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.

(1) 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:

(a) 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.

(b) 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.

(c) 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.

(d) 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:

(a) 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.

(b) 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.

My thoughts and evaluations of one-hand method:

(a) 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 if they have enough practice.

(b) 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.

(c) 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.

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.

## Comments