These counting boards were still the standard tool in Europe until a few centuries ago, but their use has been completely wiped out and nearly forgotten in a short time, since the popularization of Indo-Arabic numerals and cheap access to paper.

The way it works is that parallel lines are drawn on the surface, and counters on the line represent 1, 10, 100, etc., while counters in between the lines represent 5, 50, 500, etc. In normalized form you only ever have up to 4 counters on a line. But there is no hard requirement that numbers be normalized, and you can pile as many counters as you like on one line and still have a meaningful state of the board.

Using the counting board then consists of first plonking down counters in the easiest representation of your result (e.g. to add 22 + 34 put 2 + 4 counters on the ones line and 2 + 3 counters on the tens line), and then undertaking a series of transformations which preserve the value of the whole board but move between equivalent representations (e.g. trade 5 ones for 1 five and trade 5 tens for 1 fifty), until you get to a representation which is convenient as output.

This is closer to most types of mathematical/computational activity in later mathematics, where various manipulation is done which at each step preserves some invariants. It is also good preparation for thinking about the relation between data structures and algorithms.

The big problem with the beads-on-rods version is that there is only one possible representation of each number. So the act of trading different magnitudes of counters is always left implicit. This makes it both harder to learn and less flexible as a tool, with the advantage that in the hands of a serious expert it’s probably marginally faster. If the goal were to train a 19th century accountant or shopkeeper this might be a fair trade-off, but for promoting understanding I think it’s not worth it.

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If you want to save some tokens and make the system still more powerful, add a perpendicular line down the middle of the parallel lines. On one side tokens represent positive counts and on the other side they represent negative counts. Now in addition to the rules about trading 5 ones for 1 five or 2 fives for 1 ten, there is an additional rule that the same number of counters on opposite sides of the line represent 0 in combination (so any number of counters can be added or removed from both sides equally without changing the meaning of the configuration).

This adds is an additional convenient way to normalize numbers: try to maximally reduce the number of tokens used, allowing some negative "digits". We represent 3 as 5 – 2, 8 as 10 – 2, etc. Pick whatever convention you like for whether to round 5 up or down. In this representation, rounding a number is particularly easy: just truncate.

This is something which cannot be done on a beads-on-rods soroban, but is very helpful for understanding the meaning of negative numbers, the relation of addition and subtraction, etc.