By Professor Yuan Yue Min, University of Shandong, China
Based on the researches conducted on the practice of the Mental Arithmetic, it has revealed that it is most suitable to be carried out among the children of 4 to 12 years of age.
First of all, this age group belongs to what is often called "the period of enlightenment" and is therefore the best age for cultivating brain functions. A child of about five years begins to develop his hand muscles and this growth continues speedily until eight or nine years of age. By then, the strength has been built up and the agility of the fingers has become flexible, which is just suitable for using the beads. What is more, he could leave his parents to move around freely in his daily life, and have the intellectual skill to practice. The learning of zhusuan involves many organs such as the eyes, hands, mouth and brain, which is most appropriate for this period of cultivating and tapping the functions of the brain.
Furthermore, the education of Mental Arithmetic belongs to the basic knowledge of calculation. During this time, children do not know how to study hard. If they had the education on Mental Arithmetic early in time, not only are they able to avoid the boom of knowledge in which their studies become much harder after the primary school, but also lay a good foundation for the study of other subjects, especially mathematics, physics and chemistry. Therefore, this age group is the best period to impart basic knowledge as well as to cultivate brain functions.
If this period is subdivided, one would find that the children of 5 or 6 years in the kindergarten learn better when they are taught Mental Arithmetic. This is because there is not much studies in the kindergarten, and the teaching could be focused. The teaching time is shortened, and it is not influenced by other studies or other learning. Besides this, unlike older pupils, the children in the kindergarten know nothing of mathematics. To them it is just a piece of white paper in the brain. They have not formed any numerical concept yet, so it is easy to teach them zhusuan, while older pupils are different. Firstly older pupils have to undergo the process from numbers to beads and from beads to mathematical sticks and they have to differentiate between written calculation and zhusuan, and the contrast and adjustment in the calculating methods as well. We have performed an experiment simultaneously in the teaching of Mental Arithmetic between two groups of children - three children in kindergarten, at the age of four and a half, five and a half respectively; and two pupils aged eight and nine. They were taught for an hour every Sunday. It was found that the three children in kindergarten began forming the "image in brain" after three months. As soon as many additions and subtractions concerning two numbers were given to them, they could announce the answers immediately. But the two pupils in the second and third grades took half a year to make it.
Then we come to the reason why it is a good learning method. The education of Mental Arithmetic must start by learning zhusuan and to familiarize them with the abacus. By the repetitive practice of working on the abacus, it will be engraved on their minds naturally. At the end, the abacus cannot be used any more and the children learn to calculate directly by forming an image of the abacus in the brain. The abacus is suitable for the teaching children, because children are curious, and are fond of playing and understanding things directly. As to children who begin to learn, an abacus, as a concrete, objective and vivid calculating tool It is a teaching-learning aid and a toy as well. While they using it, they will find a number appearing when moving a bead, and the number changes when they move it some more. So it becomes a form of game with its pleasure and attraction. As a result, children become very interested in study. At the same time, it is simple and vivid, and children will learn to express and calculate numbers with an abacus.
Beads show numbers and the digits are decided by the rods, and so numbers correspond to digits with a clear arrangement. Subtractions, additions, multiplication, divisions, decimals, algorithm and many other kinds of mathematical calculations become so clear that children are able to remember and learn them easily. What is more, such actions such as listening, looking, reading, hands movement, calculating become as quick as lightning after learning Mental Arithmetic. As so, this training is highly for suitable all aural, visual, mental and physical development of children.
Children are fond of moving about and working with their hands. The education of Mental Arithmetic is different from that of general knowledge courses like Chinese language, geography and history, which are typically conducted with the teacher explaining and the students listening passively. Zhusuan is like learning music and physical education, in which the teachers instruct and students learn by working actively together with the teachers. Under the instruction of teachers, students read and count numbers, or use the abacus, or listen and look at the questions and answer them. Besides this, competitions are organized to find out who could calculate correctly and quickly, to inspire their enthusiasm and initiative for study. During the course of positive and active study, with calculation and thinking, their brain functions would have been cultivated, which makes the children become much more creative and intelligent.