We can capture quantities using the words like one-two-three, but not for a long time. The counting words tend to run away from our memory even if we support them with vocalization and gesticulation. Tokens stand. Writings stand too, but we don't count in writing, we only memorize the results. Tokens and other computing devices keep quantities and allow to change them many times.
One-two-free are mental tokens. They belong to the ordered set of the counting words. It it important to remember both words and their order. Like before, we match the mental tokens to the objects we count, but we do it in the order of the words, never skipping any of them or using more than once. If we do it right, we find the word or phrase for our quantity.
Using tokens, we can capture quantities without counting words, but practically every kid knows those words anyway. Let's teach more of them.