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:


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.


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