Anzan (mental abacus) explained: how children calculate without the beads

How do abacus kids do sums in their heads? Here is what is actually going on.

Anzan is calculating on an imagined soroban: the child pictures the beads and moves them in the mind, so numbers are handled as shapes, not as words. Brain imaging shows that experts doing anzan use the visuospatial areas of the brain (parietal and frontal), not the language areas most people use for mental arithmetic. The bead image takes six months to a year of practice with a real soroban to form, then grows one digit at a time.

How it differs from ordinary mental math

Ordinary mental arithmetic is written arithmetic done in the head: "7 plus 8 is 15, carry the 1…". It runs on words, so working memory fills up after two or three digits. Anzan runs on a picture. The child sees a row of beads, moves them, and reads the answer off the image. Nothing is spoken internally, so there is nothing to forget mid-sum. That is how a trained ten-year-old adds ten 3-digit numbers read aloud at one per second.

The three stages

1. Automatic fingers on the real soroban. 5-complements (add 4 by adding the 5-bead and removing 1) and 10-complements (carrying, borrowing) must happen without thinking. This is the longest stage: six months to a year.
2. Eyes only. The soroban sits on the desk; the child calculates by looking at it without touching. The beads are still there for reassurance.
3. No soroban. The image alone, starting from 1-digit, 2-term sums. Flash anzan, where numbers appear briefly on a screen and vanish, trains this stage.

What the research shows

• Abacus experts doing mental calculation activate bilateral frontal and parietal regions, the network for visuospatial working memory, with little use of language areas (Hanakawa and colleagues, NeuroImage, 2003).
• Grand experts remember about twice as many digits as ordinary adults, but no more letters. The digits are stored as bead images (Hatano and Osawa, Cognition, 1983).
• In a three-year randomised trial with 5–7-year-olds, children with stronger spatial working memory gained the most from mental abacus training (Barner and colleagues, Child Development, 2016).

Why the image breaks

• Complements are not automatic yet. If the child has to think "add 5 and take away… what?", words enter and the image collapses. Go back to the real soroban until the fingers never hesitate.
• Too many digits at once. 2-digit anzan this week, 4-digit next week: the image cannot hold it. One digit or one term at a time.
• Speed before accuracy. Below about 80% correct, the problem is a broken image, not slowness. Slow down.

Practising at home

1. Be accurate on the real soroban first; speed later.
2. Add one or two "eyes only" days a week.
3. Start no-soroban anzan with 1-digit, 2-term sums. Start flash anzan slow, 1 digit, 2 numbers.
4. When a mental sum is wrong, find the bead where it went wrong; a score alone does not say which part of the image failed. A tool that draws the wrong bead movement, such as Soroban Kingdom, is useful here.

The conditions of good soroban learning, visible mistakes and fine-grained levels, are what let the bead image grow without breaking.

Frequently asked questions

Will it conflict with the written method taught at school?

Early on it can, especially for carrying. Keep the child on the physical soroban until 10-complements are automatic. After the image forms, written arithmetic and anzan separate naturally: paper for school, beads for the head.

How long until a child can do anzan?

1- and 2-digit anzan after six months to a year; 3-digit mental addition of several numbers after two to three years. Ten minutes of daily practice at home roughly halves those times compared with a weekly lesson alone.

Can adults learn anzan?

Yes, usually more slowly. Adults have a strong written-arithmetic habit and try to calculate in words. The fix is not to skip stage one: fingers automatic on a real soroban before anything mental.