Counting is a game that starts with pure memorization from one to twelve, transitions to something that is a combination of both memorization and recognition for thirteen to nineteen, and from then on, twenty and higher, it is purely an algorithm. In the “Pure Algorithm” stage memorization is limited to the values of tens (e.g., twenty, thirty, forty, etc.) and then words like million, billion, quadrillion, etc.
We learn Counting, first as a collections of sounds to say or sing. Parents, friends and older siblings give us praise for doing so. We soon learn that those sounds are words that match up to quantities.
We learn we have ten fingers, five on each hand. We learn that the word dozen refers to the twelve egg in a carton. Words like ten and twelve acquire their full meaning once we can count to ten, or to twelve, and friends, older siblings and adults, encourage us to learn to count higher and higher.
You can’t play Hide and Seek with your friends if you can’t count.