#### Abacus And Mental Arithmetic

*2016-09-26*

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### Abacus - Activating the Right Brain

Abacus is a method of mental calculation. Performed on a virtual image of the abacus formed in the mind, it is based on the principles of abacus calculation.

In this case, the abacus is merely a tool, through regular practice of which children are able to visualize and internalize the image of the abacus in their mind.

How fast can it be?

By activating both sides of the brain, all students can achieve calculation speeds that were previously only achievable by math geniuses.

As a matter of fact, in Dec. 2000, a first-year student and his 2 sisters broke 4 Guinness world records with this very same method of calculation.

How can it benefit my children?

Image Abacus trains the students to use the left hemispheres (logical side) to manipulate the virtual abacus (image) on the right hemispheres (abstract side). This unique exercise fosters and strengthens the brain function and can improve the following areas:

- Confidence in calculation.
- Mental calculation, which is the ultimate resource.
- Sense of achievement as one's proficiency improves.
- Tremendious development of the right brain
- Greater mental capacity.
- Intuitive thinking.
- Problem solving capability.
- Enhances creativity.
- Memory capacity.
- Concentration and mental endurance.

In short, image abacus training will help any child to retain knowledge more effectively and become more proficient in any subject, especially math.

Abacus is a method of mental calculation. Performed on a virtual image of the abacus formed in the mind, it is based on the principles of abacus calculation.

In this case, the abacus is merely a tool, through regular practice of which children are able to visualize and internalize the image of the abacus in their mind.

How fast can it be?

By activating both sides of the brain, all students can achieve calculation speeds that were previously only achievable by math geniuses.

As a matter of fact, in Dec. 2000, a first-year student and his 2 sisters broke 4 Guinness world records with this very same method of calculation.

How can it benefit my children?

Image Abacus trains the students to use the left hemispheres (logical side) to manipulate the virtual abacus (image) on the right hemispheres (abstract side). This unique exercise fosters and strengthens the brain function and can improve the following areas:

Confidence in calculation.

- Mental calculation, which is the ultimate resource.
- Sense of achievement as one's proficiency improves.
- Tremendious development of the right brain
- Greater mental capacity.
- Intuitive thinking.
- Problem solving capability.
- Enhances creativity.
- Memory capacity.
- Concentration and mental endurance.

In short, image abacus training will help any child to retain knowledge more effectively and become more proficient in any subject, especially math.

### Introduction to Abacus

### What is an ABACUS?

before the invention of a calculator it would have been really difficult to do sums for archeology, experiments or for mere business purposes. In the earlier days a man’s hands and the pebbles used to be the counting device and there were no numerals. It was in this context that the abacus and the counting tables were born. The abacus is the olden form of our calculator, its origins dates back to 2400 BC when the Babylonians used pebbles and dust abacus for their calculations. The abacus and the counting boards were the aids which were used to ease the calculations. In no way it can be compared with the calculators that we use today. While using these aids the person is actually doing the calculation on his mind, the abacus is only helping him keep a track of his calculations; which make the mental calculations much easier.

### Abacus Origin

The origin of counter abacus with strings is however unknown but it was used in India, Mesopotamia and Egypt. Later China played an essential role in the development and evolution of abacus. The most popular abacuses are the roman abacus and the Chinese abacus suan pan.

### Abacus Teaching

Before the electronic calculators have hit the common people, the abacus was used as a teaching aid and comprehensive guide to computing for the beginners. Even today it is a fantasy toy and playing with it is an insight in to the earlier horizons of science. Many of the school projects and assignments are now focused on the construction and development of the abacus.

### Maxmind In Abacus Education

Maxmind is a mental development program which starts with use of an abacus & then child learns to do calculations mentally without physical abacus. This training enhances child's ability to calculate without aid of any instrument such as the calculator, abacus etc. The children calculate with speed & accuracy using mental power & surpass the speed of a calculator.

The finely structured syllabus is prepared by Maxmind curriculum development department. Children who undergo Maxmind arithmetic training would have several positive benefits like:

- Greater concentration
- Keen Listening skills
- Better reflexes
- Better application skills
- Better Memory
- Sharper observation
- Self confidence
- Better expression
- Better comprehension and calculation skills
- Improved reading writing and learning skills
- Improved analytical, Creative & imaginative skills

This ability relies entirely on one's mental processing skills. The program aims at stimulating the children?s right & left brain, making the whole thinking process mode efficient & effective to produce complete and confident personalities who achieve extraordinary levels in various disciplines

### Wont this create more burden on the child?

There is no extra burden on the child during the training through Maxmind but due to the fact that the brain gets developed and hence the regular studies also become easier. In fact Maxmind is a complete brain development center where child gets knowledge combined with fun & play. The whole training program is easy and burden less. The child should start taking interest themselves which is primary motive of any Maxmind center. Maxmind center presents a friendly and good atmosphere, which motivates the child to come to our center.

### Abacus in Various Cultures

The word abacus is not new to anyone. It is the most ancient tool and the wondrous thing about this is that it is still used in different parts of the world, still fits in this fast world and satisfies the requirements of the world. Abacus was invented centuries ago and till then it is widely used in different aspects of the life. Many civilizations have used it from the day it was invented and each civilization that has used it has left some mark on its face and has given it some identity. The exact date of the invention of abacus is not agreed upon by all of the historians but it is said that the first ever abacus came onto scene at about 5000 b.c.

At that time the abacus was not like the one we see today rather it was a flat hard surface either of wood or stone on which sand was spread and stick or finger was used to write letters on it.

When the calculation was done the surface was shook to reset the sand and start working again. After that pebbles were also used to calculate instead of sand. This was the rawest form of abacus.

After that many civilizations used their own versions of abacus and their own systems of calculations. Some say that firstly the Chinese introduced abacus and some speak in the favor of Babylonians.

Whoever introduced it firstly will get the credit of inventing one of the most important mathematical tool of all times. The use of the abacus with different civilizations of the world is discussed in the chronological order.

### Babylonian Abacus

Babylonians have used abacus in the primitive times. It was not the one like we use today. It was the rawest shape of abacus and used with the help of pebbles or sand sprayed on the flat surface and any other thing used to write letters on the sand surface. That device was difficult to use for complex calculations.

### Egyptian Abacus

The Egyptian abacus was very different from its time other abaci. Many historians are not sure about the exact type of abacus used in Egypt but they think that it was almost opposite in direction to that of the Greek abacus.

### Greek Abacus

It is considered as one of the oldest abacus of the complete shape. It consisted of five parallel lines equally divided by the vertical lines, capped with a semi-circle at the intersection of the bottom most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semi-circle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross when they intersect with the vertical line.

### Mathematical Development and Abacus

Since the dawn of human beings on this earth human beings have encountered with too many situations in which they have to calculate and manipulate to survive in this world. Although those situations have got complex with the lapse of time and led to many new inventions for the convenience of calculations. This development process has many stages. It relates back to the prehistoric time and the first stage of development involves the construction of abacus.

### Abacus

Abacus is a device used for the purpose of calculation. It is a simple device with a frame and a rod horizontally attached to the frame and beads placed on the parallel rods. The horizontal rod divides the frame into two parts. This device can be used for the arithmetical calculations and is time saving.

### History

The history of abacus is as old as the counting problem itself. The traces of abacus have been found to the 2400B.C.Many civilizations developed their own versions of abacus. Firstly the calculations were done on the sun dried wooden frame with the help of sand sprayed over the frame, some stick or finger was used to write on the sand and after finishing the calculation that sand was thrown off or probably reset with the help of hand. After some time a device with the wooden frame and beads attached to its rods was invented and this form of abacus can also be seen today. It is still used in some Asian countries and in some Latin American countries. Even today some clerks and small businessmen in those countries prefer to use abacus and do calculations quickly than their counterparts using electronic calculators .

It also helps to teach young children perform their arithmetic calculations especially multiplication as this causes a lot of problem to young children and abacus makes it easy to perform.

Abacus is also used to teach blind children to perform arithmetical calculations while other students learn the same things on paper. Some errors can encounter while calculating on abacus if one is not well trained but this can also happen with paper functions.

Throughout history man has developed too many types of abaci. Many civilizations have contributed to this world's asset and hence made their mark in the development of mathematics. Babylonians used abacus as early as 2400B.C. Chinese used abacus. Mayan Civilization also used abacus, their abacus is also thought to be the first device with counters that were strung on parallel rods. It is the Aztec Abacus and known as the Nepohualtzitzin in the 10th century.

During the 11th century the Chinese abacus or suan pan was invented The suanpan is generally regarded as the earliest abacus with beads on rods. The Mandarin term suan pan means calculating plate. A suan pan has two heads above a middle divider called a beam and five beads below.

The suan pan spread over to Japan through Korea and Japanese named it Soroban. It looked a lot like its Chinese counterpart. Soroban was introduced in the 15th century. In the 17th century Russians also introduced their own version of abacus and called it schoty. The schoty has ten beads per rod and no reckoning bar. Throughout the history such developments have been made in the design and the working of abaci adding a lot to the mathematical arena. It laid the foundation of mathematical development.

### Mayan Abacus v/s Chinese Abacus

### The History

History is a fascinating subject to be studied and heard as a story. It pleases all the age groups. The history of abacus is quite interesting. It is a wonderful thing that such inventions were the necessities of such a time and even today it's a mystery how the secret of abacus spread all across the globe in the same time frame.

Abacus was found in the Europe and in China, in a way of looking at it is, it was there in the far west to the east. While the history of Chinese abacus is very well known there are few other forms of abacuses which are unknown to the common people. Mayan abacus is one amongst them.

The facts about the Mayan abacus are pure history. Various historians claim that the records of the first abacus could be of the Mayan abacus, as many relics that were earthed from the Mayan civilization sites show the presence of beads strung on rods which have a similar structure of the abacus. Even though there are no clear indications of the presence and usage of such a form of abacus, it is a possibility.

### The Mayan Abacus

The unearthed objects and the cave pictures of the Mayan civilization gives some light into the type of numeral system and the counting methods they used. There are some academicians who claim that the beaded structures that were found could be a kind of toy. But the very similarity between the counting systems revert these thoughts.

These relics found in the Mayan civilization are also called as the Aztec abacus or nepohualtzitzin in the ancient times. Even though its construction and the counting method is still a debate, it shows a lot similarity to the Chinese abacus – suanpan.

The Mayan abacus is considered to be built around the 10th century. Its structure could be defined as a group of maize strung on parallel strings or wires on a frame of wood. Some of the relics and the paintings depicts abacus made with an extra separation that divides the counters into 3 above and 4 below the bar.

This separation confirms the vigesimal or the base 20 system that was believed to be present in the Aztec civilization and by the Basques in Europe. This particular study also rules out the belief that it was a toy.

Each of the 3 counters above the bar represented 5. And each of the 4 counters below the bar represented 1. This gives a possibility that a total of 19 could be represented in a column.

### Abacus in different Number Systems

Abacus is a simple device that is used for calculating simple arithmetical questions. It is a device that is used for centuries by the human beings and has been in use by the human beings for about 4500 years. The simplicity of the tool has enabled many civilizations to construct similar devices with some difference in their designs but with the same purpose of performing arithmetic calculations.

If we go into the history, many abaci can be found which are made by many civilizations one after another. The first days of abacus include the wooden pile on which sand was spread and then counting was done on that with the help of a stick or finger. In some cases pebbles were used for counting. With the lapse of time it changed its phase and took the shape of modern day abacus. Abacus is the world's first comprehensive calculator.

### Abacus Structure

From the prehistoric times, human beings have employed various methods to count things and to make their calculations much easier to perform they have come with their proposed systems of numbers. Many civilizations have used abacus in the past and they have used their own number systems for the purpose of calculations on the abacus.

This also tells about the efficiency of the tool with different sets of number systems. A brief description of the types of number systems used by various civilizations is as under.

### Tally Method

Human beings have used tally method since prehistoric times. Tally method was the first method employed to perform calculations. The first ever abacus constructed also used this method to perform its calculations. It was a simple plane with sand spread over it and tallies were used to represent the numbers of things calculated.

### Sexagesimal Number system

Sexagesimal number system is the number system with the base 60 and was fully developed at the beginning of old Babylonia period about 1950 BC.

Sexagesimal number system was used for the purpose of calculations on the abacus and the calculations were performed easily on the calculating machine. This number system is still used in the modern world and is used to measure time and angles.

### Modular Tallies

Chinese have used the notion of modular tallies to keep track of their armies and provisions. Although it is not a perfect number system but abacus has adopted itself to this number system also and proved its worth.

Abacus was easy to use in this number system because this system added strength to the best available feature of the abacus. i.e. positional notion. This system is still a reliable system especially for the illiterate persons and also for the beginners.

### Roman Number System

Romans used the system of assigning letters to numbers. This system was adopted from the Greek idea of assigning different letters to different numbers. This system was used in Europe until around 1500's.

Usage of abacus in the Roman world is not hidden from anyone in the world and it is also known that abacus was also used very frequently in the daily lives of Roman people in order to perform their calculations.

In fact Romans are the ones who made the world's first type of pocket calculators i.e. they made the abacus to fit into the pocket of the shirt of a person. Abacus was very convenient to use with the number system introduced by the Romans that is the main reason of the popularity of the abacus in the Roman world. Abacus was very compatible with the Roman number system and made people feel comfortable about their calculations.

### How Abacus Works?

The abacus is a fun tool to do math with. It helps you learn all about the base ten system (which is the one we use for ordinary math), patterns among numbers, and how to do math in your head. It is probably the best tool in the world for most people to get a good grasp of numbers with.

Why should i learn to use an abacus when can a calculator is one of the questions hear most people think that just some exotic toy would be like calling galileo italian guy. The main reason to learn how to use an abacus, is because it will teach you how to manipulate numbers - how each digit relates to the others, and how to use that knowledge to get very good at understanding how to do all the major operations - addition, subtraction, multiplication, and division.

The abacus will also give you a handle on how base systems work. For instance, you can use an abacus to do math in the decimal system (which we use in everyday math) and the binary system (which is used in computer science).

Understanding decimals becomes a breeze when you know how to use an abacus. Exponents and square roots can also be done with a little practice.

### Importance of Abacus

If we go deep into the history books we come to know that abaci was used from the ancient times to perform basic arithmetical problems by the people related to any field of life. Businessmen have used it for centuries to perform basic calculations for the purpose of their routine business.

It is a true assistant for anyone who wants to perform his calculations very quickly and with full authority. This is the reason behind the fact that even in this modern era there is thought to be a need to teach children to learn perform calculations using abacus.

The reason being the simplicity of the device and its look that makes children feel it just like their toy and never let them feel bored while performing calculations on it. It is also very easy to learn and makes calculations easier for the juvenile to learn.

When the calculations are performed on abacus, a little stress is made on the mind. People who regularly perform calculations on abacus can perform them more quickly than their other counterparts who perform those calculations on electronic calculators.

### Need of Abacus

There may arise a question in one's mind that why is there a need to teach children to use abacus or to teach them solving arithmetical problems using abacus in this time of advanced technology. But the fact is that even if the advancements are made in the technology making it possible for human beings to perform complex calculations and to explore new dimensions in the field of knowledge, the mind of the child is completely empty and it is to be written on. Child's mind could grab some things with difficulty and has the tendency of forgetting learnt topics after some time.

With the help of abacus simple arithmetical functions are easy to learn especially multiplication which may seem easier to an adult to perform but are very difficult for the juvenile to understand.

### Play-n-Learn

Nowadays abaci are also used as toys by children. These are among the things that they see quite often and are familiar with them. When children are asked to learn arithmetical calculation on their abaci they feel like playing and in this way they learn a lot without being bored at all. Children feel happy with something like abacus because of its shape. Anything, which has rods and beads attached to it, makes them feel good and relaxing while learning.

This process is easy to adapt for the beginners and puts less stress on the mind of children. Every bead of the abacus is assigned a particular value and it is relatively easy to learn those values and keep performing calculations on the device, as the beads are assigned certain values therefore there is no need to keep anything in mind rather keep fingers on the beads and place beads in their calculated positions. The result can be easily inferred from the positions of the beads on the rod.

### Abacus Necessity

Sometimes it is needed to teach children how to use abacus. For instance blind children are taught to use abacus because they cannot perform calculations on the paper. Abacus has proved out to be an ideal tool for those people as it allows them to calculate easily and quickly while being reliable. The use of abacus is easy to understand for the new beginner and it also helps in developing the mind of the children.

At the initial learning stage of a child it is almost impossible to learn all of the things in a flash. Abacus has this innate tendency to design the model for the good development of a child's brain. The study has shown that the children which have used abacus in their past could perform arithmetical calculations more quickly and comfortably when they are grown ups.

This is due to the fact that they have the golden rule of calculating long figures with the help of broken packets of that figure in their minds and it allows them to perform more conveniently in the later stage of their life.

The use of abacus as a teaching tool has decreased in the world in the past few years. But there are still some schools in the world who teach little kids with the help of abacus. Abacus is still used in some Asian and Latin American Countries but due to the ever changing technology of the world it has become obsolete. Even now with its modern day competitors, electronic calculators, abacus stands as a comprehensive tool for simple arithmetic calculations.

### Mental Math

It is an undisputable fact that the abacus had reduced the work load on calculation and laid the foundation of a calculation machine as such. Whether it is the east or west the invention of abacus had a profound effect.

It had greatly eased the mental mathematics. The merchants and tax collectors of yesterday had found this to be a great help to assist in their profession. Mental mathematics could be easy, but when it comes to decimals and complex calculations involving multiplication and division it is advised to take the help of an abacus.

It is a proven fact that the abacus was present in the same time frame in the east as well as the west. Both had many similarities and disparities too. The abacus is an ancient tool invented during Greek and Roman times. Over the period abacus has evolved into different types as it traveled across the world.

However it was in China the abacus was innovated further and used heavily in day-to-day life for calculations. Abacus mental math is a technique derived from this very old technique and fits right into the modern day world. All these years the abacus was present in the east and west and can be used to build confidence, provide a sense of achievement, promote intuitive thinking, enhance problem-solving capability, stimulate creativity and improve concentration and mental endurance.

### The Western Thinking

It is believed that the abacus formed its shape in the west, predominantly in the Roman Empire. Later it spread to the east and other parts of the world with the help of merchants traveling around the world. The roman way of abacus was catered for their number systems and their requirements of calculations like tax collection, engineering and astronomy. But when it moved to the other parts of the world it changed to suit the new inventors. With Abacus math, abacus is used as a tool to learn calculations. Beads are moved up and down and various columns to represent the number.

Other than the roman abacus there were many contenders in the west. The oldest surviving counting board is the Salamis tablet which originally thought to be a gaming board, used by the Babylonians circa 300 B.C., discovered in 1846 on the island of Salamis. It is a slab of white marble measuring 149cm in length, 75cm in width and 4.5cm thick, on which are 5 groups of markings.

In the center of the tablet are a set of 5 parallel lines equally divided by a vertical line, capped with a semi-circle at the intersection of the bottom-most horizontal line and the single vertical line.

Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them but with the semi-circle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.

### The Eastern Way

It is thought that early Christians brought the abacus to the East, note that both the suan-pan and the Roman hand-abacus have a vertical orientation. Aspects of Roman culture could have been introduced to China as early as 166 A.D, during the Han Dynasty, as Roman emperor Antoninus Pius' embassies to China spread along the Silk Road.

The Chinese abacus was developed about 5000 years ago. It was built out of wood and beads. It could be held and carried around easily. The abacus was so successful in the east that its use spread form China to many other countries. The abacus does not actually do the computing, as today's calculators do. It helps people keep track of numbers as they do the computing. This complete freedom of use of the suanpan spread to Korea, and then to Japan during the latter part of the 15th century.

The Japanese termed the abacus a soroban. Originally the soroban looked very much like its Chinese cousin having two beads above the reckoning bar and five beads below. Around 1850, it was modified to have only one bead above the reckon

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