counted and the counting labels,
- maintaining the counting labels in a fixed order,
- recognising the irrelevance of the order in which the objects are counted, and
- applying the cardinality principle, that is using the last label to represent the number of objects in the set.
All of these principles associated with what it means to count are part of the perceptual counting stage.