Oh, come on

The children are willing to accept all kinds of mathematical shorthand if I tell them that I am too lazy to write out things the long way. In the first place, this is true. In the second place, it gives them a chance to make fun of my laziness, and to feel (which is also true) that in accepting my shorthand they are doing me a kind of favor. They do not like to be told that a certain symbol “means” something. This seems arbitrary and mysterious. But if you express a relationship or an operation in terms with which they are familiar, they will soon be perfectly willing to let you use some kind of shorthand to express it. Thus we can go from “Two whites are as long as one red” to “2 whites = 1 red” to “2 X w = r.”

After all, men invented mathematical symbols to save the trouble of writing things out the long way, so what I am doing in class is both logically and historically correct. No symbol “means” anything until we decide and agree to let it mean something; so why not let children feel that they are in on this decision?

[…] Numerical arithmetic should look to children like a simpler and faster way of doing things that they know how to do already, not a set of mysterious recipes for getting right answers to meaningless questions.