22. An Overview 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 point. 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.
(a) The two-hand method has the speed and capacity advantage over a one-hand method in carrying and burrowing.
(b) Students have better concentration when they are using both hands. They are less likely to be distracted, enhancing the learning results.
(c) 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.
(d) 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.
(e) The two-hand method stimulates both brain hemispheres, which enhances their logic, reasoning, and creativity.
(a) 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. 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.
(b) 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.
(c) 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:
(a) 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.
(b) 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.
(c) 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.
(d) 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.
(e) 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.
(f) 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.
(g) 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.