# ABACUS - travel from Calculation to MENTAL ARITHMETIC

Studies reveal that only in 1980’s, Abacus Mental Arithmetic caught people's attention. In this century, Abacus workers realized that the direction for Abacus is abacus and mental arithmetic. In the preface of General Dictionary of World Abacus written in 1994, it was said, "It created a new way for simple abacus to develop abacus/ mental arithmetic. "In the last century, abacus remained the core; but in the new century by image of abacus mental arithmetic is the key. Abacus is only a model for development of abacus and mental arithmetic. Therefore, this period can be called the period of “ by image of Abacus Mental Arithmetic”.

It is an inevitable result for abacus historical development to enter the period of abacus and mental arithmetic. Abacus has shown two functions in the history .One is to calculate and the other is to develop intelligence. Because its calculating speed is faster than ancient counter-calculation, abacus has taken place of counter-calculation. In the past, abacus functioned as a calculating instrument, but in the present electronic era, this function of abacus plays in a minor position. If its function of calculation is preserved without further development, abacus will be weeded out by history as counter-calculation. Then, what is the way out? The way out is to develop its function of tapping intelligence. By doing so, we can train out new talents

of high intelligence. Abacus, as a model of abacus and mental arithmetic, itself has some exclusive advantages unavailable to many other calculating instruments. Compared with other calculation instruments, abacus is prone to develop into mental arithmetic:

1. Compared with written arithmetic: Written arithmetic features changes of abstract symbols and is difficult to be reflected in people's mind, whereas abacus features changes of practical symbols and it is easy for people to conduct image thinking. The former is a fixed code, leading to manifold calculation, onerous memory task and assiduous brain burden. Abacus is a variable code. Results can be got in a change of original code without any code reset. The less storage of memory task is convenient for mental arithmetic.

2. Compared with the other 12 calculation instruments that have been eliminated. The most fundamental advantage of abacus is high speed of changes and number recognition. Because of its own method that the number 5 is expressed with all the 5 sliders down, counter -calculation is slower than abacus on number recognition and operations. The other calculating instruments are not collective and bear no numerical value themselves, which is shown by their positions and colors. Due to difficult number recognition, they have a much lower speed, which naturally bring

about a lower speed of mental arithmetic.

3. Compared with the computer: The computer operations proceed inside, with changes of electronic units. It cannot be modeled by human's brain so computer calculation cannot develop into mental arithmetic. Therefore, in accordance with the development history of calculation instruments, abacus is the right one for mental arithmetic. The 3 -arithmetic combinations in the last period has promoted the development of mental arithmetic by image of abacus. But at present, written arithmetic is still learned in primary schools. How to promote combination of by image of abacus and written arithmetic is a new task in our educational research. Abacus and written arithmetic should not be separated from each other and written arithmetic should not go back to its old way just because we develop mental arithmetic by image of abacus. In short, mental arithmetic by image of abacus is the result of historical development. There are many research tasks in front of us, which are the new tasks for our mental arithmetic by image of abacus workers. I believe abacus and mental arithmetic has a very bright prospect.//Basheer Ahamed, Indian Abacus

(The author is Vice President of Chinese Zhusuan Association, a professor in Mathematics and Science History Research Center in Northwest University.)