Cardinality The understanding that when you count items, the number word applied to the last object represents the total amount.
Students have developed a secure understanding of cardinality when they understand that:
- counting tells you how many things are in a set. The last word in the counting sequence tells you how many items are in the set.
- once the number of items in a set has been established, the numbers before and after this number give the result of adding one or taking one away from the set.
- the number of items in a set remains constant, no matter how the objects are rearranged.
- numbers can be used to compare two or more sets without having to bring the sets together and match the items one to one.
This is a great online resource to support practitioners in helping children developing this understanding in the early years:
Look on the maths site on Glow under Training Materials – the Early Years CPD resource has lots more ideas for promoting this understanding.
I also love these links to the NZ maths site, from their professional development modules:
http://www2.nzmaths.co.nz/frames/ONPD/M8/14.aspx
http://www2.nzmaths.co.nz/frames/ONPD/M8/15.aspx
It is important to remember that, if children do not have a secure understanding of cardinality they will not be able to count on from the bigger number, and this strategy should not be rushed or taught by the teacher, however tempting! Lots of practice with the experiences from these resources will help children develop this understanding for themselves, reorganise their conceptual thinking and move on to apply the counting on strategy then securely and confidently.
Highland Numeracy Blog 