Programmed Math/Counting

Origin of Counting
Perhaps, counting began when early men did something like put a stone in a bowl or a pit in the ground for each of his flock that went out to graze. When the flock returned he would take out a stone for each returning animal. If there was a stone or stones left after the last animal returned he would know that he needed to find out what happened to that or those animals.

It is possible that he would begin to give a name for each group of stones, that is one stone, would have a name, two stones would have a name and so-forth. It is also probable that he already had a name for numbers based on counting with fingers. Counting on fingers might have been the beginning of dividing numbers into groups of ten.

Learning to Count
Watching a three year old learn to count there a number of apparent stages.

First they learn to repeat a series of sounds they hear "aye-bee-cee-dee..." and "one-two-three-four..."

Second they associate the sounds "one-two-three-four..." with pointing at a group of objects, but don't yet make the one to one association.

Then they start to learn the one to one association between the objects and the words.

Finally they start learning the rules needed to count accurately,


 * 1) Point at each object as you say the next word.
 * 2) Point at the object only once and move to the next.
 * 3) Don't randomly select the next object, but proceed sequentially.
 * 4) Remember where you've started and what you've already counted.

Demonstration
Given a set of objects,



start at one side



and proceed until



...



each has been counted.