The main purpose of learning abacus is to lay the groundwork for mental arithmetic. The difference between mental arithmetic and school math is that mental arithmetic calculation does not start at ones and carry to higher places. It is also different from finger-counting where the fingers are used to represent the numbers.
Students with good mental arithmetic ability, whether when they calculate addition & subtraction, multiplication, or division, always start from the highest place. Some students can do two digits or even three digits at a time in addition & subtraction. If students have enough training and correct techniques, they will have no problem doing multi-digit calculation in all categories. When learning mental arithmetic, students learn mental with listening and then mental with reading in order to build better fundamental skills.
Mental arithmetic with listening refers to the exercise in which teacher read out the numbers to the students. Students do not use abacus. They use the phantom abacus in the brain to complete the calculation. Once the image becomes clearer after some time, they can move into mental arithmetic with reading (students will not use abacus in this exercise) in all subjects.
Mental arithmetic with reading refers to the exercise where student completes mental arithmetic without using abacus while reading the numbers off papers or books. Both exercises include addition & subtraction, multiplication, and division variations. This is an important part of mental arithmetic training.