Rational Counting

Purpose:

For understanding the how-many-ness of a group of objects, which is a necessary pre-requisite skill for understanding the operations addition, subtraction, multiplication and division (Unglaub, 1997).

Five Principles of Rational Counting (Unglaub, 1997):

1. Numeral principle – Any group of objects can be counted

2. Stable-order principle – the order of the numbers used in counting need to stay in a particular order, i.e. one, two, three, four, five

3. One-to-one correspondence principle – When you count objects, you allocate one count per one object

4. Order irrelevance principle – when counting a group of objects, it does not matter which order you count them in as long as each object being counted received one count (no more, no less)

5. Cardinal principle – the last count that is allocated to the last object being counted in a group is indicates the total number of objects that have been counted

Implications for teaching:

· Observe children’s counting experiences to identify correct concepts of misconceptions they may have

· To develop the numeral principle, give children collections of different objects to teach them to count

Look at the number of stars on the bag and put the same number of objects inside

· To develop the stable order principle, practice singing songs and rhymes that include numbers that appear in order, e.g. one, two, three, four, five, once I caught a fish alive...


· One to one correspondence – provide opportunities to use objects such as paddle-pop sticks and cups. Ask the children to count one number word out loud as they drop one paddle pop sticks into the cup.

· Order irrelevance principle – repeat the above activity a number of times, in a number of different orders and discuss if the results are the same

· Cardinal principle – when counting objects, discuss with the children after the last count, so how many mugs are there? How many paddle pop sticks are there?

References:
Unglaub, K. (1997). What counts in learning to count. Young Children, 52 (4), 48-50