| **Ms. Shizuko Amaiwa** The Ripple Effects and the Future Prospects of Abacus Learning. Professor, Shinshu University, College of EducationJanuary 20, 2001 | **< introduction of the lecturer >** 1) The Development of Piagetian Psychology II : Cognitive-developmental Study. (Piaget Sousho 5), Kokudo-sha (1982). 2) Transfer of subtraction procedures from abacus to paper and pencil computation. The Japanese Journal of Educational Psychology, Vol. 35, No. 1, 41-48 (1987). 3) 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). 4) 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). 5) The effects of abacus learning on solving arithmetic problems : A comparative study of elementary/junior high school students at upper level and inexperienced students. Journal of the Faculty of Education, Shinshu University, No. 96, 145-156. (1999). 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. 1. 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. 2. 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. 3. 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 performance 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.
| | | Dr. Toshio Hayashi, Doctor of Engineering Professor, Osaka Prefecture University Director, Research Institute for Advanced Science and Technology (RIAST) | ### ＜introduction of the lecturer＞ **Brief personal history ** March 18, 1939: Born in Otsu, Shiga prefecture March 1962: Graduated from the Department of Applied Science, College of Engineering, Osaka Prefecture University March 1967: Completed a Master’s Program, Graduate School of Engineering, Kyoto University March 1973: Earned a Doctorate Degree in Engineering, Kyoto University July 1981: Assistant Professor, Kyoto University (Medical Polymer Research Center) April 1994: Professor, Osaka Prefecture University Research Institute April 1995: Professor, Osaka Prefecture University Research Institute for Advanced Science and Technology April 1996 to present: Councilor, Osaka Prefecture University February 2000 to present: Director, Research Institute for Advanced Science and Technology
**Specialty ** Biomaterial Design, Biodegradable Polymer Synthesis, Natural Polymer, Medical Adhesive/Bonding/Stabilizing Enzyme, Environmentally Harmonizing Material Design
**Studying** February 1975 to September 1976, Case Western Reserve University, Ohio, USA, Research in Medical Material
Awards 1987 Japan Fiber Conference Award (Research in Medical Fiber) 1999 Japanese Society for Biomaterials Award (Basics and Application of Biomaterial)
**Qualifications** Hazardous Materials Officer’s Licenses (Class A) Radioactive Isotope Officer’s License (Class I )
**Arrival of and countermeasure for the declining birth rate and aging population ** Our country cannot avoid the present situation of a declining birth rate and aging population. There are many conceivable reasons for the rapid decline in the population of citizens under fourteen years of age. We cannot forget to mention the worsening of the global environment as one of the factors. Computers have predicted that the tendency of a declining birth rate and aging population will continue even further by the year 2020. The number of people who take the abacus official examination is declining. I hope that the abacus education will diversify itself in order to attract a larger range of examinees for the official examination by developing a system in which older people can take the examinations as well. I have studied engineering in college and have done some research in polymer materials. About twenty years ago, I was given an opportunity to conduct research to develop materials for medicine. In our country that had to suddenly accept the aging population, there are many patients who were helped by the drastic development of medical technology and knowledge. National medical expenses are rising, and I worry about the future with this situation. Research for saving patients from terrible diseases and injuries is important, but now the search for healthy living conditions seems more important to me. Public Nursing Care Insurance System is now available, but what is most important is to live a happy, healthy life without having to depend on that system. There is an old saying that worry is often the cause of illness. Recent medical research has shown that various diseases are influenced by how the patients deal with their state of minds. People with active minds maintain their youthful energy longer. What can we do to heighten our brain activity?
**Development of human brain ** What is the structure of our brain like? How does the brain develop? Cerebral physiology has seen great developments. However, there still is much that is unknown about our brain. Our brain is truly amazing. What we know up to this point includes that the human brain is created at an early stage of embryo development and that cerebral nerve cells are already made by the time of birth. Within the brain, the brain stem (all living animals have it, and it controls the functions necessary for survival such as the functions of the heart and internal organs) and the cerebral archicortex (which controls basic instincts such as appetite, sexual desire, sleep, desire to belong to a group, and emotions such as pleasant and unpleasant feelings, fear, anger,etc) are basically completed while in the womb. On the other hand, among animals of higher order, humans have the highly developed cerebral neocortex that can create nerve cells (some say there are 14 billion nerve cells!). This cerebral neocortex does not fully function at the time of birth. In the following years, suitable stimuli start to activate (to connect motor nerves and sensory nerves) the nerve cells in the neocortex. This is why children grow up well in many aspects if they receive appropriate stimuli that develop the nerve cells in the neocortex. The archicortex is more or less completed at the time of birth, but it of course can develop even further after birth. What is important here is that the archicortex requires “to be loved” and is responsible for the cultivation of aesthetic sentiments. Humans cannot live without “being loved”. Only those who grew up being loved can learn to love as they grow older. With the help of a good archicortex, the neocortex will be activated efficiently. Even with hard work, efficiency will not improve without cooperation from the archicortex. In order to activate the nerve cells in the neocortex, information or stimuli from outside the brain have first to be perceived as “pleasant” by the archicortex. This is when the activation of the brain improves and the systems to process information in the neocortex are most efficiently completed. On the other hand, if the information or stimuli are perceived as “unpleasant”, the activation of the brain does not occur and the neocortex is suppressed to grow any further.
**Move the fingers and talk in a loud voice ** What does the activation of the nerve cells in the neocortex mean? Nerve cells in the neocortex consist of 14 billion sets of motor nerves and sensory nerves. These sets create the network (synapses) in which they contact each other and make up a living nervous system. The importance lies in how many sets of nerve cells we can activate in our lives. We can activate the nerve cells by providing “stimuli”. Moving fingers and talking aloud lead to activation by providing appropriate stimuli in the large part of sensory to motor domains in the cerebral neocortex. In this sense, starting abacus learning as young as possible is useful in activating the brains of young children. However, if children learn to use the abacus without wanting to do it, there will be no positive effects. If they come to like learning the abacus and move the beads on the abacus with fun, they will receive benefits from this experience. There is a key in making abacus-learning fun for young children so that they will grow to like it.
**Development of the right brain by the abacus method of mental calculation ** The human brain consists of the right brain and the left brain. The shapes of these two parts are similar, but differences have been gradually found in their functions. The left brain is also referred to as the digital brain. It controls reading and writing, calculation, and logical thinking. The right brain is referred to as the analog brain. It controls three-dimensional sense, creativity, and artistic senses. These two work together to allow us to function as humans. The Japanese are thought to speak Japanese with their left brain, and this allows their left brain to be more efficient. On the other hand, westerners also utilize their right brain to learn their languages, so their right brain is usually more efficient. It is natural that young Japanese students are better at mathematical calculation than students in western countries who are the same age. It is also natural that, because of the better development in their right brain, students in western countries are more creative and original than Japanese students. In recent years, some have argued for the necessity of the Venture Promotion in Japan, but in order to foster this type of environment we need to develop an education system that would train the students’ right brain first. In addition, it is also found that if one trains the right brain, it is less likely to get dementia. Here, I would like to introduce the abacus method of mental calculation. In the abacus method of mental calculation, the learners manipulate abacus beads in their head to carry out a calculation. This had led us to speculate that this operation was effective in training the right brain or the analog brain. Thanks to the development of cerebral physiology and machines that can accurately measure the amount of blood flow in the brain, recent studies have proven that the abacus method of mental calculation is extremely effective in activating the right brain. This validated the speculation we had before. Therefore, I would like to ask all the abacus teachers to teach all learners the abacus method of mental calculation, no matter how briefly it may be. I consider the completion of abacus learning the mastery of the mental calculation.
**Shining brain ** Having grown up to be workers in various work places and providers for their families and contributors to society, many people retire from the forefront of the society and start the second stage of their lives. For these people, it is very important to live ample and healthy lives. In order to achieve this way of living, they have to remember to activate their brain as much as possible. There are many different ways to activate the brain, and one of them is the calculation with the abacus. In the abacus method of calculation, the abacus is not only the best way to exercise fingertips, but also positively influences the right brain to be activated. Although it may take a little more time than for younger people, activation in the cerebral nerve cells certainly does occur even at the age of a hundred. In this case also, they have to come to like the abacus first. Throughout the lifetime there is truth in the saying that you do well at what you like. A “master of life” is a person who has a cooperation of the archicortex and the neocortex throughout their lifetime. To become a “master of life”, we have to always aim high. There is happiness in this process to achieve the goals of our life. We all shine by pursuing our dreams with high hope and something to live for. The higher the goal of our growth, the better our lives are. If the purpose of life is the process to achieve this goal, then I believe that the abacus education can be one of the significant guidelines for life. I would like us all to be “life-long healthy people with abacus”. (This article is the summary of a lecture presented in Nikko Kinugawa, Tochigi, Tochigi prefecture on July 30th, 2000.)
| | | Ms. Kimiko Kawano Researcher, Nippon Medical School, Center for Informatics and Sciences | ### ＜introduction of the lecturer＞ We have been studying brain waves (EEG; electroencephalography) during various kinds of brain activities for more than ten years. In the beginning of the study, subjects were mainly students. We made them listen to music or calculate mathematical problems and than measured their EEGs to investigate the brain activity. After statistically analyzing the data obtained from over two hundred students, we have found the tendency that b waves, which indicate the active area of the brain, appeared on the right hemisphere while listening to music and on the left while calculating. This confirmed the hypothesis that the right brain is used to recognize images, figures and music and the left brain (the linguistic brain) to deal with logical thoughts, such as a calculation. At that time, we were asked from one TV program to measure the brain waves of an abacus champion. I thought, however, it would be difficult to prove some differences in the EEGs which involved quite large individual variances.
**Neural activity in the right brain ** When we measured the champion, a middle school student, during the mental calculation, the result was unexpected. Usually the left temporal region is used for calculation, but here, it was almost entirely unused. Instead, the b waves appeared on the right occipital region. In other words, the student carried out calculation using the right brain. I was not quite convinced from only one person's result, because there are always exceptions and some individual differences in brain waves. However, we conducted the same investigation with another expert only to find the result almost identical to the previous case. We than asked more abacus users with high 'dan' (ranks) to let us measure their EEGs, and found almost the same results with only little individual variances. We inquired how they were calculating, and most of them gave the same reply that the image of the abacus beads in their head moved rapidly.
**Verbal thinking and image processing ** Usually, ordinary people calculate in their mind using inner voice, as in one hundred minus 7 is 93. They put mathematical notions into words. On the other hand, abacus users simply visualize an image of abacus in their head. They do not replace the image into words. This difference can be seen clearly in the EEGs. These tendencies in the brain uses can also be observed in professional players of Shogi, (Japanese chess,) while they are playing the games or solving Shogi problems. However, when they calculate, they use their left brains just as ordinary people do. This is the same with the abacus users. They do not use their right brains in all cases.
Yet it does not mean that abacus learning improves everything about the right brain, such as a sence of art and music. What is important is that the ability to visualize can be put to use for other subjects and behaviors. Some abacus experts use their ability for memorizing whole page of textbook or years in history. The abilily developed by abacas can be used effectively in different ways. Not only for the experts but also for the beginners, abacus learning is useful to easily grasp images in addition and subtraction problems, because the beads are moving in front of their eyes. It also allows to understand the decimal system and the concept of digit positions. Once children understand numbers, they will probably become fond of mathematics. They will be more confident there may be many positive impacts in other subjects at school. The contemporary education focuses on theory and its rote memorization. Theory of course is important but many students cannot get an actual feeling of comprehension only through it. I believe an effective application of image thinking induces human creativity and inspiration. |