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" with children. But he didn't know how to integrate the hands-on experiences into the learning process, how to be systematic.
He lacked the idea of building concepts upon many small elements, one upon another, and the idea that you cannot skip any of these steps.
But he found out all that, and wrote an excellent book about how to teach elementary math.
...and the other big surprise was that
- During his teaching career in the elementary school he actually learned a LOT of mathematics... not new facts, but subtleties: how that concepts we adults think are easy, are actually built upon other simpler concepts and notions, and how children need to be explained ALL those little steps.
For example, Aharoni learned that he couldn't just present first graders a question such as
"Donna has 4 pencils more than Joseph. How many pencils does Donna have, if Joseph has 5 pencils?"
He had skipped stages. Children couldn't do it. They needed first to learn the concept of there being a certain number more than another number.
You can read how he handled the lesson from that on, and many other things.
The last part of the book goes through all important concepts in elementary mathematics from grade 1 to grade 6, and explains these subtleties and little steps that you should teach.
I highly recommend this book. It costs $19.95, you can find it at www.sumizdat.org.
Please note, I'm not affiliated with this; I'm not getting a penny for promoting the book. I just truly feel that reading it is a MUST for each and every teacher and parent who's teaching elementary math.