Gelman’s
Counting Principle
How do we know
whether children can count ?
If knowing how to
count just means reciting
the numbers (i.e.,
‘‘one, two, three...”) up to “five” or
“ten,” perhaps
pointing to one object with each numeral,
then many
two-year-olds count very well.
Of course, counting
only tells you number of things if you do it correctly,
following the three
‘how-to-count’ principles identified by Gelman and
Gallistel (1978). These are :
enumerating a set,
one and only one [numeral] must
be assigned to each
item in the set.”
counting must be used in the same order in any one
count as in any other count.” and
(3) The cardinal principle, which
says that ‘‘the [numeral] applied to the
final item in the set represents the
number of items in the set.”
As Gelman and Gallistel pointed
out, so long as the
child’s counting obeys these
three principles, the numeral
list (‘‘one,” ‘‘two,”
‘‘three,”... etc.) represents the cardinalities
1, 2, 3,... etc.
However, observations
have shown that three-year-old
children often
violate the one-to-one principle by skipping
or double-counting
items, or by using the same numeral
twice in a count.
Children also violate
the stable-order principle, by producing different
numeral lists at different
times.
The cardinal principle can also be
viewed as something more profound
– a principle stating that a numeral’s cardinal meaning is determined by
its ordinal position
in the list. This means, for example, that the
fifth numeral in
any count list – spoken or
written, in any language – must
mean five. And the third numeral
must mean three..
If so, then knowing the cardinal
principle means having
some implicit knowledge of the
successor function – some
understanding that the
cardinality for each numeral is generated by
adding one to the cardinality for
the previous numeral.
Thus Gelman feels that
preschoolers learn to count as a result of the
perfecting of counting
procedures.
Do you agree ?
Marina Ho-BSc08
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