History of the Abacus

History of the Abacus

In this lesson, you will learn the definition of an abacus. You will review the history of the abacus and learn about the oldest abacus known to man. You will also learn about different types, such as the Chinese, Japanese and Russian abacuses, as well as some modern-day uses of the abacus.

What Is an Abacus? ---
The word abacus is derived from the Latin word abax, which means a flat surface, board or tablet. As such, an abacus is a calculating table or tablet.

The abacus is the oldest device in history to be used for arithmetic purposes, such as counting. It is typically an open wooden rectangular shape with wooden beads on vertical rods. Each bead can represent a different number. For simple arithmetic purposes, each bead can represent one number. So, as a person moves beads from one side to the other, they would count, 'one, two, three', etc.

An abacus can be used to calculate large numbers, as well. The columns of beads could represent different place values. For example, one column may represent numbers in the hundreds, while another column may represent numbers in the thousands.

History of the Abacus ---
The written numbers did not exist many, many years ago. But individuals still needed a way to count, especially merchants selling fruits, vegetables and other goods. This is how the abacus came of use. It has been said that the first abacuses were just flat boards. Rocks would be placed on the board and moved about for calculation purposes. Other abacuses had a film of sand or dust on the top of the surface and one would use their finger to make calculations.

Using rocks, seashells and fingers on the abacus could only be helpful to a certain extent. That is when the wooden beads became helpful.

The oldest abacus known to man is the Salamis Tablet, named for the island of which it was found--Salamis Island in Greece--the nearest island to the capital of Athens. It was found in 1846 and can be dated back to 300 BCE. The Roman hand abacus was the next abacus to be discovered. It was used in 300 CE in business, engineering and architecture. This is when the Romans were using Roman numerals. The abacus has come a long way since being used in ancient times by the Greeks and Romans.

Chinese, Russian and Japanese Abacuses ---
One of the most popular kinds of abacuses is the Chinese abacus, also known as the suanpan. Rules on how to use the suanpan have dated all the way back to the 13th century.

On a Chinese abacus, the rod or column to the far right is in the ones place. The one to the left of that is in the tens place, then the hundreds, etc. So, the columns are different place values and the beads are used to represent different numbers within those place values. For addition, beads on the suanpan are moved up towards the beam in the middle. For subtraction, they are moved down towards the bottom or outer edge of the suanpan. The rules of use are a bit more intricate and complicated, but this is the general idea of how one is used.

The Japanese abacus is called a soroban. Like the suanpan, the soroban is divided into two levels. The modern-day soroban has only one bead on the upper level and four beads on the lower level. For both the suanpan and the soroban, the top beads represent heaven, while the bottom beads represent Earth.

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A Brief Introduction to the Abacus

A Brief Introduction to the Abacus

The abacus is a mechanical aid used for counting; it is not a calculator in the sense we use the word today.

Anatomy & Construction :
The standard abacus can be used to perform addition, subtraction, division and multiplication; the abacus can also be used to extract square-roots and cubic roots. The beads are manipulated with either the index finger or the thumb of one hand.

The abacus is typically constructed of various types of hardwoods and comes in varying sizes. The frame of the abacus has a series of vertical rods on which a number of wooden beads are allowed to slide freely. A horizontal beam separates the frame into two sections, known as the upper deck and the lower deck.

ABACUS PARTS :
The various parts of the abacus are identified here: the frame, the beam, the beads and rods and the upper and lower decks.


Preparation & Bead Values :

PREPARING THE ABACUS:
 The abacus is prepared for use by placing it flat on a table and pushing all the beads on both the upper and lower decks away from the beam by sliding the thumb along the beam.

BEAD VALUES: 
Each bead in the upper deck has a value of 5; each bead in the lower deck has a value of 1.
Beads are considered counted, when moved towards the Beam— the piece of the abacus frame that separates the two decks.

Counting :
After 5 beads are counted in the lower deck, the result is "carried" to the upper deck; after both beads in the upper deck are counted, the result is then carried to the left-most adjacent column.

The right-most column is the ones column; the next adjacent to the left is the tens column; the next adjacent to the left is the hundreds column, and so on. Floating point calculations are performed by designating a space between 2 columns as the decimal-point and all the rows to the right of that space represent fractional portions while all the rows to the left represent whole number digits.

Abacus Applet:
 Numeric representation of the number: 87,654,321. If your browser is Java-capable then the applet, above, will identify the parts of the abacus in your browser's status-area as you move your mouse-pointer over it; the beads will move when you click on them and the value of each column will be displayed on the top frame.
Referring to the Figure/Applet above, the third column, representing the number 8, is counted with 1 bead from the top-deck and 3 beads from the bottom-deck ; the sum of the column is 8.

Similarly, the fourth column representing the number 7, is counted with 1 bead from the top-deck and 2 beads from the bottom-deck; the sum of the column is 7.

Technique :
Proper finger technique is paramount in achieving proficiency on the abacus. With a Chinese abacus, the thumb and the index finger together with the middle finger are used to manipulate the beads. Beads in lower deck are moved up with the thumb and down with the index finger. In certain calculations, the middle finger is used to move beads in the upper deck.

The Java version of the abacus is a limited simulation of the real device because the fingering technique is completely obfuscated by the mouse. Abacus Apps on touch-screen tablets are better simulations. With a real abacus, constant practice is indispensable in achieving virtuosity in calculating speed.

Finger Technique:
 A Japanese textbook published in 1954 shows the proper technique for moving the beads. It shows the thumb being used to count beads in the lower deck and the index finger being used in all other cases.
With the Japanese version, only the index finger and thumb are used. The beads are moved up with the thumb and down with the index finger. However, certain complex operations require that the index finger move beads up; e.g. adding 3 to 8.

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Why Master Mind Abacus ?

Why Master Mind Abacus ?

"The ancient Abacus coupled with modern technology”.

The Abacus training program for kids has gained popularity over the world. We are a premium company that operates on International and National levels. Master Mind Abacus offers quality teaching services to all its students and equips them with excellent course material that directly reflects on the students’ positive performance.

Listed below are the benefits which are unique and only applicable to Master Mind Abacus :---
School curriculum based system :--

Most of the abacus companies follow the calculating methods that works from left to right. While, the methods that are taught in schools perform calculations from right to left. We at Master Mind follow the same pattern as that of schools.

This system works in alignment with the school curriculum. It enables the students to adopt school system in Master Mind Abacus classes. Moreover, it does not confuse them, unlike other abacus programs.

E.g.:

Master Mind Abacus & School System
24 
x 12 
48 
24 x 
288

Play and Learn Method :--

Considering the child psychology wherein playful activities are more enjoyable for children, every class of Master Mind Abacus including the study material has been designed with a ready-made game for each day. The children unknowingly learn to practice complex math calculations without being stressed.

Speed Building Software :--

This software has been specifically designed like an animated video game which increases the child’s accuracy and speed, and also gives them an environment that feels like a play.

Score Board Method :--

Unique teaching technique developed by Master Mind Abacus to ensure that the teacher is able to guide and control all students in a hassle free manner. Through this method, the students indulge into gaining a feeling that they are into a play and also compete with each other so as to earn more points. Beyond that, every student will get equal attention in the class, thus ensuring overall development of the entire batch.

Point Card System :--

To give motivation to students, Master Mind Abacus adopts a technique in the form of Point Cards, which the child accumulates in every class. These points can then further be redeemed for gifts.

Online Competitions :--

Online Competitions- We conduct Center, State and National level competitions, providing convenience for students’ to appear for it from their home town. These competitions :
 Saves time and Money
 Reduces workload of trainers giving 100% accurate results
 Evaluates real-time results

Cost effective :--

Master Mind Abacus program is affordable to all segments of society. Furthermore, at the franchisee front Master Mind does not charge any royalty.

Exclusive Study Material :--

The books and its contents along with the online abacus learning are one of the best study material provided to students across the abacus industry. The colorful environment provided by us attracts the students more towards the course and gives them a pleasurable experience.


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What is Computer

WHAT IS COMPUTER

       A computer is a device that can be instructed to carry out arbitrary sequences of arithmetic or logical operations automatically. The ability of computers to follow generalized sets of operations, called programs, enables them to perform an extremely wide range of tasks.

       Such computers are used as control systems for a very wide variety of industrial and consumer devices. This includes simple special purpose devices like microwave ovens and remote controls, factory devices such as industrial robots and computer assisted design, but also in general purpose devices like personal computers and mobile devices such as smartphones. The Internet is run on computers and it connects millions of other computers.

       Since ancient times, simple manual devices like the abacus aided people in doing calculations. Early in the Industrial Revolution, some mechanical devices were built to automate long tedious tasks, such as guiding patterns for looms. More sophisticated electrical machines did specialized analog calculations in the early 20th century. The first digital electronic calculating machines were developed during World War II. The speed, power, and versatility of computers has increased continuously and dramatically since then.

       Conventionally, a modern computer consists of at least one processing element, typically a central processing unit, and some form of memory. The processing element carries out arithmetic and logical operations, and a sequencing and control unit can change the order of operations in response to stored information. Peripheral devices include input devices, output devices, and input/output devices that perform both functions. Peripheral devices allow information to be retrieved from an external source and they enable the result of operations to be saved and retrieved.

        According to the Oxford English Dictionary, the first known use of the word "computer" was in 1613 in a book called The Yong Mans Gleanings by English writer Richard Braithwait: "I haue read the truest computer of Times, and the best Arithmetician that euer breathed, and he reduceth thy dayes into a short number." This usage of the term referred to a person who carried out calculations or computations. The word continued with the same meaning until the middle of the 20th century. From the end of the 19th century the word began to take on its more familiar meaning, a machine that carries out computations.

       The Online Etymology Dictionary gives the first attested use of "computer" in the "1640s, "one who calculates,"; this is an "... agent noun from compute". The Online Etymology Dictionary states that the use of the term to mean "calculating machine" is from 1897." The Online Etymology Dictionary indicates that the "modern use" of the term, to mean "programmable digital electronic computer" dates from "... 1945 under this name; theoretical from 1937, as Turing machine".

       Concept of modern computer

The principle of the modern computer was proposed by Alan Turing in his seminal 1936 paper, On Computable Numbers. Turing proposed a simple device that he called "Universal Computing machine" and that is now known as a universal Turing machine. He proved that such a machine is capable of computing anything that is computable by executing instructions stored on tape, allowing the machine to be programmable. The fundamental concept of Turing's design is the stored program, where all the instructions for computing are stored in memory. Von Neumann acknowledged that the central concept of the modern computer was due to this paper. Turing machines are to this day a central object of study in theory of computation. Except for the limitations imposed by their finite memory stores, modern computers are said to be Turing-complete, which is to say, they have algorithm execution capability equivalent to a universal Turing machine.

       

Central processing unit :--

          The control unit, ALU, and registers are collectively known as a central processing unit. Early CPUs were composed of many separate components but since the mid-1970s CPUs have typically been constructed on a single integrated circuit called a microprocessor.

Computer main memory comes in two principal varieties :--

         random-access memory or RAM

         read-only memory or ROM

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Early childhood education

Early childhood education is a branch of education theory which relates to the teaching of young children up until the age of about eight. Infant/toddler education, a subset of early childhood education, denotes the education of children from birth to age two. It emerged as a field of study during the Enlightenment, particularly in European countries with high literacy rates. It continued to grow through the nineteenth century as universal primary education became a norm in the Western world. In recent years, early childhood education has become a prevalent public policy issue, as municipal, state, and federal lawmakers consider funding for preschool and pre-K. It is described as an important period in child's development. It refers to the allround development of a child's personality. ECE is also a professional designation earned through a post secondary education program. For example, in Ontario, Canada, the designations ECE and RECE may only be used by registered members of the College of Early Childhood Educators, which is made up of accredited child care professionals who are held accountable to the College's standards of practice.

 The history of early childhood care and education refers to the development of care and education of children between zero and eight years old throughout history. ECCE has a global scope, and caring for and educating young children has always been an integral part of human societies. Arrangements for fulfilling these societal roles have evolved over time and remain varied across cultures, often reflecting family and community structures as well as the social and economic roles of women and men.

                         

Children remember and repeat actions they observe.While the first two years of a child's life are spent in the creation of a child's first "sense of self", most children are able to differentiate between themselves and others by their second year. This differentiation is crucial to the child's ability to determine how they should function in relation to other people.The tools they learn to use during these beginning years will provide lifelong benefits to their success. Developmentally, having structure and freedom, children are able to reach their full potential.

 The Developmental Interaction Approach is based on the theories of Jean Piaget, Erik Erikson, John Dewey and Lucy Sprague Mitchell. The approach focuses on learning through discovery. Jean Jacques Rousseau recommended that teachers should exploit individual children's interests in order to make sure each child obtains the information most essential to his personal and individual development. The five developmental domains of childhood development include.

 The way in which a child interacts with others Children develop an understanding of their responsibilities and rights as members of families and communities, as well as an ability to relate to and work with others. Emotional: the way in which a child creates emotional connections and develops self-confidence. Emotional connections develop when children relate to other people and share feelings.

 In the past decade, there has been a national push for state and federal policy to address the early years as a key component of public education. At the federal level, the Obama administration made the Race to the Top Early Learning Challenge a key tenet of their education reform initiative, awarding $500 million to states with comprehensive early childhood education plans. In addition, a largely Democratic contingent sponsored the Strong Start for America’s Children Act in 2013, which provides free early childhood education for low-income families. Specifically, the Act would generate the impetus and support for states to expand ECE; provide funding through formula grants and Title II Learning Quality Partnerships, III Child Care and IV Maternal, Infant and Home Visiting funds; and hold participating states accountable for Head Start early learning standards.

  Head Start grants are awarded directly to public or private non-profit organizations, including community-based and faith-based organizations, or for-profit agencies within a community that wish to compete for funds. The same categories of organizations are eligible to apply for Early Head Start, except that applicants need not be from the community they will be serving.

Many states have created new early childhood education agencies. Massachusetts was the first state to create a consolidated department focused on early childhood learning and care. Just in the past fiscal year, state funding for public In Minnesota, the state government created an Early Learning scholarship program, where families with young children meeting free and reduced price lunch requirements for kindergarten can receive scholarships to attend ECE programs. In California, Senator Darrell Steinberg led a coalition to pass the Kindergarten Readiness Act, which creates a state early childhood system supporting children from birth to age five and provides access to ECE for all 4-year-olds in the state. It also created an Early Childhood Office charged with creating an ECE curriculum that would be aligned with the K-12 continuum.

Early childhood care and education as a holistic and multisectoral service
Unlike other areas of education, early childhood care and education places strong emphasis on developing the whole child – attending to his or her social, emotional, cognitive and physical needs – in order to establish a solid and broad foundation for lifelong learning and well-being. ‘Care’ includes health, nutrition and hygiene in a warm, secure and nurturing environment; and ‘education’ includes stimulation, socialization, guidance, participation, learning and developmental activities. ECCE begins at birth and can be organized in a variety of non-formal, formal and informal modalities, such as parenting education, health-based mother and child intervention, care institutions, child-to-child programmes, home-based or centre-based childcare, kindergartens and pre-schools. Different terms to describe ECCE are used by different countries, institutions and stakeholders, such as early childhood development, early childhood education and care, early childhood care and development, with Early Childhood Care and Education as the UNESCO nomenclature.

Economic benefits of early childhood care and education.Decades of research provide unequivocal evidence that public investment in early childhood care and education can produce economic returns equal to roughly 10 times its costs. The sources of these gains are (1) child care that enables mothers to work and (2) education and other supports for child development that increase subsequent school success, labour force productivity, prosocial behaviour, and health. The benefits from enhanced child development are the largest part of the economic return, but both are important considerations in policy and programme design.The economic consequences include reductions in public and private expenditures associated with school failure, crime, and health problems as well as increases in earnings.

Curricula in early childhood care and education is the driving force behind any ECCE programme. It is ‘an integral part of the engine that, together with the energy and motivation of staff, provides the momentum that makes programmes live’. It follows therefore that the quality of a programme is greatly influenced by the quality of its curriculum. In early childhood, these may be programmes for children or parents, including health and nutrition interventions and prenatal programmes, as well as centre-based programmes for children.

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Abacus Teaching System

Abacus Teaching System

The #abacus is a deceptively simple #calculating tool still used all over the world. It's a useful learning device for the visually impaired, as well as for anyone who wants to learn the roots of the modern calculator. After learning the basics of counting on the abacus, you can quickly perform arithmetic like addition, subtraction, multiplication, and division.

#Counting

Orient your abacus properly --- Each column in the top row should have one or two beads per row, while each column in the bottom row should have four. When you start, all of the beads should be up in the top row, and down in the bottom row. The beads in the top row represent the number value 5 and each bead in the bottom row represents the number value 1.

 Assign each column a place value --- As on a modern calculator, each column of beads represents a "place" value from which you build a numeral. So, the farthest column on the right would be the "ones" place, the second farthest the "tens" place, the third farthest the hundreds, and so on. You can also assign some columns to be decimal places if necessary. For example, if you are representing a number like 10.5, then the furthest right column would be the tenths place, the second column would be the ones place, and the third column the tens place. Likewise, to represent a number like 10.25, the furthest right column would be the hundredths place, the second column would be the tenths place, the third the ones place, and the fourth the tens place.

Start counting with the beads in the lower row --- To count a digit, push one bead to the "up" position. "One" would be represented by pushing a single bead from the bottom row in the farthest column on the right to the "up" position, "two" by pushing two, etc. You'll find it easiest to use your thumb to move the beads in the top row, and your index finger to move the beads in the bottom row.

 Complete the "4/5 exchange.”--- Since there are only four beads on the bottom row, to go from "four" to "five," you push the bead on the top row to the "down" position and push all four beads from the bottom row down. The abacus at this position is correctly read "five." To count "six," push one bead from the bottom row up, so the bead in the top row is down and one bead from the bottom row is up.

 Repeat the pattern for higher numbers --- The process is essentially the same across the abacus. Go from "nine," in which all the beads in the ones place are pushed up and the bead in the top row is pushed down, to "ten," in which a single bead from the bottom row of the tens place is pushed up. For example, 11 would have one bead in the second column pushed up, and another in the first column pushed up, all on the bottom row. Twelve would have one in the second column and two in the first column, all pushed up, and all on the bottom row. Two hundred and twenty six would have two in the third column pushed up in the bottom row, and two in the second column pushed up in the bottom row. In the first column, one bead on the bottom row would be pushed up, and the bead on the top row would be pushed down.

#Adding and #Subtracting

 Input your first number --- Say you've got to add 1234 and 5678. Enter 1234 on the abacus by pushing up four beads in the ones place, three in the tens place, two in the hundreds place, and one in the thousands place.

Start adding from the left --- The first numbers you'll add are the 1 and the 5 from the thousands place, in this case moving the single bead from the top row of that column down to add the 5, and leaving the lower bead up for a total of 6. Likewise, to add 6 in the hundreds place, move the top bead in the hundreds place down and one bead from the bottom row up to get a total of 8.

 Complete an exchange --- Since adding the two numbers in the tens place will result in 10, you'll carry over a 1 to the hundred place, making it a 9 in that column. Next, put all the beads down in the tens place, leaving it zero. In the ones column, you'll do essentially the same thing. Eight plus 4 equals 12, so you'll carry the one over to the tens place, making it 1. This leaves you with 2 in the ones place.

 Count your beads to get the answer --- You're left with a 6 in the thousands column, a 9 in the hundreds, a 1 in the tens, and a 2 in the ones: 1,234 + 5,678 = 6,912.

#Multiplying

 Record the problem on the abacus --- Start at the farthest left column of the abacus. Say you're multiplying 34 and 12. You need to assign columns to "3", "4", "X", "1", "2", and "=". Leave the rest of the columns to the right open for your product. The “X” and “=” will be represented by blank columns. The abacus should have 3 beads up in the farthest column left, four up in the next farthest, a blank column, a column with one bead up, two beads up in the next, and another blank column. The rest of the columns are open.

 Multiply by alternating columns --- The order here is critical. You need to multiply the first column by the first column after the break, then the first column by the second column after the break. Next, you'll multiply the second column before the break by the first column after the break, then the second column before the break by the second column after the break. If you are multiplying larger numbers, keep the same pattern: start with the leftmost digits, and work to the right.

 Record the products in the correct order --- Start recording in the first answer column, after the blank one for the “=” sign. You will keep moving beads on the right hand portion of the abacus as you multiply the individual digits. For the problem 34 x 12: First, multiply 3 and 1, recording their product in the first answer column. Push three beads up in that seventh column. Next, multiply the 3 and the 2, recording their product in the eighth column. Push one bead from the upper section down, and one bead from the lower section up. When you multiply the 4 and the 1, add that product to the eighth column, the second of the answer columns. Since you're adding a 4 to a 6 in that column, carry one bead over to the first answer column, making a 4 in the seventh column and a 0 in the eighth. Record the product of the last two digits 4 and 2, in the last of the answer columns. They should now read 4, blank, and 8, making your answer 408.

#Dividing

 Leave space for your answer to the right of the divisor and the dividend --- When dividing on an abacus, you will put the divisor in the left-most column. Leave a couple blank columns to the right, then put the dividend in the columns next to those. The remaining columns to the right will be used to do the work leading to the answer. Leave those blank for now. For example, to divide 34 by 2, count 2 in the left-most column, leave two blank columns, then put 34 over to the right. Leave the other columns blank for the answer section. To do this, push two lower beads from the bottom portion up in the left-most column. Leave the next two columns alone. In the fourth column, push three beads from the bottom portion up. In the fifth column from the left, push four beads from the bottom portion up. The blank columns between the divisor and the dividend are just to visually separate the numbers so you don't lose track of what's what.

Record the quotient --- Divide the first number in the dividend by the divisor, and put it in the first blank column in the answer section. Two goes into 3 once, so record a 1 there. To do this, push one bead from the bottom portion up in the first column of the answer section. If you like, you can skip a column between the dividend and the columns you want to use for the answer section. This can help you distinguish between the dividend and the work you do as you calculate.

Determine the remainder --- Next, you need to multiply the quotient in the first answer section column by the dividend in column one to determine the remainder. This product needs to be subtracted from the first column of the dividend. The dividend should now read 14. To make the dividend read 14, push two of the bottom portion beads currently pushed up to the center bar at the fifth column back down to their starting position. Only one bead in the lower portion of the fifth column should remain pushed up to the center bar.

Repeat the process --- Record the next digit of the quotient in the next blank column of the answer section, subtracting the product from the dividend. Your board should now read 2, followed by blank columns, then 1, 7, showing your divisor and the quotient, 17. Two beads from the bottom portion of the left most column will be pushed up to the center bar. This will be followed by several blank columns. One bead from the bottom portion of the first answer section column will be pushed to the center bar.

In the next answer section column, two beads from the bottom portion will be pushed up to the center bar, and the bead from the top portion will be pushed down to it.