The term abacus and mental arithmetic refers to an abacus-based mental arithmetic technique.  While the abacus calculation entails utilizing the abacus in carrying out multiple number of addition, subtraction, multiplication and division, extraction of a root.  The abacus computing techniques come with certain rules and tips.  Skilled users are not only be able to quickly derived at the answer but could benefit from abacus computation to develop a mental abacus by perfecting the abacus scenarios, scale and shifts, a mental image that is referred to as a virtual impression that helps us conclude abacus mental calculation through the cognition, mental image and memorization of mental abacus computing.

          In day-to-day living, the numeral concept is all encompassing in all things we do, for however simple or complicated one’s life is, it is virtually impossible to leave behind the concept and tabulation of numbers even for a day.  And as we look to resolve numeral issues in our daily living, the need to possess essential resolution has compelled us to study math and adopt useful means.  The means adopted come in many forms, i.e. written calculation, mechanical calculation, ruler calculation, abacus calculation and so forth.

          Abacus is an invention of the Chinese, and remains an affordable and practical means of computing, and is easy to adapt and highly portable, for any question relating to numeral computing can be easily and accurately solved using an abacus.  And the study of how to compute using an abacus would constitute the term abacus computation.

          As one of the great inventions of the Chinese, the origin of the abacus begins quite early with varied hypotheses, with some speculating that it began during the founding emperor, Han dynasty, Sung dynasty, or even Yuan dynasty.  According to historical archival excerpts, it is unquestionable that abacus existed in Han dynasty since the term abacus was mentioned in the book written by Hsu Yueh in late Han period.  Abacus was a rare commodity in Tang and Sung periods that was reserved for the select few, and its becoming a popular means of computing did not happen until after Ming period. While the abacus as a study begins to excelling following a host of publications by abacus maestros, such as Ming abacus expert Wu Jing’s “A compendium of nine chapters of computations”, Wang Wen-shu’s “Practical computations”, Cheng Da-wei’s “Calculation Encyclopedia”, and “Concise Computational Compendium” and Ju Tsai-yu’s “New Theories on Mathematical Computations”.

          An individual’s brainpower development is often tied to dextral exercise, while maneuvering the abacus in a faster and more delicate manner exactly fits the principle.  Many local and foreign education researchers do reckon that abacus and mental arithmetic, as a higher form of abacus computing, helps to excel one’s brainpower development.

          And as human brain comprising of two halves, with the left brain focusing on speech, writing and computing related extrapolation and of thinking and judgment rendering function, whereas the right brain focuses on the ability to describe spatial correlation, mimicking, imaging types of cognitive reasoning or emotional related musical capabilities.  The abacus computing process is of an integrated thinking and motoring functions that requires instantaneous memorization on one hand and stirring the virtual abacus beads mentally on the other; it helps to stimulate one’s logical thinking process, memorization, attention, spatial imagination, necessary to complete the task, all of which makes abacus mental calculation to require a coordinated efforts from two sides of the brain, hence making it a gold key in unleashing one’s intellectual brainpower.  

           As a general principle, abacus learning is to start as young as possible for human brain development concludes at the age of around three, which excels to 100% between the age of 4 and 12.  The abacus learning process, which entails familiarizing abacus configurations to instill mental images, while the brain cell growth serves as a driving power behind image developing.  On the other hand, adults, whose brain cells have fully developed, tend to be from developing mental computing images through abacus and mental arithmetic learning to excel their equanimity, thinking process, memorization, imaging to grow more exponentially.

          In physiology makeup, abacus and mental arithmetic learning remains a skill-oriented hands-on learning experience that calls for physical coordination and balance.  Learning at a young age, poor posture or poor habits could result in light that a young individual has not yet fully developed small muscle nervous coordination and organ balance, and the varied teaching quality and incorrect teaching concept could instill the learner with erroneous numerical concept that might greatly discount the chance of rebuilding one’s self confidence.

          As a result, it is advisable that beginners at the age of 6 to 9 are deemed most suitable to take up abacus learning, meaning those attending senior kindergarten classes and up to third grade in grade school.  

           In abacus and mental arithmetic teaching process, abacus computing serves as the foundation, whereby through hands-on abacus computing the learner gets to understand the variation and methods in the four fundamental operations of arithmetic.  As one’s techniques are perfected, the learner will gradually develop a mental image to develop mental calculating capability through simulated mental image computing, which makes mental arithmetic a higher form of abacus computing.  And abacus computing and mental arithmetic can be likened to the two feet of mankind, as one simply cannot move forward without missing either.

          Abacus computing learning helps to develop computing aptitude and memory capability.  While abacus-computing images remain a most crucial element in the mental arithmetic process in terms of memory manifestation, for abacus computing images allow a person to quickly conclude an answer through the flipping and stirring of abacus beads.  Hence in the abacus and mental arithmetic learning process, abacus computing and mental arithmetic are to be acquired concurrently with abacus computing being the foundation and mental computation being an instantaneous prompting.  As the level of difficulty excels, abacus computing may slow down, whereas mental arithmetic remains barrier-free.  And it is indicative that one has achieved the highest level of perfect when one’s mental arithmetic capacity exceeds whose abacus computing limitations.  

          The addition and subtraction methods remain most fundamental to all computations, and general applied calculations whether it be multiplication, division or other types of complex issues are none other than deriving from addition and subtraction, making practicing addition and subtraction particularly important in that they are everywhere in our day-to day lives.  A basic practice of addition and subtraction lies in a repetitive practice in sequential orders incorporating a natural adaptation of utilizing the full scale of abacus beads, dextral methods in order to build a sound foundation.  Basic practice for addition and subtraction come in four types: one, continuous addition; two, multiple addition; three, continuous numeral addition; and four, continuous subtraction.

          The multiplication serves as a mean to derive a given figure in multiple number, or rather a simplified method of a continuous addition; the multiplication method can be divided into:  one, Kan Tou multiplication; two, Puo Tou multiplication; three, Shin Tou multiplication; and four, continuous multiplication.  

          The division is of one of the fundamental computations in mathematics, and a reverse of multiplication, whereby two factors’ sum and one of which’s factor are used to derive another factor.  Simply put, it is of a method for dividing a number into certain shares, or a method for computing how many times a number is to another.  

          Mental arithmetic does not require any tangible computing tool, and let along the speed that mental arithmetic provides, it could poise to save a lot of precious time, money and to train one’s brainpower and intellect to showcase is unparallel superiority.  Some of the characteristics of it are itemized as follows:  first, it ensures an accurate computation on day-to-day events; second, an intangible tool; third, a common knowledge that most local residents already possesses; fourth, it culminates skills and improves one’s intellect; fifth, it helps to cut down computing processes.  

          The term mental arithmetic entails a method of computing using the brain without relying on an abacus or any other tool, and is referred to as an intangible computation.  The methods come in the writing mental arithmetic and abacus mental arithmetic, where the former takes to a computing method based on written figures.  In elementary school math, mental arithmetic practice, or aptitude mental arithmetic, is often deployed, which relies on computing with brainpower yet often results in psychological fatigue for being mentally draining and a slow process.  Whereas the latter takes to a mental abacus calculating means, which helps to achieve computing through stirring mental abacus images.

          As mental arithmetic is a higher form deriving from abacus computing, in method, mental arithmetic and abacus computing are exactly the same, and the only element that sets them apart lies in that mental arithmetic relies on memorizing the shapes of abacus beads, while abacus computing a computation reflected on an abacus using mental computing capability.  In the learning process, one would need to memorize the configuration of the beads in order to acquire mental arithmetic, for one would need to memorize the bead configuration in order to alter one’s memorization method.  Thus, based on the foresaid factor, we can summarize a few points as follows, first, learning mental calculation needs to being with learning abacus calculation; second, one’s mental images would be the facsimile of abacus images; third, mental arithmetic and abacus computing remains two sides of a coin and are interrelated.  

           The accounting voucher is a form of original accounting records.  It is used to distinguish debit and credit, which is used by voucher processing department personnel as a written authentication for processing accounting entry, accounts receivable/payable and audit.  The accounting authentication method taking to a statement orientation serves as a most fundamental cataloging unit for every transaction made, and is essentially one of the accounting authentications referred by Taiwan’s accounting law.

          In support of the practical day-to-day computation in the industry, commerce and banking sectors, the abacus computing subject has streamlined voucher tallying under the curriculum with standard printed practice booklet featuring five lines of certain numbers on a page, made to resemble varied vouchers for tallying purposes.  There are three methods of computing: one being to place the vouchers to the left of an abacus for computing; two being to place the vouchers to the upper left of an abacus, and three being to place the vouchers to the upper right of an abacus.  Using the above itemized computing technique, the voucher pages are turned more ideally using the thumb and index finger.