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Cardinality,
a fundamental underpinning to number concept, refers to the concept of
total quantity. Though usually described in relation to counting—the
number of the last object counted in a set is the total number of objects
in the set—cardinality is more general in the sense that it applies
to a variety of understandings related to quantity, from implicit visual
recognition at very early ages to numerical understandings. Over the past
two decades, research evidence of very early beginnings, initial cardinality,
have impacted the extent to which we now believe preschool children can
learn about number and operations.
 Visual recognition of quantity
In
studies where four-month-old infants were habituated (accustomed to seeing)
a certain number of objects, findings have indicated that they are able
to discern differences between that number and pictures containing a different
number of objects (Antell & Keating, 1983; Starkey et al., 1990; van Loosbroek
& Smitsman, 1990). In each trial, researchers controlled for all properties
(e.g., distance between objects, size of objects, etc.) other than number
of objects.
Recognizing
changes in quantity
Similar
studies utilizing habituation have led researchers to claim that these
earliest understandings of cardinality help infants to realize the consequences
of adding and subtracting small numbers of objects (Simon et al., 1995;
Wynn, 1992). For instance, when shown one or two objects, then a screen
in front, then a hand placing another object behind the screen, and then
the objects with no screen, five-month-old infants showed an expectation
that the number of objects would be different. Sometimes they saw what
they expected—a new object had been added to the one or two originally
behind the screen—and sometimes they did not—researchers did
not actually leave the new object with the others.
Visual
recognition of quantity
 The extent to which infants looked at the pictures
or displays behind screens was the measured factor. Given that children
are usually three or four years old before they demonstrate the ability
to distinguish between sets with four or more objects (Starkey & Cooper,
1980; Strauss & Curtis, 1984), researchers have attributed the findings
with infants to quick visual recognition, in this context a process called
subitizing. This is substantiated by findings that indicate similar abilities
among five-year-olds as well as adults to subitize when presented with sets
containing four or fewer objects, but not more (Chi & Klahr, 1975). For
certain circumstances we continue to draw on the ability throughout our
lives. For others (e.g., larger numbers of objects), we begin to develop
and draw upon another special strategy—counting (see the PreKorner
article Count With Me!).
Antell, S.,
& Keating, D. (1983). Perception of numerical invariance in neonates.
Child Development, 54, 695-701.
Chi, M.,
& Klahr, D. (1975). Span and rate of apprehension in children and adults.
Journal of Experimental Child Psychology, 19, 434-439.
Simon, T.,
Hespos, S., & Rochat, P. (1995). Do infants understand simple arithmetic:
A replication of Wynn (1992). Cognitive Development, 10, 253-269.
Starkey,
P., & Cooper, R. (1980). Perception of numbers by human infants. Science,
210, 1033-1035.
Starkey,
P., Spelke, E., & Gelman, R. (1990). Numerical abstraction by human infants.
Cognition, 36, 97-128.
Strauss,
M., & Curtis, L. (1984). Development of numerical concepts in infancy.
In C. Sophian (Ed.), The origins of cognitive skills. Hillsdale,
NJ: Erlbaum.
Van Loosbroek,
E. & Smitsman, A. (1990). Visual perception of numerosity in infancy.
Developmental Psychology, 26, 916-922.
Wynn, K.
(1992). Addition and subtraction by human infants. Nature, 358,
749-750.
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