Anzan (暗算), often called mental abacus, is the stage where children stop moving real beads and calculate with an imagined soroban. For many families it is the most exciting part of soroban learning — and the part most often rushed.
Introduced at the right time and in small steps, anzan becomes a natural extension of abacus practice rather than a difficult leap. This guide explains the signs of readiness, a four-stage progression, first exercises and how to handle common difficulties.
What anzan is — and how it works
In anzan, the child pictures the soroban and updates the image as they “move” beads mentally. To add 3 + 4, they see three lower beads, then imagine bringing down the 5-bead and removing one lower bead, and read 7 from the image.
Research shows that trained mental-abacus users really do store numbers as visual images: verbal distractions disturb them little, while their errors look like misplaced beads (Frank & Barner, 2012). This is why anzan depends so much on a clear, automatic image of the abacus.
Signs your child is ready for anzan
There is no fixed age. Check these signs instead:
- Shows and reads any number from 0 to 99 on the soroban without counting beads.
- Uses the friends of 5 and 10 correctly and without hesitation.
- Solves short sequences such as 3 + 4 − 2 accurately on the real abacus.
- Sometimes moves fingers in the air or looks up while thinking — a sign the image is forming.
If several signs are missing, spend more time on the physical soroban. Our friends of 5 and 10 guide and the learning path help consolidate these basics.
Your first anzan: try 3 + 1 − 2
On the real abacus, set 3 on the ones rod. Push up one lower bead to add 1 (4), then push down two to subtract 2 (2). Say the value aloud after each step. This example needs no 5-bead and no carry.
Now look at the 3 on the abacus, look away and imagine the same movements while you say “3, plus 1, minus 2” slowly. The answer is 2. If the image fades, it is fine to look back at the real abacus.
Other starters: 2 + 2 − 1 = 3 and 4 − 1 − 2 = 1. Check each one on the beads at first. These are introductory examples, not age-based targets or exam questions.
Four stages from beads to mental calculation
Move to the next stage only when the current one feels easy for several days.
| Stage | What the child does | Example task |
|---|---|---|
| 1. Look and calculate | Calculates on the abacus, then repeats mentally while looking at it | 3 + 1 − 2 |
| 2. Glance, then calculate | Looks at the starting number, then calculates without looking | 4 + 3 (friend of 5) |
| 3. Eyes closed, fingers moving | Imagines the abacus and moves fingers in the air | 6 + 3 − 4 |
| 4. Fully mental | Calculates from the image alone, then checks | 12 + 5 + 3 |
Finger movements in the air are normal and useful in stage 3: they link the physical practice to the mental image. Many children reduce them naturally over time; there is no need to stop them early.
Exercises to build the mental image
Short, varied exercises strengthen the image without overload:
- Flash reading: show a number on the abacus for one second, hide it, the child says the number.
- Listening chains: say three single-digit numbers slowly; the child adds them mentally, then checks on the beads.
- Picture and check: the child imagines 7, adds 2 mentally, then verifies on the soroban.
- Flash numbers on screen with the training mode, at a slow pace first.
When answers do not match: where to go back
If the child also makes mistakes on the real abacus, pause anzan and review number setting and the addition or subtraction movements. If the physical abacus works but the mental version loses track, shorten the problem to two numbers, such as 3 + 1. Success does not mean you must add digits quickly.
A simple practice log helps choose the next starting point: the problem, whether it worked on the abacus, whether it worked mentally and where the child hesitated. If the child is tired or reluctant, end the session — anzan needs a fresh mind.
Common mistakes when teaching anzan
The most frequent mistake is starting anzan before abacus basics are stable. The second is giving long number chains too early. Both make anzan feel like a talent only some children have. Keep first problems short and accurate, tie them closely to the real abacus and go back to beads whenever needed.
Anzan is also different from other mental strategies such as “make 10”. Both are useful; our mental arithmetic guide for kids explains the non-abacus strategies.
Conclusion
The right time to introduce anzan is when bead reading and basic rules are automatic on the physical soroban. Move through the four stages gradually, start with short single-digit problems, accept finger movements, and return to the real abacus without hesitation. Introduced this way, anzan is not magic — it is the natural next step of soroban learning.
Frequently asked questions
What is anzan in soroban?
Anzan is mental calculation using an imagined soroban. The child pictures the beads and moves them mentally to find the answer.
At what age can children start anzan?
There is no fixed age. Readiness depends on automatic bead reading, secure friends of 5 and 10, and accuracy on short sequences.
Is it okay to move fingers during anzan?
Yes. Finger movements help many children keep the image. They often become smaller over time.
What if my child cannot do anzan yet?
Go back to the real abacus, shorten the problems and try again later. Usually the step was too big, not the child unable.
Does every child need to learn anzan?
No. Anzan is a valuable extension, but solid calculation on the physical soroban is already worthwhile.