The Soroban – Japanese Abacus

14 Pages·2017·0.91 MB·English

The Soroban – Japanese Abacus
Simon Wetherley

Oldest known soroban1

Introduction
This document provides a resource designed to assist teachers to make a soroban and teach
their students how to use it. A brief history of the soroban and its influence on Japanese
mathematics is followed by an overview of the various parts of a soroban. Curriculum links
are outlined followed by six modules that are designed to be standalone lessons, or parts of
lessons, that teachers can use to make a soroban (or source a digital one), display numbers
and perform addition, subtraction, multiplication and division. QR codes are provided that
should be given to students to discover the content. Links to videos explaining soroban use
are also provided to assist teachers to learn to use it prior to teaching their class.
History
Japan enjoyed a peaceful time during the Edo period (1600-1868) with no wars within
Japan nor abroad which provided a stable society2. In 1639, Portuguese ships were forced
out of Japan and trade was strictly controlled with the Dutch and Chinese via Nagasaki
although some western science and art did enter the country during this time2. This
effectively isolated Japan from the influences of western mathematics, although it was
influenced by Chinese mathematics. Amateur Japanese mathematicians learnt Japanese
mathematics (“wasan”) which focused on computation rather than generalisation.
The soroban (Japanese abacus) is believed to have first arrived in Japan in 1592 when a
soldier returning from Korea had one in his possession that he had presumably acquired in
China1. The soroban played a vital role in wasan because it could be used to quickly do the
required computations. The soroban was the only tool used for calculation and Arabic
numbers weren’t used2.
During the Edo period, the Japanese population were taught in private schools (Terakoya)
based in temples where they received a good quality, Japanese based education where
mathematics was often taught, leading to a generally well-educated population2,3. At this
time, Japanese numbers were written vertically and there were no place values making it
difficult to perform calculations manually, hence the popularity of the soroban for
performing numerical calculations3.
The Edo period was followed by the Meji Restoration in 1868 which resulted in modern,
centralised education2. In 1872, it was declared that only western mathematics should be
taught which meant the soroban should no longer be used. This was met with great
resistance from the teachers at the time because they had been brought up on wasan which
was heavily focussed on using the soroban and didn’t know western mathematics2.
In 1932, the soroban was modified to remove two of the beads to produce the modern
soroban still used in lower school in Japan. It was in widespread use in the 1960s when
over one million people participated in Soroban exams3. The increasing use of computers
in the 1970s led to a decline in use of the soroban although it is still taught in modern day
Japan in lower school3. Since its introduction to Japan in 1592, the soroban has had a
dramatic impact on Japanese mathematics.
The Soroban
The modern soroban is typically made up of 13 columns of five beads on a rod made of
wire or wood. The beads are separated by a bar with one above the beam (“heaven” beads)
and four below (“Earth” beads)4. Each rod represents a place value (e.g. 1, 10, 100 etc).
The heaven bead has a value of five and the earth beads have a value of 1 (Figure 1).

Figure 1: Structure of the soroban including place values5.
Beads are moved towards the beam (up for earth beads and down for heaven beads) to
represent numbers. For example, twenty-eight would have two earth beads against the
beam on the 10’s rod and three earth beads and one heaven bead against the beam on the
units rod (3+5 = 8; Figure 2).

Figure 2: Representation of numbers on the soroban4.
Teaching Resource
The teaching resources have been broken into discrete modules. Depending on how much
time you want to devote to the set of modules, you could just teach the students addition
and subtraction and leave the multiplication and division as extension work for the brighter
students. The length of time each module will take will depend on the class and the level of
detail the teacher wants to go into. Each module has either one or several QR codes that
can be given to the students to take them to the instructions on how to perform calculations
on the soroban.
Learning to use the soroban – teacher resources
Prior to teaching the modules to the class, it is important for the teacher to have a good
working knowledge of at least addition and subtraction and depending how far you wish to
take the teaching, you will also need a good knowledge of multiplication and division (you
can also use the soroban to find square roots if you are keen! This would provide an
excellent extension activity for brighter students).
There are many videos available on-line that describe how to use the soroban that may be
useful for the teacher to learn techniques or for students to watch prior to coming to class.
Links to some of these are provided in the relevant section below. These could also be
provided to the students for reviewing at home (QR codes are provided below).
There are six modules in this learning package and these are described below. QR codes
are provided for each of the modules to direct students to instructions for making a
soroban, general use, addition, subtraction, multiplication and division. They will require
concentration and focus on the student’s part so may not be appropriate in all school
contexts. Regardless, many worked examples should be done with the students to ensure
they have a good understanding of the concepts. Teachers could provide the videos to the
students as an alternative to using the written documentation. There are several on-line
sorobans that teachers will be able to use to demonstrate procedures to classes.
Module 1: Source your soroban
There are several options for sourcing sorobans for your class. You could purchase a set
from an appropriate supplier – there are several on line sources available. Another option is
to get students to make their own sorobans (preferred option) and instructions to make a
refined one and a basic one are provided in this module. The final option is to use an online
version or an app. This is not the preferred option because it doesn’t provide a physical
object for the students to manipulate although may be useful to set homework and to assist
students learning the arithmetic processes.
Make Your Own Soroban
Links to two soroban designs are provided here. There is an opportunity to work with your
Design and Technology teachers to assist in making the first one. The second one is
relatively straightforward and should be able to be made in any classroom.
Design 1:

http://www.instructables.com/id/Make-You-Own-Soroban-Abacus/
Design 2:

http://www.ee.ryerson.ca/~elf/abacus/popsicle-abacus.html.
On-line or apps
There are several browser based sorobans available. One is provided below:

http://www.mathematik.uni-marburg.de/~thormae/lectures/ti1/code/abacus/soroban.html
A good soroban for Android is “Simple Soroban”. This not only allows you to use your
phone as a soroban, but also provides questions and challenges that will help reinforce the
techniques. On iOS, “Master Soroban” looks quite reasonable.
Module 2: Displaying Numbers
In this module, students are introduced to the various parts of the soroban and the basics of
displaying numbers. They are also challenged to display some number facts about Japan on
their sorobans (refer to page 26 of the document below).

http://webhome.idirect.com/~totton/abacus/pages.htm#Soroban1

http://www.japansociety.org.uk/wp-content/uploads/2015/01/soroban_1.pdf

Videos to assist teachers are available here:

https://www.youtube.com/watch?v=3gDibLEZc20
Module 3: Addition
In this module, students learn how to add numbers on the soroban. It includes examples
and practice sums at the end. The worksheet is slightly modified from

http://webhome.idirect.com/~totton/abacus/pages.htm#Addition1

Videos to assist teachers are available here:

https://www.youtube.com/watch?v=3gDibLEZc20

Module 4: Subtraction
In this module, students learn how to subtract numbers on the soroban. It includes
examples and practice sums at the end.

http://webhome.idirect.com/~totton/abacus/pages.htm#Subtraction1
Videos to assist teachers are available here:

https://www.youtube.com/watch?v=bEvwSlA88fU&t=1s
Module 5: Multiplication
In this module, students learn how to multiply numbers on a soroban. This process is more
complex than addition and subtraction and will help students improve their mental maths.
It should also give students an insight into how multiplication of larger numbers works
because they do it step by step. Worked examples are provided with practice problems at
the end.

http://webhome.idirect.com/~totton/abacus/pages.htm#Multiplication1

Videos to assist teachers are available here:

https://www.youtube.com/watch?v=uNDwqGB9cSw

https://www.youtube.com/watch?v=nldWkfwLQbQ&t=11s
Module 6: Division
In this module, students learn how to complete division on the soroban. This operation is
the most difficult of all and will certainly help students to understand more deeply how
long division works if they are able to master division on the soroban. Worked examples
are provided with practice problems at the end.

http://webhome.idirect.com/~totton/abacus/pages.htm#Division1

There are many ways of doing division on the soroban and no videos were available that
explained the process used in the worksheets. There are however, several videos available
that describe the overall process and will be useful for teachers to learn the mechanics if
used in conjunction with the worksheet. Search “soroban division” on YouTube.
Rationale
This resource provides instructions for students to build their own soroban (an easy one
and a more robust one), and how to add, subtract, multiply and divide numbers. The
resource can be used in many ways from improving mental calculations for low achieving
year 7 students, calculating roots for year 10 students, linear equations for year 10 students
or a simple enrichment exercise for any middle school class. Here it is designed to be used
for a year 8 class.
Using the soroban as a calculation tool provides students with the opportunity to improve
their mental mathematics (addition and subtraction relies on using complementary numbers
that add to five and ten) and will assist them to better understand how multiplication and
division work numerically. Although the ideal time for introducing the soroban is in
primary school, many high school students still struggle with mental calculations which
can be improved with the soroban.
Year 8 students are on the transition between Piaget’s concrete and formal operations
stages6,7 and will find being able to physically manipulate the soroban while doing sums
will help them to solidify their knowledge and enhance their understanding.
Australian Curriculum links
The resource is designed to cover part of the number and algebra, general capabilities and
cross curriculum priorities areas of the Western Australian Curriculum: Mathematics8. All
areas of the curriculum that are covered are summarised in
Table 1.
As students use the soroban, they will develop mental strategies for carrying out addition,
subtraction, multiplication and division and possibly find their own rules, or modify
existing rules which covers part of the number and algebra in the year 8 mathematics
curriculum.
The Japanese heritage of the soroban links with the cross curriculum priority of Asia and
Australia’s engagement with Asia (OI.1 and OI.3). Literacy general capability is covered
because the detailed instructions on how to operate the soroban are provided in written
form. Critical and creative thinking is covered by the detailed instructions/procedures that
the students need to analyse and understand to operate the soroban. As students use the
soroban they should gain respect for the simplicity and functionality of it and hopefully
develop a respect of Japanese culture to develop the intercultural understanding section of
the general capabilities part of the curriculum.