Posted by eoffg on October 02 2006 07:45 AM
Yeah, you seem to have got it. Where in the upper column, each bead represents 5, and the 2 beads in the row as 10.
In regard to hundreds, thousands and doing multiplication and division. Along with square roots and cube roots. The explanations that I have found so far, I find rather confusing?
Yet I became aware of what is reportedly the best book on using an Abacus. "The Japanese Abacus: Its Use and Theory".
By Takashi Kojima.
Which I was happy to find and buy on Ebay 2 weeks ago. But unfortunately it seems to have disappeared in the Post?
But thanks to your questions, I did an internet search?
Where I'm happy to report that I just downloaded the book for Free!
Despite it being written back in 1954, it has stood the test of time.
Though at the same site, I was also able to download his:" Advanced Abacus; Japanese Theory and Practise."
It covers different types of Abacus, and particularly the other Japanese one. That has one bead in the upper column instead of two.
The books have exercises from beginner through to advanced.
Where it even showed how to do a 'three digit multiplication'; 267 X 346
Yet it also looks at the important issue of developing a 'Mental Abacus'.
Which is the main aim.
Though for your son, you say that the issue is with 'teens'?
Yet this involves 'conceptual thinking', where 1 can also represent a 'group' of units.
Which is the value of the 'upper column', where it develops a natural understanding of a 'group' being represented by a single bead/ unit.
So for your son at the moment, it could just involve simple addition and substraction exercises.
Where he physically adds single digits that result in a teen. 8+3=.
Also deducts from 'teens' to result in a single digit 14-5=.
Here's a link to the website, where the books are listed under: 'More Abacus Stuff'.