Mr. Okahisa Yasuo

Vice President of League for Soroban Education of Japan. Inc.

**1. Foreword**

Japan proposed in the *5th Science and Technology Basic Plan* that, following the hunting society, agricultural society, industrial society and information society, the new society that we should work hard to achieve in the future is a highly integrated system of cyberspace (virtual space) and physical space (real space). At the same time, it advocates the use of this system to establish a “people-oriented society” that can take into account economic development and the solution to social issues. In global terms, this can also be a common goal for many countries.

To cultivate the survival ability of children in the future society, and inherit and carry forward traditional Japanese “abacus” skills, or abacus education, we need to take into account the following issues: Where are we going in the future, what steps should be taken to achieve our goals, whether there is a better solution to problems, etc.

This paper looks at the status quo and future of abacus in Japanese schools and private education, provides an opportunity to further explore the advantages of abacus and mental arithmetic education, and reconfirms and accurately grasps future priorities, making the contribution to opening up a new path of abacus education with subsequent efforts.

**(1) Elementary School Syllabus**

MEXT has introduced abacus-related contents in the mathematics section of the Elementary School Syllabus since April 2020.

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① Grade 3 Teaching Content A: Numbers and Calculations (8) and Instructions

Mathematical activities in which numbers are represented and calculated using an abacus by students so that they can master the following skills under instructions.

A. Master the following knowledge and skills:

(a) Learn how to represent numbers using an abacus.

(b) Understand calculation methods for simple addition and subtraction, and perform calculations.

B. Master the following skills of thinking, judging and expressing.

(a) Think about how to calculate large numbers and decimals according to the mechanism of the abacus.

Instructions ○ Enable students to express integers and decimals using the decimal system. Integers to the ten thousand place, decimals to 1/10.

○ Teach the addition and subtraction of one and two digits in an integer.

② Grade 4 Teaching Content A: Numbers and Calculations (8) and Instructions

Mathematical teaching activities in which numbers are represented and calculated using an abacus by students so that they can master the following skills under instructions.

A. Master the following knowledge and skills:

(a) Perform addition and subtraction calculations.

B. Master the following skills of thinking, judging and expressing.

(a) Think about how to calculate large numbers and decimals according to the mechanism of the abacus.

Instructions ○ An integer representing billions or megabits on an abacus, and for decimals, to the 1/100 decimal place.

○ In terms of integers, students are able to add and subtract 2-digit numbers and understand the method for simple calculations in billions or megabits, such as “200 million + 600 million”, “10 trillion +20 trillion”, etc. In terms of decimals, students are able to understand the method for simple addition and subtraction of 1/100 decimal places, such as “002+085”.

**(2) Prospect**

In the elementary school syllabus to be revised and implemented by 2030, it’s recommended to further increase the teaching of “abacus” in the arithmetic section, and to explore the situations of using abacus as an effective teaching tool when solving arithmetic problems so that the students can not only learn how to use the abacus, but also use it for a learning purpose. The recommendations are as follows.

1 Increase the class hour of “abacus” in arithmetic - Introduced from Grade 2 onwards -

The current syllabus stipulates that abacus class should be set in Grades 3 and 4. So why is it proposed to introduce it from Grade 2? The abacus is a calculating tool that requires to use the brain. Students in Grade 2 can learn a lot simply by representing numbers on an abacus or reading numbers represented on an abacus. There are five main reasons for this.

a. Each rod consists of one upper bead for 5 and four lower beads for 1, with the advantage of identifying numbers from 0 to 9 at a glance.

b. Each rod can only represent numbers from 0 to 9, which makes students understand decimal numbers and digits easier and deepen their understanding of decimal counting.

c. As the upper bead represents 5 with one bead, it naturally deepens students’ understanding of cardinal numbers.

d. Students in Grade 2 are exposed to a lot of three-digit numbers. The abacus is an important tool that allows them to identify numbers with null such as 301 with their eyes and understand large numbers.

e. By representing 240 on the abacus, students can understand that “in 240, the hundreds digit is 2, the tens digit is 4, and the single digit is 0. It is also the combination of two hundreds and four tens”. They can also easily deepen their understanding of the number structure and relative size by holding the tens digit with fingers and then realizing that “240 is a number made up of 24 tens”.

It can make students in Grade 2 learn simple carry and abdication such as “3+8” and “12-9” more efficiently. On the one hand, it prevents failure when students start to learn two- and three-digit written calculations, and improve their understanding of ten-place notation.

By introducing the abacus at the beginning of Grade 2, students can learn the abacus while reviewing the number and calculation areas learnt in Grade 1, which can also be interpreted as a new form of spiral learning. Children who start new “abacus” learning can realize deep learning to consolidate the concept of numbers, while further deepening their understanding of numbers.

The current syllabus for Grades 3 and 4 requires students to: (i) Know how to use an abacus to represent numbers; (ii) Understand the method for simple addition and subtraction, and perform calculations; and (iii) Think about how to calculate large numbers and decimals according to the abacus mechanism. The purpose and objectives are described in detail in the instructions. In our opinion, by “using the abacus”, that is, using the abacus mechanism to perform mathematical activities, these goals can be achieved beyond expectations.

2 Use of “abacus” in arithmetic

When used as a teaching tool, the abacus has the advantage of deepening students' understanding of the number mechanism and enriching their sense of numbers by letting students focus on number units, think about their fractions and grasp the relative size of numbers. In other words, we believe that by perceiving numbers visually, a better teaching effect can be generated. Moreover, for any one of the decimal notations, the calculation can be performed according to the principle of decimal counting.

Not only as a computing tool, but also a teaching tool close to children, the abacus enables children to find problems independently and gain opportunities and experiences for cooperative and exploratory learning. It can also be used as a teaching tool in many scenarios for cultivating rich thoughts and thinking ability about numbers among students. Here are some examples.

Example 1: Abacus is the most suitable teaching tool for deepening students’ understanding of number structure. As shown in (1) (e) above, the use of an abacus to represent numbers helps students think about numbers. By looking at the numbers expressed on an abacus, students can also think about large numbers and decimals in units of millions, billions, and trillions.

Example 2: Each rod of the abacus has an irregular part consisting of 1 upper bead and 4 lower beads, and also a part of beads of the same shape and size, which is also of significance. The same ball, for example, gets ten times bigger every turn to the left. This mechanism makes decimal notation easy for students to understand. Moreover, it can also help students think about calculation methods and deepen their understanding as a teaching tool.

The names and functions of various parts of the abacus are as follows: ❶Frame: The function to deepen the understanding of decimal counting is included in one framework. ❷Fixed point: A marker or unit of quantity used to read digits. ❸Rod: In addition to seeing the digits, each rod can only represent numbers from 0 to 9, which helps to understand the decimal notation. ❹Beam: The counting beads are divided into 1 upper bead and 5 lower beads. ❺5-bead and❻ 1-bead; Objects with a semi-concrete nature that make it easier to understand numbers and enable five beads to represent numbers from 0 to 9. In addition, by means of counting beads by manipulation, students can see the addition and subtraction, composition and breakdown of numbers. The sound produced by counting beads is also likely to boost motivation. In particular, by operating the lower beads, students can see numbers and deepen the understanding of one-to-one correspondence between numbers, while the upper bead represents 5 by a bead, which can be used to understand cardinal numbers. As mentioned above, each part of the abacus has many functions.

Example 3: Students can think about calculating “4+8” with an abacus in different ways. Since 8 plus 2 is 10, when you decide to use the add-factorization method, put 4 first and then take 2 plus 10 to get 12. It’s found that “4+7”, “3+9”, and “4+6” can be summed in the same way.

In addition, the same instruction can be given for problems with an abdication nature such as “12-9”, as well as for the synthesis and decomposition of 5 in “2+3”, “6-4”, etc. By thinking about how to operate the beads, the abacus “visualizes” the process of thinking and calculating.

Example 4: There are three modes of operation for adding 2 using an abacus: “1+2”, “3+2” and “9+2”. And there are also three modes for adding 7: “1+7”, “4+7” and “5+7”. In case of only the operation of adding 2, two modes of “11-8” and “13-8” can be added to the above three modes, making it five. When using the abacus for calculation, there are a variety of algorithms. In the process of obtaining correct judgment by using an abacus, one can develop not only the ability of thinking, but also the ability of concentration, accurate finger movement and the sense of numbers. Learning these algorithms is also likely to improve the ability to understand programming thinking.

Example 5: Unit conversion related to quantity. For example, make four cards representing length units km, m, cm, and mm, and then ask children which part of the abacus beam they want to stick each of these cards on, instead of sticking them in place. The process of repeated trial and error until they are aligned in the right place is very meaningful to deepen children’s understanding of unit conversion.

“How many kilometers is 203m”? This is a question that is often answered incorrectly. We would like to know what idea its answer is based on. An effective solution to this problem is using an abacus. As shown in the right photo, after expressing 203m on the abacus, we can easily achieve the conversion between 20,300cm, 203,000mm and 0.203km, thus deepening the understanding of unit conversion through the “visualization” of numbers.

Using an abacus for spiral-type learning, children are asked to express the length of 1m or 30cm with their hands. It is also important that children measure things around them based on this, such as the length of a blackboard, desk or classroom.

This offers a good opportunity for them to find out what kind of buildings or shops are within 203m of their home or school gate, and deepen understanding.

This method is also applicable to the left photo. After representing 4,100mL on the abacus, children are asked to find out the capacity of plastic bottles, cans, cups, etc. While increasing their interest in quantity, they will have an opportunity to learn a lot about unit conversion.

**3. Abacus in Private Education**

**(1) Level examination**

In Japan, there are many private educational institutions that use the contents of abacus level examinations as textbooks or exercises to learn abacus. Level examination is divided by level and band, respectively according to the stage set from the primary level. After passing the examination at a level, the examinees can proceed with the next level. Progress will be made by achieving the small goal at hand (higher level), which can be regarded as a curriculum for abacus teaching.

The following shows some contents related to applied calculation and extraction of a root (square root and cube root) of the band examination in the *Abacus Level Examination* revised by us in 2022. The former has 30 questions with a time limit of 10 minutes, while the latter has 20 square root questions and 10 cube root questions. There are a total of 30 questions with a time limit of 7 minutes.

1 Applied computing

b. Percentage

○Production of Product A was 82,060 units last year and 57,350 units this year. What is this year’s production as a percentage of that of last year? (Percentage rounded to one decimal place)

○50,190 yen worth of food are sold at a 15% discount. What's the price with 8% GST? (Minus a GST of less than 1 yen)

c. Least common multiple/greatest common divisor problem

○Pile up the blocks of 21cm thickness and 28cm thickness, respectively. How many centimeters is it the first time the blocks piled up reach the same height?

○There are 175 pencils and 70 ballpoint pens. After dividing pencils and ballpoint pens equally among as many children as possible, with no surplus, how many children can receive?

d. Ratio

○When combining melon juice and soda water at a ratio of 25:38 to make 1,764ml of melon soda, how many milliliters of melon juice are needed?

○There is a rectangular pond with a length-width ratio of 37:15 in the park. When the pond has a length of 925m, how long is its width?

e. Speed

○How many kilometers per hour is equivalent to 47.3m per second? (Kilometers rounded to one decimal place)

○ How many meters per second is equivalent to 525km per hour? (Measured in meters, rounded to one decimal place)

f. Compound interest…… Wider use of addition and multiplication

○What is the total amount of principal and interest of 627,000 yen to be deposited for four years, with an annual interest rate of 3%, compounded annually? The scattered period is calculated using the simple interest method, and the amounts less than 100 yen per period are not subject to interest.

○What is the total amount of principal and interest of 348,000 yen to be deposited for three years and six months, with an annual interest rate of 4%, compounded annually? The scattered period is calculated using the simple interest method, and the amounts less than 100 yen per period are not subject to interest.

g. Area

○What is the area (m^{2}) of a circle with a diameter of 67m? Pi is set to 3.14.

○How much is the area (cm^{2}) of the trapezoid with an upper bottom of 37cm, a lower bottom of 68cm and a height of 49cm?

2 Square root (Rounded to the places shown below)

**(2) Prospect**

In the future, it’s important that we develop a new textbook upon study that uses the abacus as a teaching tool for acquiring number concepts, rather than just using it as a calculation tool. Despite continuous progress in digital development of education, the abacus still has its advantages prominent in many ways. While seeking to upgrade our skills in a shorter time, we should not ignore new methods.

Recent days have seen other problems. Current level examinations are designed based on the fact that students practice in teaching classes five times a week, but many classes now require students to practice about twice a week, so such level examinations are no longer appropriate; a shortage of teachers may occur in the future; and students’ interest and expectation in learning abacus may decline as well.

Abacus has certain advantages that are only known to those who are engaged in abacus education. Therefore, positive publicity is very important, so are the cooperative measures.

**4. Conclusion**

The abacus we use now is an effective teaching tool of perfect shape and material, no exaggeration to say. Since its development about 200 years ago through repeated improvements, its materials, techniques and tools have changed incomparably. We look forward to the “new abacus” in the 22^{nd }century.

References: Society5.0 (Government of Japan)

Citing Literature: Elementary School Syllabus Description (Published in 2017): Arithmetic

(Mr. Okahisa Yasuo is the Vice President of League for Soroban Education of Japan. Inc. This is his speech at the International Academic Seminar on Commemoration of the 20th Anniversary of the Founding of WAAMA (The 7th Abacus and Mental Arithmetic Education Academic Exchange Seminar) on October 28th, 2022)