The Principles of Counting
You may be aware of the five principles of counting:
1. Stable Order
- The number names need to be said in a conventional order.
2. One-to-One Correspondence
- Each item is counted once as the corresponding word is spoken.
- Often items are in a linear arrangement and students typically count left to right.
3. Cardinal Value
- The last number spoken indicates the total for the group.
Sometimes a student might interpret the question “How many are there?” as an instruction to recount. To encourage the child to trust the count simply cover the collection and ask how many are in the collection.
These first three principles are sometimes called the “How to Count” Principles.
The next two principles are sometimes referred to as “What to Count.”
4. Order Irrelevance
- Students can count a scattered arrangement and don’t have to count left to right.
While I love bead strings if you only count left to right along the string you are not progressing to order irrelevance. Dropping counters (same colour and shape and size) and counting a scattered arrangement will help.
Abstraction
Physical items can be different colours, shapes, type, and sizes. This is why a variety of counters are important, not just standard round ones, e.g. dinosaur counters.
Students might count the number of claps – something that cannot be seen. That is why I like counting marbles dropped into a tin. You see, then you don’t see and then you hear and count. You can pause and then drop more marbles into the tin, developing counting on strategies.
Implications
- You need different type of counters.
- Many counting posters placed on walls are too busy and can interfere with students learning the first three “What to Count” Principles.
As you can see, counting to 5, then 10 and later to twenty, where place value will cause some issues, is complex. That is why we have created the Bond Blocks Counting to 10 & 20 Kit that covers all of the 5 counting principles as well as the early predictors that indicate students will struggle with number as they get older.
Reference:
Gelman, R. & Gallistel, C. (1978) The Child’s Understanding of Number. Cambridge, MA. Harvard University Press.
