## Sunday, August 18, 2013

### Gelman's Counting Principle

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 :

(1) The one-to-one principle, which says that ‘‘in

enumerating a set, one and only one [numeral] must

be assigned to each item in the set.”

(2) The stable-order principle, which says that ‘‘[Numerals] used in

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