2 + 3 = 5, 3 + 2 = 5, 5 - 2 =3, and 5 - 3 = 2 are not four facts, but four different ways of looking at one fact. Furthermore, that fact is not a fact of arithmetic, to be taken on faith and memorized like nonsense syllables. It is a fact of nature, which children can discover for themselves, and rediscover or verify for themselves as many times as they need or want to.

The fact is this:

***** <--> *** **

If you have before you a group of objects--coins or stones, for example---that looks like the group on the left, then you can make it into two groups that look like the ones on the right. Or--and this is what the two-way arrow means---if you have two groups that look like the ones on the right, you can make them into a group that looks like the one on the left.

This is not a fact of arithmetic, but a fact of nature. It did not become true only when human beings invented arithmetic. It has nothing to do with human beings. It is true all over the universe. One doesn't have to know any arithmetic to discover or verify it. An infant playing with blocks or a dog pawing at sticks might do that operation, though probably neither of them would notice that he had done it; for them, the difference between ***** and *** ** would be a difference that didn't make any difference. Arithmetic began (and begins) when human beings began to notice and think about this and other numerical facts of nature.

----John Holt, Learning All the Time