Tuesday, February 21, 2006


Richard Cohen of the Washington Post wrote this essay. I won't debate Richard here. He knows the problems with his arguments. He conveys sympathy.

In response, Gary Stix, at Scientific American wrote this less sympathetic one.

For me, the glass is twice as big as it needs to be - not half full or half empty.

One can blame the student for not working hard enough or being smart enough all one wants. One can blame the teachers too. One can blame the system, the President, the school board. It doesn't change anything. However, it turns out that there are superior teaching techniques. My math skills happen to be excellent, and as an engineer, I depend on them. But when I was a kid I took piano lessons for three years before dropping it. I had no idea why I was making so little progress. I didn't even know that was happening, I was just frustrated, and quit.

In my forties, it became partly my job to help my son with his education. When his arithmetic was falling behind, I taught him the Soroban (Japanese abacus) and a variant of finger math where one can add and subtract two digit numbers on one's fingers. His math came up to snuff in a couple months, and permanently. This is a technique that, when I was in high school, allowed me to perform twenty digit mental arithmetic - for example, it took about a minute to multiply two ten digit numbers and get a twenty digit answer. And, without the technique, I couldn't remember twenty digits.

My wife got my son into Suzuki Violin, and more recently Suzuki Piano. As a parent teacher for both, it has become clear that the general teaching methods and techniques are clearly superior to what I struggled through as a kid. There's nothing wrong with my dexterity or aptitude, and if I'd had the opportunity to learn music this way, I have no doubt I'd be considered a music savant now. Even now, it's clear that just a few years of study will improve my performance to much more enjoyable levels. It isn't too late, and I expect thirty or more years of enjoyment to come.

There are two keys to these teaching and performance techniques. And they are the same as each other. The first is that the material is broken down into very short consumable parts. That allows steady progress with minimal frustration. The barrier to entry is lower. More students will be able to get it. Everyone will get it faster, and learn it better. The second is that the techniques themselves are made up of these simple ideas, put together. They really work.

For example, in the Soroban, there are ten lessons to learn addition. Each takes about five minutes and can be explained in one or two sentences. There is then about a week's worth of practice, maybe twenty minutes a day. In the resulting addition, there is a simple set of steps. When there is a carry to handle, it is handled right away, and the procedure mechanically takes care of it. At any moment, there is only one thing to remember, and one next thing to do, and it is obvious. The result is addition that is quick and reliable. It isn't that important that it be quick. What is important is that it is reliable. If the answer is off by one, it is still wrong. The student knows if their answer is wrong, and it is frustrating, which leads to failure, which leads to more failure. So, this technique is simple, produces the right result every time that the procedure is followed, at least in contrast to doing arithmetic on paper as taught in school. So, it is easier to learn and less frustrating to use. So, fear of math vanishes.

Algebra is built on arithmetic. If the arithmetic is easy, algebra becomes that much easier.

These techniques have been available for more than fifty years. They are already in wide spread, but not universal, practice. They invariably show their superiority. By comparison, the teaching techniques used today for nearly all education looks like the teachers are doing whatever the first things that come into their heads. It's stupid. As great as these techniques are for subjects such as music and math, the general concepts are applicable to a wide variety of fields of study. If this has been done, I'm not aware of it. We need to be smart about teaching, and not just for math.

It is my opinion that algebra should be a high school diploma requirement. The diploma should mean something.


FreeThinker said...

I'm with ya. There's way too much "grade inflation" these days!

Anonymous said...

What was the method that you taught your child? I too am experiencing my son getting things off by one. If there is a more effective system, I would like to know what it is.

Stephen said...

Rather than hide it in a comment, i'll devote a post to it. Maybe more than one. Real Soon.

lien said...

Are you able to devote a post to using a soroban for multiplication and division please? I'm trying to learn how to do this so I can teach my children. I've learnt addition and subtraction

Greg said...

I have searched your blog and I couldn't find any multiplication or division. I took chismbop as a kid and stopped after addition and subtraction. I found this post... lien said...
Are you able to devote a post to using a soroban for multiplication and division please? I'm trying to learn how to do this so I can teach my children. I've learnt addition and subtraction

Sunday, September 23, 2007 12:17:00 AM

Stephen said...

You should know that the book "The Japanese Abacus" is available at Tomoe - http://www.soroban.com

It's the best English book on the market, as far as i know. This is a little dismal, IMO.

The way i do multiplication is to use my soroban as an accumulator, and do multiplication like you do on paper. You have to remember where to add the numbers. Since you're counting digits from the right to place the numbers, i add the digits right to left. It might be handy to remember 4 * 6 = 4 and twenty, but i don't bother. Remember that carries can move your place.

I have a multiplication problem generator at


I have a division generator written, but haven't put it up as yet.