From physical bead to anzan: the Kani Math app roadmap
Anzan — doing arithmetic on an imagined abacus — is the goal of the entire soroban method. Here is exactly how the Kani Math app stages that journey, and where on the ladder kids cross each invisible line.
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 Math app stages those graduations on its level path, in the order of the nine-level ladder.
Stage 1 — Beads on screen (Foundation)
Foundation is read straight off the soroban on screen: one rod, then two, until a bead pattern reads as a number at a glance. The hands learn the moves beside the app, on a wooden soroban or the free virtual one. The goal here is not speed but cleanliness of bead manipulation: the thumb raises lower beads, the index finger does the rest, no improvising.
Stage 2 — Numbers on the card, beads in the hands (Basic to Elementary A)
After the bead-reading cards, each card shows the numbers and the child types the answer. The beads move on the child's own abacus, so every direct move and every small friend is made by hand before it is ever pictured. The digit row under each rod on the virtual abacus can be switched off at any time; reading the bead pattern instead of the label is where the mental abacus starts to form.
Stage 3 — The first mental cards (Elementary B)
Elementary B brings big friends and, beside them, the first cards marked Mental: a ten-row chain and five rows of two-digit numbers, worked on a picture of the abacus instead of the real one. The first time it feels impossible — and then the child does it. These cards ask the same 80% as every other card, so expect a few runs before one counts.
Stage 4 — Mental chains grow (Intermediate A and B)
Intermediate A puts both friends into one move and stretches the two-digit mental chains; Intermediate B takes them to three digits and then four. The physical abacus becomes a refresher rather than the main tool. This is the practical anzan threshold: a child here is doing genuine mental arithmetic on a soroban they cannot see.
Stage 5 — Full anzan (Higher A through Grand)
From Higher A the new work is multiplication and then division, written on one line with no frame on screen, while the mental addition chains reach five digits in Higher B and Grand. The mental abacus is no longer something the child consciously visualizes; it is reflexive, the way most adults can hold a 3-digit number in their head without explicitly picturing it.
- Foundation: every question read off the beads on screen.
- Basic to Elementary A: numbers on the card, beads on the child's own abacus.
- Elementary B: the first Mental cards, two-digit chains pictured instead of touched.
- Intermediate A and B: mental chains of two, three and four digits — the practical anzan threshold.
- Higher A through Grand: multiplication and division from the head, five-digit mental chains. Beyond Grand, ten Practice levels mix everything so far, and the mental abacus stays as a tool 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.— Illustrative example
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.