Abacus tournaments in Japan
nytimes.com
nytimes.com
Abacuses are a niche hobby in Japanese schools, in the same fashion that e.g. competitive poetry recital is a niche hobby in American schools, and are factually not taught in the fashion that e.g. poetry is taught in American schools.
I played around with it a bit, it was great fun but no match for Excel.
The Japanese ones, conforming to stereotype, seem to be the most elegant.
I started off with some easy ones, and he nailed them. I went up to 5 and six digit numbers (different operations, no less), and he still nailed them. He mocked me for speaking so slowly, but my Japanese was pretty fast, especially for something as easy as numbers (not auctioneer fast, but still...).
All I can say is that I was thoroughly impressed. He had the correct answer within a fraction of a second of me finishing my last number every time.
To make it “tougher”, he suggested we do it in English. His spoken English was not very good, but his listening may have been ok.
He nailed the simple stuff, but I was able to break him a few times by going over 10,000. Japanese counting uses base 10k, while English counting uses base 1k, so it throw him off a bit — he didn’t slow down enough to process exactly what I was saying. That said, I’m sure he could have nailed the English version just as well as the Japanese with just a little bit of practice.
If you ever get a chance to meet these mental soroban folks, I encourage you to ask them about their experiences.
If you read the article, it specifies that advanced soroban is taught in some private school, and that it was phased out in the 1970s. Currently elementary students get a total of 4 hours of instruction spread over grade 3 and 4 (which is probably just enough that, a couple years later, they would still know what it is). So while the title is grammatically correct, it is also misleading.
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It gave them great intuitive understanding of arithmetic later.
Highly recommend.
These counting boards were still the standard tool in Europe until a few centuries ago, but their use has been completely wiped out and nearly forgotten in a short time, since the popularization of Indo-Arabic numerals and cheap access to paper.
The way it works is that parallel lines are drawn on the surface, and counters on the line represent 1, 10, 100, etc., while counters in between the lines represent 5, 50, 500, etc. In normalized form you only ever have up to 4 counters on a line. But there is no hard requirement that numbers be normalized, and you can pile as many counters as you like on one line and still have a meaningful state of the board.
Using the counting board then consists of first plonking down counters in the easiest representation of your result (e.g. to add 22 + 34 put 2 + 4 counters on the ones line and 2 + 3 counters on the tens line), and then undertaking a series of transformations which preserve the value of the whole board but move between equivalent representations (e.g. trade 5 ones for 1 five and trade 5 tens for 1 fifty), until you get to a representation which is convenient as output.
This is closer to most types of mathematical/computational activity in later mathematics, where various manipulation is done which at each step preserves some invariants. It is also good preparation for thinking about the relation between data structures and algorithms.
The big problem with the beads-on-rods version is that there is only one possible representation of each number. So the act of trading different magnitudes of counters is always left implicit. This makes it both harder to learn and less flexible as a tool, with the advantage that in the hands of a serious expert it’s probably marginally faster. If the goal were to train a 19th century accountant or shopkeeper this might be a fair trade-off, but for promoting understanding I think it’s not worth it.
* * *
If you want to save some tokens and make the system still more powerful, add a perpendicular line down the middle of the parallel lines. On one side tokens represent positive counts and on the other side they represent negative counts. Now in addition to the rules about trading 5 ones for 1 five or 2 fives for 1 ten, there is an additional rule that the same number of counters on opposite sides of the line represent 0 in combination (so any number of counters can be added or removed from both sides equally without changing the meaning of the configuration).
This adds is an additional convenient way to normalize numbers: try to maximally reduce the number of tokens used, allowing some negative "digits". We represent 3 as 5 – 2, 8 as 10 – 2, etc. Pick whatever convention you like for whether to round 5 up or down. In this representation, rounding a number is particularly easy: just truncate.
This is something which cannot be done on a beads-on-rods soroban, but is very helpful for understanding the meaning of negative numbers, the relation of addition and subtraction, etc.
https://gdaymath.com/courses/exploding-dots/
which I think I first learned about here on HN.
It teaches place value but also expands the concept into all sorts of other areas of algebraic structure, including polynomials. It's actually quite similar to a counting board plus some interesting manipulation rule variations.
Having base ten arithmetic split into 5 × 2 (as was done historically) is convenient for practical use, but does slightly complicate the concept. Having a single number base as Tanton does makes explanations a bit simpler.
It’s nice how Tanton shows that counting boards can be used with alternative rules to represent more advanced/abstract systems of calculation. We can make up counting boards for doing complex arithmetic, working in other number fields, working with formal polynomials, working with binary logic, ...
Modern computer registers/memory aren’t much different than a (very large) counting board. When we combine a basic counting board with a human operator, we have a Turing-complete computing machine.
I think http://www.mernick.org.uk/lnc/jetton/jetton.htm was a good reference I found when I first used jettons, but it’s been so many years now that I can’t say for sure. http://www.chicagocoinclub.org/projects/PiN/juh.html has some information too.
Yes, this is true in a sense but it is definitely hyping up the "mysterious Japan" angle.
I wont deny that handwriting is useful, but having it taught as the primary writing skill, the first and main one, while the keyboard, the device that will probably be used 95% of the time people have to write something in their lives, is still seen as a niche skill is shocking to me.
Paper furthermore remains a much more flexible and fluent tool than computer interfaces for a wide variety of tasks.
Any of the activity you mention would be a better way to train manual dexterity.
Personally I think students should learn some type of simplified italic-type script, using a pen with ink that flows well enough that they don’t need to use much pressure.
https://www.nytimes.com/2014/06/03/science/whats-lost-as-han...
But also, learning to type is a huge barrier to entry. For kids, writing is faster.
However, I do still have links to some of my favorite videos showing some really amazing soroban or flash anazn feats:
Soroban - All in the mind[1], Flash Anzan at the All-Japan National Soroban Championship 2012[2], and Mental Arithmetic World Champion - Flash Anzan[3]
There's an excellent, free book on it: Abaucs: Mystery of the Bead[4]
r/soroban and r/mentalmath are worth peeking in to.
I also really enjoyed reading a blog called Going Gaijin, written by a woman who took formal soroban classes in Japan.[5]
There are a lot of cheap, decent sorobans on amazon and ebay, if you want a physical device. I also found the "Simple Soroban" Android app to be useful for practice.
[1] - https://www.youtube.com/watch?v=Px_hvzYS3_Y
[2] - https://www.youtube.com/watch?v=7ktpme4xcoQ
[3] - https://www.youtube.com/watch?v=JawF0cv50Lk
I was looking at it at some point and realised that when you use the beads as numbers, rather than counting them, you can go incredibly high. I must have known this earlier in life, but I completely forgot about it. After this I heard a lot about the benefits to learning maths with an abacus versus learning how to do math with a calculator. One of the claimed benefits is that, when you learn maths with an abacus, you get better at doing calculations mentally, whereas if you learn math with a calculator you don't become better at that.
Does anyone know of a good resource to learn how to do math with an abacus? I know I can just duckduckgo it, but maybe there is some exceptionally good source somewhere?
However, many parents want to send their kids to soroban classes after school, especially when they're around ages 7-11 or so. There's a feeling that it makes you much faster with arithmetic. My wife (Japanese) is very quick at doing sums in her head.
It shouldn't be beaten into kids ("learn your timestables!!" is not an effective teaching method), but if using an abacus or similar helps people calculate faster, it is likely a good thing.
It would be nice to get an ALU implanted in my brain, it would be much more efficient for calculation than using a neural network.
On top of everything you get a nice tactile feeling with it. Will it replace my desk calculator, probably not, but it could.
If my school had offered this, I would have found it useful.
It is quite useful for quick mental addition and subtraction. How do you multiply and divide using an abacus though?