immediate cardinal perception

The rods allow immediate access to the idea of a cardinal number, which is number as a whole. The ‘fiveness’ of 5, the ‘fourness’ of 4 etc.  Look at this:

4,1

If the white (wooden-coloured) rod is called 1, then the pink is worth 4. When looking at the pink, because it has no marks on it, 4 is seen as a whole, as a true number.

If you counted out 4 things, such as the four 1-rods, young children find it somewhat confusing to distinguish between the last thing counted and the whole group of objects. The number 5 is not the last thing counted, it is the whole.

Only things with no marks can be purely called wholes.

When you look at a 4-rod you see the cardinal 4.

A young child looking at this, perceives, without counting, that a whole 3 and a whole 2 is equivalent to 5. This is a very powerful insight. More than you might think. They will easily come to learn this relationship, without counting on.

3+2=5

He might also see many other things in this image, as you might, but that is enough for now.