“This is the very heart of addition. Addition
involves three classes, two subordinate classes and a
super-ordinate class. The composition of two
classes to make a third class is basic to addition.
Addition does not involve place value, nor does it
involve carrying or lining up digits in a vertical
column. It is basically concerned with the composition
of two groups. We could have done the same
thing with actual beans or sheep, or people at a
party, or tally marks