__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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