Teaching elementary mathematics - don't skip stages

I received recently a book called "Arithmetic for Parents. A book for Grownups about Children's Mathematics" by Ron Aharoni.

I want to tell you a little bit about this book, because I think it is exceptionally good, and a very worthwhile book to read if you're a teacher OR a parent.

Ron Aharoni was like many: he thought he could easily teach elementary school math because he knew college level math and beyond (he was teaching math in a university).

But... he was in for a big surprise when he entered the fourth, fifth, and first grade classes in a backward town in northern Israel, in 2000.

One surprise he had was that...

• ...he did not know how to teach elementary mathematics.

For example, during his first lessons he took children outside to measure shadows of trees, buildings, and the children themselves. The idea was to use the ratio of a child's shadow to his height to find the height of a tree or a building.

He took children outside to draw circles on the pavement and measure diameters, and compare them.

But as he admits in the introduction to his book, his first lessons were just a mess and confusion, with little meaningful teaching going on.

He wanted to do "hands-on experimentations