Ms. Shizuko Amaiwa
Professor, Shinshu University, College of Education
January 20, 2001
I have been engaged in research concerning the abacus for many years from the perspective of a psychologist. My research findings show that abacus study not only improves the ability to calculate both on the abacus and mentally, but also provides a beneficial ripple effect on other disciplines. This paper will explain what ancillary disciplines are influenced and the reasons for it. I will also discuss the characteristics of and future prospects for abacus learning.
The first effect is improvement of numerical memory. The second is improvement of memory in spatial arrangement. The third is progress in solving general mathematical problems taught in elementary school, including the four fundamental arithmetic calculations and word problems.
The first effect, the improvement of numerical memory, can be demonstrated by asking students to remember three- to nine-digit numbers read aloud and to recite the memorized items orally. Abacus students are found to be superior in the accuracy of their memory and the number of digits they are able to memorize when compared with non-abacus learners of the same age. This is because abacus students place numbers on the abacus image in their head as they mentally calculate with the abacus method. The retention of the numbers is certain if the number of digits does not exceed the limit of the mental image of the abacus. Utilization of the abacus image enables students even to recite the memorized numbers backwards. This is possible because of the application of the procedures used in the abacus method of mental calculation to solving the memorization assignment.
The second beneficial effect is the improvement in memory of spatial arrangement. This was examined by assigning students to remove the location of several small black dot. These dots were placed on different intersection point of squares made with 3 to 5 lines in both vertical and horizontal directions. The students first looked at these dots for a few seconds to memorize their location, then they were asked to recreate the same picture by placing black dots on blank squares. As a result, abacus learners were found to score higher than non-abacus learners. The spatial arrangement of the dots does not have the same numerical values as beads on the abacus board. However, we can speculate that the training to obtain the abacus image visually had the effect of making students sensitive to spatial arrangement.
The following three points are confirmed in terms of the effects of abacus study on progress in solving mathematical problems.
To acquire the ability to calculate rapidly and accurately and to calculate mentally
Based on the results mentioned above, some advantages and characteristics of abacus learning are revealed. One of the advantages of abacus study is that learners can calculate simple mathematical problems rapidly and accurately. In addition, they acquire the ability of do mental calculation utilizing the abacus image, which allows quick calculation without actually using the abacus.
These characteristics show positive ripple effects on the solution of various mathematical problems. On the other hand, the learners' calculation methods become fixed, and the students tend to lack flexibility in thinking out innovative ways to solve problems. It goes without saying that spending time on thinking out new ways to solve problems (such as thinking about the meaning of the calculation, or coming up with other ways to solve the problem) can be negative in terms of the amount of time needed to solve problems when the primary goal is rapid and accurate calculation. Since abacus training consists of accurate erformance of simple procedures, there is no reason to change the method of traditional abacus education. However, I believe that some measures must be taken to keep the learners from being bored, since repetition of simple procedures is often accompanied by boredom.
I am currently considering adapting the principles of the abacus to computer software that teaches the concepts of digit position (meaning of zeros in numbers) to mentally challenged children. I have been trying to teach numbers and simple calculations to these children. They have great difficulty in understanding the concept of digit position, even though they could read and write numbers and do addition and subtraction of one-to two-digit numbers. In order to make learning fun, I have used an activity in which children carry a certain amount of money and go to their favorite store to buy something they like. However, the distinction between 13 yen and 130 yen was hard for them to grasp. I think the following reasoning could be used to provide a more easily comprehended explanation of the concept for them. On the abacus board, there can only be up to 9 in the units position. If 1 is added to 9, there will be a number in the 10s position and nothing, or zero, in the units column.
At the beginning of this, new century, I hope to expand the abacus education and give it new applications while, valuing its history.