Valtteri Suomalainen's book "Sauna Syyriassa" describes a similar method being used by the Syrians, using e.g. rocks. Say we want to multiply 10 by 6:

- Make two piles of rocks (or what ever material is being used) side by side, 10 rocks in one and 6 in the other. Let's name the piles A
_{0} and B_{0} (the order doesn't matter). In this case, let's call the bigger pile A_{0}.
A B
0 10 6

- Make another pile (A
_{1}) under pile A_{0}, containing half as many rocks as there is in A_{0}, rounding down; in this case, 5 rocks (floor(10/2) rocks). Then make a new pile (B_{1}) under pile B_{0}, with twice the number of rocks in pile B_{0}; in this case, 12 rocks.
A B
0 10 6
1 5 12

- Repeat the previous step until you get a pile A
_{n} with only 1 rock, and a corresponding pile B_{n}. In this case, B_{n} will contain 48 rocks.
A B
0 10 6
1 5 12
2 2 24
3 1 48

- Remove all the lines k where A
_{k} is even. In our example, these are lines A_{0} (=10) and A_{2} (=2).
A B
~~0 10 6~~
1 5 12
~~2 2 24~~
3 1 48

- Add together all the remaining B's:
B_{1} + B_{3} == 12 + 48 == 60 == 10 * 6

QED.

Any information on the origins of this particular method would be most welcome.