Addition with a Soroban Abacus

Soroban Abacus; Shown is the number 123456789 (zero is represented with all the beads pushed toward the sides)

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Early on I decided that I wanted to teach Little BBQ how to add using an abacus, so I always assumed that I was going to either buy or make an abacus with 10 beads per column since we use a base ten system in our society. However, when I started reading, Here's Looking at Euclid by Alex Bellos, I started to change my mind. He made some sound arguments that our brains can quickly differentiate between 1, 2, and 3 items but as we go higher in the number scale it becomes harder and harder for your brain to process more than three (p 14).

It seems that many ancient cultures understood this phenominon. You can see from the diagram below that the Chinese, Romans, and Idians all used dash marks for numbers 1, 2, and 3, but once you got past 3 they changed the symbol to another unqiue symbol in order to quickly distinguish the higher number (p 14).

Armed with this new found perspective I decided that an abacus with 10 beads did not make sense because Little BBQ would not be able to quickly distinguish the difference between 6 beads or 7 beads. I wanted the abacus to be an efficient tool for learning, and not a source of frustration. Many modern abacuses designed for children use brightly colored beads to distinguish the different numbers, but I still think that fewer beads will allow for faster processing.

I decided that a soroban abacus made the most sense. The soroban abacus uses five beads per column. By adding an extra horizontal line bisecting the columns you can quickly represnt the numbers 0-9 on one column. The soroban abacus was used between the seventh and nineth centuries in Japan to accomidate a new merchant class of people who needed to be able to quickly add numbers (p 40). To ease the transition between the abacus and the electronic world an abacus attached to an electronic calculator was sold in Japan for many years (p 41). Interestingly, addition is still quicker with an abacus than an electronic calculator since the answer to an addition problem is in front of you as soon as you  input the values while the calculator still needs to be told to process the information to come up with an answer (p 40). The efficiency of the abacus is probably why it is still a popular tool studied in Japan today by school children who form after school clubs to compete in adding a long series of numbers as quickly as possible using a soroban abacus (pp 40-41).

When a student becomes an soroban abacus master, he can move on to azan. Azan is a technique for visualizing a soroban abacus to quickly add numbers. Proficient pupils in azan can add a series of 15 numbers quicker than a person can use an abacus, pen and paper, or calculator. The catch is that each number is only shown for 0.2 seconds (p 42). That is hardly long enough to process the number on the screen. Azan students keep a visual soroban abacus in their head and when a new number is flashed the student visually moves the beads on the soroban abacus around in his head keeping a running tally of the sumation (p 42).

Interestingly, nueral imaging studies have shown that adding with soroban abacus stimulates areas of the brain that are associated with visuospatial processing while pen and paper addition stimulates areas of the brain that are associated with linguisting processing. In other words, the abacus uses the right side of the brain while the pen and paper method uses the left side of the brain. The soroban abacus is an excellent learning tool for visual students.

Want to really stimulate your brain? Some Japanses students can play shiritori while practicing azan (p 43). Shiritori is a word game where the first person says a word then the next person says a word that starts with the last syllable of the original word and then the first person makes a new word using the last syllable of the second word. The game continues on in this pattern. Bellos gives this demonstration of a young Japanese girl who is a soroban prodigy while she plays shiritori. In the demonstartion the girl is shown 30 three digit numbers during a 20 second time period while playing shiritori (p 43). Her shiritori dialogue with another student is shown in the text below

Ringo
Gorira (gorilla)
Rappa (trumpet)
Panda (panda bear)
Dachou (ostrich)
Ushi (cow)
Shika (deer)
Karasu (crow)
Suzume (sparrow)
Medaka (killifish)
Kame (turtle)
Medama yaki (fried egg)

At the end of the 20 seconds the girl states that the summation of the 20 numbers is 17,602 (p 43).

Given the sucess of soroban abacus training, I have decided to teach Little BBQ addition using a soroban abacus. To make the experience more person for him, we made our own soroban abacus out of a card board box.

Materials

card board box, lid removed
paint
ruler
knife or scissors
string
breads
tape

Procedure

1. Have the student paint the card board box.
2. Decide how many columns you want the abacus to contain. Cut notches into the top and bottom flaps of the cardboard box equal distance apart for the set number of columns that you chose (we  made our abacus with nine colums all 3.2 cm apart).
3. Cut the string to stretch across each the box from one notch to the other. Place 5 beads on each string. Insert the string in the notches and tape the string to the box. Continue in this pattern until all the columns are finished.
4. Make two notches on the sides perpendicular to the columns. These notches should be close to the top of the box but far enough away from the edge so one bead can comfortably fit abvoe the string line. We decided to use a red string to distinguish this line from the columns in our soroban.
5. Insert the string in the notches perpendicular to the columns. Tape the string.

Posted on Tutorial Tuesday

All references are from the book: