# Ms. Shizuko Amaiwa

# The Ripple Effects and the Future Prospects of Abacus Learning

Ms. Shizuko Amaiwa

Professor, Shinshu University, College of Education

January 20, 2001

## Introduction of the Lecturer

- The Development of Piagetian Psychology II : Cognitive-developmental Study. (Piaget Sousho 5), Kokudo-sha (1982).
- Transfer of subtraction procedures from abacus to paper and pencil computation.The Japanese Journal of Educational Psychology Vol. 35, No. 1, 41-48 (1987).
- Effects of abacus learning on 3rd-graders’ performance in paper-and-pencil tests of calculation.Japanese Psychological Research Vol. 31, No. 4, 161-168 (1989) (Joint work).
- A continued instruction on number and calculation for handicapped-class students : A study of Improving methods of Instruction.Journal of the Faculty of Education, Shinshu University, No. 94, 95-105. (1998).

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 Ripple Effects of 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 improvement of numerical memory

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.

## High marks due to improvement in memory of spatial arrangement

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.

## Progress in solving general mathematical problems

The following three points are confirmed in terms of the effects of abacus study on progress in solving mathematical problems.

- Findings from an investigation with third grade students show that about a year of study at an abacus school enabled the learners to score higher than non-abacus learners on certain mathematical problems. These mathematical problems include addition of one-digit numbers, multiplication of one-digit numbers, addition of multi-digit numbers, subtraction of multi-digit numbers, word problems in addition and subtraction, and fill-in-the-blank problems (e.g. providing the missing items in the following equation: [ ]－7=27). However, no difference was found in problems where conceptual thinking was required, such one in which students were asked to figure out the digit positions (i.e. to decide if the following two items are the same: {nine 10s + nine 1s} and {eight 10s + ten 1s}). Even beginning abacus learners can be said to benefit from the ripple effect in solving mathematical problems, except for those involving conceptual understanding.According to the statistical analysis, the addition of one-digit numbers was affected most directly by abacus study. Accurate and rapid calculation of one-digit numbers was found to lead to better marks in multi-digit mathematical calculation, which further led to better marks on word problems and fill-in-the-blank problems. We can speculate that students had more time to think about the problems, and therefore scored higher on the assignment because they needed less time to work out simple calculations as a result of their abacus background.
- On the higher level, advanced abacus learners were found to have received even more desirable effects in solving certain types of mathematical problems compared to non-abacus learners. These problems include the comparison of the size of the numbers (i.e. put the following five numbers in order: 0.42, 12, 3.73, 0.95, 10.1), the calculation of numbers with multiple choices of proposed answers (i.e. choose the correct answer from five choices of proposed answers for 1026.95 ÷ 103.1), and word problems. In addition, a positive effect was seen, not only in mathematical problems with integers and decimals, but also in those with fractions, especially when higher level thinking is required to solve them.In the abacus training, there are no fractions involved, but the ripple effect even affected problem solving in fractions. The abacus students were found to have transformed the fractions into decimals, in order to solve problems with fractions. They tried solving the problems by changing the numbers into the form they understood best.
- As mentioned above, abacus learners tend to solve problems in a form in which they can utilize their knowledge of abacus calculation when confronted with various mathematical problems. This tendency was shown when abacus students were given problems of computational estimation (such as an assignment where students were to pick the figure in the largest digit position of the answer). In solving these problems, many abacus learners first calculated the whole problem then picked the figure of the largest digit position in the

The Ripple Effects and the Future Prospects of Abacus LearningMs. Shizuko AmaiwaProfessor, Shinshu University, College of EducationJanuary 20, 2001

## Introduction of the Lecturer

- The Development of Piagetian Psychology II : Cognitive-developmental Study. (Piaget Sousho 5), Kokudo-sha (1982).
- Transfer of subtraction procedures from abacus to paper and pencil computation.The Japanese Journal of Educational Psychology Vol. 35, No. 1, 41-48 (1987).
- Effects of abacus learning on 3rd-graders’ performance in paper-and-pencil tests of calculation.Japanese Psychological Research Vol. 31, No. 4, 161-168 (1989) (Joint work).
- A continued instruction on number and calculation for handicapped-class students : A study of Improving methods of Instruction.Journal of the Faculty of Education, Shinshu University, No. 94, 95-105. (1998).

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 Ripple Effects of 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 improvement of numerical memory

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.

## High marks due to improvement in memory of spatial arrangement

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.

## Progress in solving general mathematical problems

The following three points are confirmed in terms of the effects of abacus study on progress in solving mathematical problems.

- Findings from an investigation with third grade students show that about a year of study at an abacus school enabled the learners to score higher than non-abacus learners on certain mathematical problems. These mathematical problems include addition of one-digit numbers, multiplication of one-digit numbers, addition of multi-digit numbers, subtraction of multi-digit numbers, word problems in addition and subtraction, and fill-in-the-blank problems (e.g. providing the missing items in the following equation: [ ]－7=27). However, no difference was found in problems where conceptual thinking was required, such one in which students were asked to figure out the digit positions (i.e. to decide if the following two items are the same: {nine 10s + nine 1s} and {eight 10s + ten 1s}). Even beginning abacus learners can be said to benefit from the ripple effect in solving mathematical problems, except for those involving conceptual understanding.According to the statistical analysis, the addition of one-digit numbers was affected most directly by abacus study. Accurate and rapid calculation of one-digit numbers was found to lead to better marks in multi-digit mathematical calculation, which further led to better marks on word problems and fill-in-the-blank problems. We can speculate that students had more time to think about the problems, and therefore scored higher on the assignment because they needed less time to work out simple calculations as a result of their abacus background.
- On the higher level, advanced abacus learners were found to have received even more desirable effects in solving certain types of mathematical problems compared to non-abacus learners. These problems include the comparison of the size of the numbers (i.e. put the following five numbers in order: 0.42, 12, 3.73, 0.95, 10.1), the calculation of numbers with multiple choices of proposed answers (i.e. choose the correct answer from five choices of proposed answers for 1026.95 ÷ 103.1), and word problems. In addition, a positive effect was seen, not only in mathematical problems with integers and decimals, but also in those with fractions, especially when higher level thinking is required to solve them.In the abacus training, there are no fractions involved, but the ripple effect even affected problem solving in fractions. The abacus students were found to have transformed the fractions into decimals, in order to solve problems with fractions. They tried solving the problems by changing the numbers into the form they understood best.
- As mentioned above, abacus learners tend to solve problems in a form in which they can utilize their knowledge of abacus calculation when confronted with various mathematical problems. This tendency was shown when abacus students were given problems of computational estimation (such as an assignment where students were to pick the figure in the largest digit position of the answer). In solving these problems, many abacus learners first calculated the whole problem then picked the figure of the largest digit position in the answer.

## Merits of abacus study

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.

## At the beginning of the new century

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.