From physical bead to anzan: the Kani app roadmap

Anzan is the end goal — and the most misunderstood part of mental arithmetic. Parents new to the method often picture it as a single leap: one day the child is using a physical abacus, the next they are solving in their head. The reality is the opposite. Anzan is built by a long sequence of small graduations the child does not even notice. The Kani app stages those graduations explicitly, on a fixed roadmap aligned to the nine-level ladder.

Stage 1 — Visible abacus, every problem (Foundation to Elementary A)

In the first 3 to 4 months, the app shows the soroban on every drill. The child touches beads — actual taps on the screen for the abacus drill, or a digit input for the flash drill that lets them visualize bead movements while computing. The mental abacus has not formed yet; the visible abacus is doing the work. The goal here is not speed but cleanliness of bead manipulation: thumb-up, index-down, no improvising.

Stage 2 — Beads visible, digits hidden (Elementary B to Intermediate A)

Around the small-friends / big-friends boundary, the app introduces a small but important option: the digit display under each rod can be hidden. The child still sees the beads, but is forced to read the bead pattern itself rather than the convenient digit label below. This is where the mental abacus starts to form. Within weeks of practising with digits hidden, kids start reading values directly from the visual bead pattern — and a few weeks later, they can construct the mental version of that pattern in their head.

Stage 3 — Mental drills introduced (Intermediate A)

By Intermediate A, the app starts inserting short mental-only drills: 2 or 3 problems per session where the abacus does not appear at all. The child has to commit the answer using only the mental image. The first time this happens it feels impossible — and then the child does it. The accuracy is low at first (around 50–60%) and the app does not penalize the dip; it tracks it as a separate metric and watches the trend.

Stage 4 — Mental majority (Intermediate B)

Halfway through Intermediate B, the ratio flips. More than half of every session is mental-only drills; the visible abacus drills become refresher exercises rather than the main work. This is the practical anzan threshold. A child here is doing genuine mental arithmetic on a soroban they cannot see — and the speeds are competitive with adults doing the same problems on paper.

Stage 5 — Full anzan (Higher A through Grand)

By Higher A, the visible abacus appears only for new-material introduction (multiplication, division). All routine drill is mental. By Grand Level, a child can do multi-digit multiplication entirely in their head at speeds that startle adults who have not seen it. The mental abacus is no longer something they consciously visualize; it is reflexive, the way most adults can hold a 3-digit number in their head without explicitly picturing it.

• Foundation through Elementary A: 100% visible abacus.
• Elementary B through Intermediate A: 70% visible / 30% partial-mental.
• Intermediate B: 50% visible / 50% mental — the practical anzan threshold.
• Higher A through Grand: 10% visible / 90% mental.
• Beyond Grand: 100% mental. The mental abacus stays as a tool the child uses for life.

The first time my daughter answered a 2-digit problem with the screen blank — no abacus, no scratch — I asked her how. She just shrugged: "I saw it." That is anzan.

— Parent at month 9 of practice

How to know your child is crossing the threshold

The signal is simple: ask your child to answer a problem at their current level without looking at the screen. If they pause, close their eyes for a second, and answer correctly within 4–5 seconds, the mental abacus has formed. This usually happens somewhere in Elementary B for the smaller problem types, and is robust by mid-Intermediate B for full 2-digit work. Once the threshold is crossed, it does not retreat; the mental abacus stays once built.