One-hand method and Two-hand Method: A Comparison

 

Preface:

 

In abacus and mental arithmetic, there are two principal methodologies: the two-hand method that is used mainly in China, and the one-hand method that is favored by Japan, Taiwan, and Korea. The two methods currently co-exist, and both can be found in many countries. Whichever method a country adopts mostly depends on its cultural and geographical history. Usually, people prefer the method that they are exposed to first.

 

Three decades ago, immigrants brought abacus and mental arithmetic to many countries. Back then, most teachers used the one-hand method and introduced it to Malaysia, Singapore, Thailand, Hong Kong, United States, Canada, Brazil, Australia, and more. In the last ten years or so, China, with its economic rise, also introduced the two-hand method to many other countries, including Russia, Kazakhstan, South Africa, Uzbekistan, Turkey, Morocco, Iran, Saudi Arabia, United Arab Emirates, Jordan, Lebanon etc.

 

With more countries practicing abacus and mental arithmetic, international organizations started to appear. The objective of an abacus and mental arithmetic organization is mainly to coordinate international competition and exam and provide training to instructors if needed. Many teachers have the same questions when they first come to the training session. Which method is better? What are their differences? Do they have different emotional effects on students? Do they share the same curriculum and materials? Is there any difference in learning results? Surprisingly, a simple tool like abacus can present so many variations because there are two different methods, which makes this a worthy topic for discussion.

 

I would like to outline the differences between these two fundamental methods of abacus from my own experience as a teacher. Hopefully, this will help the teachers improving their skills by giving them more insights and new ideas.

 

 

1. The origin of one-hand and two-hand methods

Abacus is a Chinese invention, and it was deemed an intangible cultural heritage by UNESCO in 2013. Abacus was able to stand the test of time, even as new technology emerges, proving its significance in human intellectual development. Before calculators and computers, the abacus is an essential tool in commerce. People rely on it to crunch numbers in trade. Abacus was designed for adults at this time. Therefore, the early Chinese abacuses were made of bigger beads in a "two-on-top, five-on-bottom "configuration. Abacus Association of China was founded in 1980. The two-hand method and "one-clear multiplication and division" were its focus, and the organizations promoted the techniques heavily in all provinces within China. After 40 years, the two-hand method is still the curriculum basis of AAC. The only change it made was moving to a 1-4 abacus configuration.

 

Although abacus originated in China, 1-4 abacus was a Japanese innovation. Taiwan and Korea very likely imported the one-hand abacus system from Japan initially. Taiwan and Korea were both once under Japan's rule for over 50 and 30 years, respectively. 1-4 abacus has smaller, diamond-shaped beads, making it easier for young children to operate. The distance between each column is also shorter, making it ideal for one-hand use.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. Features of Two-hand Method

Abacus Association of China stresses that using two hands to operate abacus serves two main functions: increased speed over the one-hand operation and stimulating both brain hemispheres for balanced development. They released several essays to support the claims. From an academic stand of view, I fully support the points. However, they do not always apply in the classroom. When using the two-hand method, the left hand is responsible for carrying or borrowing. The right hand is mainly accountable for manipulating the beads. Using both hands at the same time can improve hand-brain coordination.

 

Advantages:

  1. The two-hand method has the speed and capacity advantage over a one-hand method in carrying and burrowing.

  2. Students have better concentration when they are using both hands. They are less likely to be distracted, enhancing the learning results.

  3. Students can start by learning two-digit calculations. Usually, it takes at least six months to finish learning all the basic formulae. If students practice correctly and adequately, they will establish a good foundation in the abacus rules. In other words, they will start to have an abacus image in their head, putting them in a good position for mental arithmetic.

  4. If students have a good learning attitude at the very beginning of training with the two-hand method, they will have good concentration and a good foundation.

  5. The two-hand method stimulates both brain hemispheres, which enhances their logic, reasoning, and creativity.

 

​Discussion:

  1. Many schools lower the admission age of students to three years old only to seek financial gains. The finger muscles of young children are not fully developed yet. Whether they are ready for subtle motor movements like writing and doing abacus or whether they understand the concept of numbers and values are not guaranteed. Children of this age are active explorers and are very distracted. Usually, they do not have enough focus and patience to sit through a long session and finish homework at home. Sometimes, children are only doing what they think to please their parents. If parents push them too hard, it can affect their creativity and independent thinking. If students do not oppose to coming to class and have good results, everything might work out fine. Otherwise, students might grow wary of learning for a very long time. Regardless of the method, do not accept students who are too young. The two-hand method is more complicated than the one-hand method. If you are to allow students under six years old, start with 9-bead abacus or 1-4 abacus. These two options have lower initial difficulty. With the two-hand method, only students who are at least six years old are recommended. Do not worry about losing students to other schools. Building a good reputation is the best advertisement.

  2. Abacus and mental arithmetic are an intensive mental exercise. Students are now exposed to a variety of activities and lessons. Most of them have fun and attractive materials, tools, or exercises. Abacus is a comparatively simple tool. Students come to the class every week and complete the same practices. They have to finish homework at home. All of these are significant challenges for student's patience. Students need at least six months to complete all the two-digit formulae using a two-hand method. During these six months, students need to learn six sets of formulae and calculate with proficiency. They can only do this by spending ample time practicing. I once had a seven-year-old student who sighed and told me, "Abacus class is so boring." This harmless remark from a young student prompted many years of self-reflection. I came to the conclusion that the most important thing is to create a sustainable and fun classroom setting and not on scores or results, which only serves the purpose of boosting teacher's evaluation or performance. In the first six months of two-hand method instruction, the teachers should take both the instruction quality and student emotions into account. Diversify the activities and tools to make coming to class more fun is the better way to achieve good learning results ultimately. Otherwise, students might lose interest in this early stage. I suggest adding mental arithmetic with listening and reading to practice formulae that students already know. Teachers can use tablets or computers for these exercises. Students can also start memorizing the multiplication table.

  3. A good sitting posture is essential. Sit firmly in the chair. Place both hands on the table when doing a calculation. Keep the eyes on the fingers. We often see students in videos or competitions who stand in their seats and wave their hands around when they calculate. Regardless of how well they perform, these behaviors are already in violation of the rules. First, they are disturbing other students. Second, standing allows them to peek at the answers of other students and cheat potentially. Standing did not leverage the advantages of the two-hand method. Students learn nothing from the two-hand method by standing and they are also severely slower and less accurate. Furthermore, it does not inherit the true values of abacus and mental arithmetic, which are the states of extreme focus.

My thoughts and evaluations of two-hand method:

  1. The two-hands method is suitable for older or smarter students. If students come to the class twice a week, spending one hour each class on addition and subtraction is the best arrangement.  If students only come to the class once a week, they might spend more time on addition and subtraction since there are many intricacies in two-digit formulae.

  2. In the two-hand method, usually, the left-hand goes before or at the same time with the right hand. Some teachers teach students to do the reverse, most often in 10's complement formulae. For example, +1 = -9 +10 is changed to +1=+10-9. In another example, -1 = -10+9 is changed to -1=+9-10. Although these changes do not the answers, they are against mathematical principles.

  3. The two-hand method brings students very quickly to two-digit questions. Some students will find them challenging, mainly because students are not proficient with one-digit calculations yet. Also, the fact that abacus calculation starts from higher places different from mathematics taught in school contributes to the difficulty.

  4. Using the two-hand method, we need to position the abacus either on the top or bottom of the page. Students are not moving the abacus along with the numbers they are working on, making it easier to omit or repeat a calculation.

  5. Since there are more variety of carrying or borrowing with two-hand method, students need to spend more time learning each formula. The good thing about is that students will have a better mental image and make less mistake. The downside is that some teachers lack the experience and do not know how to manage class time and student reactions, making the lesson boring and student losing interest.

  6. Whether doing abacus or mental arithmetic, the sitting posture and the calculating finger movement will all affect learning results. Always remind students to sit straight.

  7. There is no need to overemphasize the benefit of utilizing both hemispheres of brains. One-hand method has the same benefit once students progress to mental arithmetic. Many other activities offer the same benefits, such as playing sports, chess, solving Rubik's cubes, playing game consoles. Consider student's ages, interests, comprehension, frequency of the class, and learning results.

 

3. Features of one-hand method

Abacus was brought into Japan and Korea during the Ming Dynasty over 500 years ago. Initially, 1-5 abacus configuration was used, but it was soon replaced by 1-4 abacus, which persisted to this day. In the early days, multiplication was solved by the "compartment method" and "tail-to- first method." Today, "head-to-head" method is the preferred option. Division was explained by "formulae division" and now by "quotient division method." In the last decade, some abacus schools in Japan switched to the "tail-to-tail" method to incorporate the technique in regular schools. Historically, the one-hand method has remained relatively untouched. Only the calculation method and the finger had small adjustments. Since most humans are right-hand dominant, most people use the right hand to manipulate the abacus and left hand to hold it. Abacus was only a calculator, so there was no need to pursue speed.

Advantages:

  1. The one-hand method requires only the thumb and index finger on the right hand. It has simpler rules, and it is easier for students to learn. Holding abacus with the left hand ensures correct posture, which is suitable for learning.

  2. The one-hand method usually starts with a one-digit calculation, making it easier for younger students. There are six sets of formulae. The first four sets of formulae include 5's complement addition and subtraction, and 10's complement addition and subtraction. It is recommended that students memorize these formulae at home before the class, so they can quickly learn the finger rules in class. Not only will this accelerate the learning progress, but it can also prevent students from developing repeated mistakes. There is no need to memorize the last two sets of formulae. They can be learned through demonstration for the best results.

  3. Because the one-hand method has fewer rules for one-digit calculation, students can advance to mental multiplication and division with listening quicker. They can even begin two-digit addition and subtraction, multiplication and division earlier. Hence, there are more variables to the curriculum, making it more exciting for young students.

  4. Abacus is deeply rooted in Asia for hundreds of years. Asian parents are usually willing to cooperate with the demands of the class. In other countries, parents might not want to see their children spend more time doing extra assignments outside of school. The one-hand method should be more fitting for these students. It is easier to learn. It has a distinguished level system, and parents can see the learning results in the short term, putting less pressure on them and the students.

 

Discussion:

  1. The one-hand method begins with one-digit calculation (for older or smarter students, they can also start with two-digit calculation instead). Students can learn the formulae much quicker because there is only one digit to work with. If students do not practice enough, or they are not familiar with the formulae, it will be common for them to develop repeated mistakes. Younger students can avoid developing repeated mistakes by memorizing the formulae well.

  2. The two most important topics for teachers are eliminating the repeated mistakes (and not just correcting wrong answers) and the right timing to start mental arithmetic. I suggest giving students a simple test after the complete the first four sets of one-digit formulae. The test consists of 30 one-digit, four rows questions. Give students 10 minutes. If they can complete all the questions with at least 80% accuracy, they are ready to learn mental arithmetic with listening. Skip the fifth and sixth sets of formulae and go directly to two-digit simple addition and subtraction. After completing the first four sets of two-digit formulae, give students another test. This test consists of 30 two-digit questions with a time limit of 10 minutes. If they can finish all the questions with 80% accuracy, they can begin mental arithmetic with viewing. Then they can learn the fifth and sixth sets of formulae for one-digit and two-digit calculations. Since most repeated mistakes are related to mixed addition and subtraction, memorizing the first four sets of formulae and postponing learning mixed formulae will reduce these mistakes.

  3. Abacus's configuration is designed to accommodate the decimal system. The further on the left you go on the abacus will give you a bigger number. The new on the right you go will provide you with a smaller number. Abacus is designed for right-handed people. Some teachers think both hands are interchangeable, and students can decide on their own. There are a few considerations to be made here:

  1. The formulae in the one-hand method corresponds to the right-hand movement from left to right. The movements using the left hand are opposite of the formulae.

  2. Holding the pen or pencil with the right hand will keep the force centralized in the palm. Holding the pen or pencil with the left hand will disperse the divide of the force between the fingers. What if students both hold the pen and calculate using the left hand? Since the calculation depends on the formulae, using the left hand still contradict the formulae.

  3. Using the left hand in the early stage is still feasible. However, once there are more digits, students will find it increasingly difficult to solve the questions, and they will become slower. This most likely happens when they advance to 4-digit addition and subtraction on the abacus, 6-digit multiplication, or 5-digit division onward.

  4. If the students only plan to learn abacus and mental arithmetic for no more than three years. Then the issue of using the left or right hand does not matter.

 

My thoughts and evaluations of one-hand method:

 

  1. The one-hand method is suitable for beginning students aged around 5 to 6. If students come to the class for one hour twice a week, it is best to spend the first six months on abacus addition and subtraction. If students only come to the class once a week, they can have a slower curriculum but more flexibility as long as they have enough practice.

  2. There are many subjects under abacus and mental arithmetic. It is not easy for young students to comprehend everything. It is important for teachers to prepare and train themselves. Use simple language in the class. Try to introduce stories and characters to explain the concepts. Students will find learning more fun and memorable. When practicing mental arithmetic, ask students to use the correct finger movements legitimately. If they do not do the movements correctly, it is easy for them to think or guess the answers.

  3. Many companies write their own books. This is commendable. However, there are many rules that require professional knowledge throughout all the levels. A random number generator cannot do the job. I suggest giving your books to experts for review. I do not recommend writing higher-level books. In addition, organizing and using the correct practice papers in the class is an important skill for the teachers, for example, the ability to organize the one-digit and two-digit addition and subtraction papers by their units and difficulties. Teachers will then completely understand the order of the curriculum and manage the class efficiently.

  4. Calculating using the one-hand method will be slower than the two-hand method in the early stage. The difference in speed will gradually disappear once students get to a higher level, especially in mental arithmetic, where high-level contestants complete all the calculations in their heads without the constrains of finger movements. Some one-hand method teachers also teach students to use the left hand for assistance in the calculation. For example, in the division, place the question on the abacus and subtraction with the right hand. If students are not using an abacus with a reset button, use left hands to clear the abacus and write the answer with the right hand. These are great time-saving techniques.

 

 

Conclusion

 

In the early days of calculators, the abacus was still a tool relied in all professions. Government departments, banks, companies still use abacus for their daily operations. People who learn abacus are usually post-secondary students. Abacus was used primarily independently. Mental arithmetic was only had a supplementary role. In 1975, a company called "Chinese Mental Arithmetic "started the trend of young students learning abacus. This unstoppable trend reached all corners of Taiwan. Seventy percent of children aged six years or above have gone to an abacus class. Mental arithmetic rose from backseat to the frontstage. A practical tool became an educational weapon that cultivate intelligence. Abacus education reached an unimaginable level. Forty years later, its impacts are still felt around the world, even becoming more recognizable. In the early days, China used the term “abacus brain arithmetic” and Japan used the term “blind abacus arithmetic”.

 

Later, the abacus and Mental Arithmetic Association brought its two-hand method and one-clear technique to other countries, making another huge wave internationally. The speed of mental arithmetic reached unfathomable height, almost comparable to a computer. One-clear technique is a generational invention that pushes abacus and mental arithmetic to the top. We urge young and capable students to keep improving and strive for constant improvement. Not everyone will be interested in this challenge, but, for those willing, this is a worthy goal.

 

The purpose of this article is to compare the differences of one-hand and two-hand method, as opposed to picking a better method. As written previously, the choice comes down to the objects and purposes of individual students. Each profession has its limits and its values. It all depends on the people. Running is a good exercise and an important competition. In 1936, humans first broke the ten-second barrier of 100 meters dash. Scientists theorized that it was the limits of the human body. However, today the record has been pushed to 9.58 seconds after decades of hard work. When you are running, are you only exercising or training for the record?

 

I think learning abacus is the same in this regard.

SAMA Founder and Chairman of Taiwan, David Liao

Taipei City, Taiwan

©2017 BY SAMAGLOBAL.