“If you stay with meaningful mental arithmetic longer, you will find that your child, if she is average, can do problems much more advanced than the level listed for her grade. You will find that she likes arithmetic more.
“And when she does get to abstractions, she will understand them better.
“She will not need two or three years of work in primary grades to learn how to write out something like a subtraction problem with two-digit numbers. She can learn that in a few moments of time, if you just wait.”
—Ruth Beechick, An Easy Start in Arithmetic
What Do You Mean by Mental Math?
Mental math is doing calculations in your head, with perhaps the aid of scratch paper or a whiteboard to jot down notes along the way.
But you cannot simply transfer the standard pencil-and-paper calculations to a mental chalkboard. That’s far too complicated.
Denise Gaskins' Let's Play Math 