I am curious what are the strengths and weaknesses of different mental calculation methods.
In these two articles, I describe how the visual working memory operates, and how it relates to the soroban and mental math.
- Optimizing Working Memory for Mental Calculation – World Mental Calculation
- Verbal Mental Math – World Mental Calculation
Soroban is simply a way of processing numbers visually, as an alternative to using regular numbers. I don’t recommend it for adults, but many children—especially in India where it is very popular—have learned to get very, very fast with it.
Maybe get one for your child, teach them how to count and do basic sums as fast as they can. If they like it then maybe take it further.
Hello,
I apologize for the English. I didn’t understand why adults shouldn’t learn it. On the contrary. It’s a brilliant exercise in brain acceleration. At 61 years old, I’m adding, subtracting numbers to seven places on the soroban.
very quickly. Of course, I’m absolutely no match for Indian kids.
I think what @Daniel_360 meant, was in terms of mental calculation technique. You’re right, of course, that it’s a great exercise even for adults… just like learning how to play an instrument, learning how to juggle, or learning a new language would be beneficial to your brain as you get older.
For adults however, when it comes to mental math and being fast in competitions, there are “easier” ways to improve your speed by applying algebra to the arithmetic you’re facing. A lot of systems, such as Vedic math or Trachtenberg, rely on these rearrangements (algebra) of data to speed up the calculations.
Soroban is basically a fast mechanical process. For Anzan you basically start with the physical device, then eventually replace it by just the finger movements in the air, and ultimately you can just visualize the calculation. Once you’ve replaced the physical device by its mental equivalent, you can start talking about doing mental math again.
The drawback is that it’s brute force in a way and less creative when compared to Vedic math for example. The problem with Vedic math on the other hand is that you’ll have 16 different ways to shoot yourself in the foot and you need to develop a good understanding of which algorithm is best suited for the problem you are working on.
I guess you could liken it to speed skating versus figure skating where the skates are the math problem and now it’s your choice which competition you’d like to partake in to win a gold medal.
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The Soroban, the Japanese Abacus is the most efficient at base 10 arithmetic. Chinese abacus can do base 16 and is more cumbersome.
The basic computing power of the abacus in any form is that it performs addition or subtraction just by recording the numbers. If you set a 3 on to the soroban and then add the beads for 8, you read 11 directly off the board. Soroban users are experts at the finger movements required to manipulate the beads. These are strictly prescribed by an institute that studies the matter and determines the most efficient movements. But the consequence is that the operator does not have to confront the relationships between the numbers and how they interact. It’s a bit, just a bit, like like learning to press buttons on a calculator and reading the display.
A “western calculator” doing mental math must know a whole lot of things about numbers themselves and their relationships.
This is very nicely encapsulated in this story about Feynman which I post everytime the subject comes up here
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But the consequence is that the operator does not have to confront the relationships between the numbers and how they interact. It’s a bit, just a bit, like like learning to press buttons on a calculator and reading the display.
A “western calculator” doing mental math must know a whole lot of things about numbers themselves and their relationships.
Sorry but I think you’re totally wrong with that comparison. As a Soroban user you intuitively learn something about the structures and relationships between the numbers that you could not easily memorize. It’s not at all like using a calculator. With the Soroban you have control and an overview of even the smallest arithmetic operation at all times.
For example, I’ve developed a feeling for when I’ve miscalculated. Of course, this also comes from the many exercises. Likewise, I automatically see a factorization of an existing number (up to about 6 digits) within a few seconds. That’s the experience at Division. I’ve memorized a lot of numbers, but never any factoring.
Your idea of ​​"western calculator" is also very questionable. I see no reason why you should know more than 1x1 by heart. The rest is just practice, practice, practice. Of course you can also find solutions in a very creative way without investing thousands of hours of practice. However, if you want to effectively increase the speed of individual operations, you shouldn’t just rely on shortcuts.
Are there different soroban methods? Maybe some are better at teaching number theory than others?