Saturday, August 27, 2005


Last Autumn, i decided to teach my son how to do arithmetic. I would do it right. I went online and purchased a "how to" book, an abacus for myself and an abacus for my son. He was seven.

I joined a Yahoo discussion group that i found somehow. They're totally focused. I participated avidly for a bit, then got down to business.

The abacus that i'm talking about is the Japanese Soroban. The more common Chinese abacus has a dividing bar with five beads below and two beads above on each rod. It seems to be optimized for doing hexadecimal math - base 16. This used to be used in China for weights and monetary computations. You know, 16 ounces in a pound... that sort of thing. The Japanese abacus, called the Soroban, has four beads below the bar, and one above. It is optimized for decimal. Base ten. By an odd coincidence, that's what we use here in the US. We have a decimal money system, as well as decimal weights and measures. That's right, Congress passed a law in the 1800's proclaiming that everyone should use the metric system for weights, distances, etc. in the United States. That's why speed limit signs are in kilometers per hour.

One can add, subtract, multiply and divide easily on the soroban. I taught myself how to perform arithmetic on the soroban when i was about 17. After three months, i was quite proficient. Then i came on a chapter which told me that i no longer needed the physical instrument. Just imagine one, and move the beads. I was skeptical, but tried it. I went through all the exercises in the book in my head. That includes multiplying two four digit numbers together, and getting an eight digit answer. Or dividing a six digit number by a three digit number, and getting a three digit answer.

Two things struck me about the technique. I was always right. That is to say, after adding and subtracting perhaps a thousand numbers, and performing perhaps a hundred multiplications and divisions, i had not made a single mistake. Had i performed this on paper, i'd have made dozens of errors. It wasn't me. The technique is that good. The reason seems to be that it handles carries and borrows in a simple and immediate manner. There's nothing to remember.

The other thing that struck me was how fast it was. Addition and subtraction on the Soroban was about the same speed as an electronic calculator - which i owned in 1975. Addition and subtraction via mental arithmetic (anzan) was faster. Multiplication and division were faster on the calculator, as you'd expect.

Today, the draw of the abacus for me is that it has the potential to take the fear of math out of students. If there is no fear of math, then math based skills, like science, will have less or no fear as well. Technology is based on science. Our society is based on technology. Under no circumstances do i want my son to be incompetent at life.

Its been less than a year. My son performs two digit adds and subtracts. He's not always right, but he's much better than with pencil and paper. He's faster too.

My own mental arithmetic skills have disappeared from disuse. The brain is like a muscle. You have to use it, or it becomes weak. My mental skills have not come back, as yet. There are hints that it may, if i keep at it. I'm currently performing mixed addition and subtraction with ten five digit numbers, basically every day. Perhaps just one problem over breakfast. I'm still making mistakes from time to time. These stem from losing my place or getting distracted in the middle. Soon, however, i'll move on to multiplication and division. Then, square roots, logarithms and trigonometry functions. I once performed a problem like sin(23.7 degrees) to ten digits in my head. It took about 35 minutes, and i was correct. Those were the days.


FreeThinker said...

Well, I've about given up on numbers, but not on words. Scrabble keeps the mind sharp too!

Andy said...

Hello :)
I realised it has been like three years since you posted your blog about the soroban. And im not sure if you will ever get this comment. But if you could, could you email me at

I have a few questions regarding the soroban Id like to ask if it's not too much trouble.. Thanks in advance. Andy

Anup S Nair said...

Soroban is an effective mental math learning tool and helps develop memory power.

Stephen said...

Absolutely on both counts. In high school, i could divide one twenty digit number by another twenty digit number in my head. At that point, i'd never heard of anyone who could do that. And, around the same time, i spent a little over two months to memorize ten digits of pi. So, i could work with sixty digits during the division using short term visual memory, but had to work hard to remember ten digits. Without an effective technique, i would never have achieved these results on my own.

There are other techniques for memorization that i've tried now. And memorizing ten digits of pi would be easier and quicker now, despite my advancing age.