Iām far far from an expert but have some thoughts or hunches on this.
There are perhaps people that use classic abacus for mental math vs soroban, but from what I can gather, the anzan or mental math kids/adults that Iāve seen all over the internet have always used the soroban.
Really the only difference is the beads. If Iām not mistaken, the classic abacus has two heavenly beads and 5 earthly beadsā¦ well, thatās 15 just in the ones column alone. I might be wrong about this, and some of the newer abacus have either 2 heavenly or 5 earthlyā¦ meaning you can have 10 in the ones column.
Well, the soroban uses place value exceptionally well. There can only be 9 in the ones column (or any of the columns). If you go over 9, then youāre going to have use the tens column (the next column up).
And this is how we write the numbersā¦ 9 is single digit, 10 is two digit. 100 is three digit. The soroban mimics this perfectly.
Because it mimics so perfectly, it gives you an excellent mental representation of the number itselfā¦ and so when you do the calculation you just look to the hundreds column, the tens column, and the ones column to see how many beads are in each column effectively giving you the number. If you had 10 in the ones column, it might get confusing (IMO)
I also like having heavenly and earthly beads; My wife bought a melissa and doug abacus that has just 10 beads on each rod. I plan on using this for early counting, but I think it would suck for calculating. The heavenly bead makes a 5 chunk that allows for quicker manipulationā¦ you donāt have to grab say 6 beads and slide themā¦ with heavenly beads you just push the 5 chunk up and remove an earthly beadā¦ just easier to see, but perhaps harder to understand AT FIRST.
This is one reason why I like Singapore math. They really emphasize number bonds (what equals 5, and what equals 10)ā¦ it seems like a good set up for soroban use (from my limited look at their early text)
Oh, and the sliding horizontally vs verticallyā¦ again it mimics how we write the number. 1,000 is written left to right. Imagine thinking of the number like this:
1
0
0
0
This is a little more difficult to get with a mental snap shot. Additionally, the horizontal sliding abacus that Iāve seen require or use a very long rod (which is excellent for counting and really SEEING how the counts relate to each other) - longer rod means larger movements which will also mean slower calculation because the moves take longer to execute. Having said that, it takes some fine motor skills to use a sorobanā¦ the beads are small and the moves are small and distinguishedā¦ I donāt think any little kid can just start working with one; they have to develop the ability (or have a soroban geared for small fingersā¦ like large crayons)