abacus

I’ve become interested in using the Japanese abacus, or Soroban, as a maths teaching aid in  primary school.  Not only are they fun and fascinating to use, making one is also a really good, do-able, DT project.

There is an excellent, step by step, guide on the instructables web site about making and using the Soroban.  There are also some links on my blog post here, and some fascinating links and videos on my blog post about Alex Bellos’ Radio 4 programme, ‘The Land of The Rising Sums’ here.

The Japanese talk about the Soroban encouraging ‘mechanisation’ and ‘thoughtlessness’.  Initially this doesn’t sound very encouraging, however what I think they mean by this is quite fascinating.  By mechanisation they don’t just mean using a machine to calculate, they also mean using a mechanical mental system to calculate.  This is linked to what they mean by thoughtlessness.  When they calculate using Soroban they are not really thinking about what they are doing, they are following a mechanical mental and physical process to reach the right answer.  This might sound as if they do not really understand what they are doing , but actually in order to use the Soroban effectively you need to have a really good understanding of number.  I think that the mechanical nature of the calculation encourages the use of different parts of the brain, perhaps the parts more associated with visual processing.  Soroban users ‘see’ the answers.  They ‘know’ the answers without really, consciously, thinking about them.

Soroban users progress from using the physical abacus – I got mine for a few pounds from ebay – to using the ‘Anzan’.  You can’t get an Anzan from ebay, it is the Soroban in your head!  In Japan they have yearly ‘Flash Anzan’ competitions instead of the X Factor.  Numbers are flashed sequentially on a screen and the competitors add them up in their heads.  This year’s record was fifteen 3 digit numbers in 1.70 seconds.  You can see this via the Guardian article here.  If you wait for the end of the video – you won’t have to wait for long! – there are all sorts of other You Tube links displayed.

Adding and Subtracting on the Soroban are simple.  You need to keep track of where your units are.  The beads above the bar represent five (or 50, 500 etc.), the beads below the bar are 1 to 4 (or 10-40, 100-400 etc.).  The Japanese have all sorts of strict rules about where on the Soroban you operate and which fingers to manipulate the beads with.  I don’t see that these are really necessary unless you are intending to become a real expert.  The interesting part comes when there aren’t enough beads to add or subtract from a particular column.  When this happens you are forced to use ‘complementary’ numbers.  The complementary numbers are the number bonds that make five and ten.  For five they are: 4-1 and 3-2.  For ten they are: 9-1, 8-2, 7-3 and 6-4.  So if you need to add seven units to a column that already has eight beads you are going to have to add a ten in the column to the left and subtract three from the first column.  This really encourages a great deal of rapid mental calculation, far more than when using a calculator, and since calculators are to be banned from  primary schools this must be a good thing!

Since the Soroban is such a physical, visual, thing the best way to understand is to have a go.  There are several on-line versions, try here.  You can download that one too.  The Japan Society will lend Sorobans (easier to write than abaci) including a large, teaching, Soroban.

Multiplication and division, as in real life, are a little more complicated.  There seem to be several methods, some of which have ‘official’ status.  All of them require a good knowledge of times tables up to 9 x 9.  I don’t think that children have to know all of their times tables before they have a go on the Soroban.  I think they can be learned in parallel and will complement each other.  Children will also need a good understanding of place value, but again using the Soroban will encourage this.  When you start on multiplication it is obviously important to start with single digits or with a two digit number multiplied by a single digit number.

Multiplication vocabulary:
multiplicand : the number to be multiplied
multiplier : the number to be multiplied by
(In multiplication these terms are generally interchangeable)
product: result of the multiplication

Choose where you want the units of the product to end up and count to the left the number of digits in the multiplicand and the multiplier.  So if our sum is 5286 x 654 (as in this example), count 7 columns from the right hand side (or wherever you want the units to end up) and start there.  Some methods involve entering all three numbers on the abacus, I think, for beginners, it is easier to just enter the product.
Do your first multiplication, 5 x 6 and enter the answer in the seventh and sixth columns, 3 and 0.  Then do the next numbers 2 and 6 and enter the result, 12, in the sixth and fifth columns.  Continue until you have multiplied all the numbers in the multiplicand by six.  You have then finished with 6 and can repeat the process with 5, because there are now only 6 digits, we start in the sixth column.  Complicated? – yes, but a good learning exercise I think.

Division vocabulary:
dividend: number to be divided
divisor: number to be divided by
quotient: result of the division

Division:  I have read about several methods, most of them I have found quite confusing.  Again, if you are serious about using the Soroban you should probably use an official method.  A simple method that I can understand is: work out how many columns you will need using the following method – dividend minus divisor plus 1.  So if we are doing: 8965 divided by 5 we will need 4 columns (4-1+1=4).  Enter the dividend somewhere on the left of the Soroban.  Starting from left to right divide 8 by 5.  Enter the result, 1 in the 4th column to the left of your chosen units column.  Replace the 8 in the dividend with the remainder, 3.  Now divide 39 by 5 and enter the answer, 7 in the 3rd column and replace the 3 and the 9 with the remainder, 4.  Continue until you have used up the whole dividend.

There is an exercise generator here – don’t frighten yourself, the 1st kyu is the hardest!

Dividing by more than one digit divisors:  I have yet to get my head around this!  You can see for yourself here – this is the simplest explanation that I have found.

 

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