The abacus is a mechanical aid for counting and doing arithmetic. It is wrong to think of the abacus as a calculating device like an electronic calculator or a slide rule, because is not a machine and it performs no calculations itself. It is really just a tally device that stores the results of a series of small computations made mentally by the user.
An abacus has a number of columns that represent place values in a number system. For a decimal system, if a particular column may represents ones, the column to its left represents tens, the column to its right represents tenths, and so on. Each column has beads that slide up and down on a thin rod and is divided into an upper part and a lower part by a bar. The positions of those beads represent a numerical value for that column.
The modern abacus
The abacus is not an obsolete antique; it is still being used actively in China, Japan, and in other countries that have been strongly influenced by Chinese culture. It is not unusual to see an abacus being used at counters in shops, with a cash register or computer in hand's reach. Elementary school children in those countries learn the abacus as part of their basic math curriculum.
The most common configuration for a modern abacus has between 10 and 30 or so columns. Each column has four beads in the lower part and one bead in the upper part. An older configuration that has five beads below and two beads above can still be seen, but with rapidly diminishing frequency. The rods and beads that form the columns are held together by a rectangular frame made of wood or plastic. The thin bar separating the upper and lower parts (which are called 'heaven' and ' earth' in Japanese) has dots on every third column that can serve as the decimal points or as commas do in written numerals to show which place values the columns represent and make the result easier to read. Size varies, especially with the number of columns, but most modern abacuses are small enough to hold in one hand and operated with the other.
The abacus evolved from the earliest forms of tallying or counting. According to the American Heritage Dictionary, the word abacus is rooted in the Hebrew term abaq, which referred to 'sand used for drawing and counting'. Later, there was the classical Greek abax, and then the Latin abacus, which was absorbed into Middle English and handed down to us without change.
Sand was eventually replaced by pebbles as a counting medium, and people began placing the pebbles in columns for counting. Later improvements include the use of grooved boards to hold the pebbles or beads. It is difficult to date the counting board, because they were made of wood or other non-durable materials, but the oldest surviving artifact is the Salamis tablet, which was used in Babylonia some three centuries BC. The Salamis tablet is a marble slab inscribed with eleven vertical lines that enclose 10 columns. A horizontal line crosses through the vertical lines about half way from top to bottom. This is the basic configuration of the abacus, but without the beads.
The hand abacus appeared sometime in the later Roman or Greek era before 500 AD. That abacus had five columns, wth four beads on the bottom and one on the top. In the Middle Ages, the abacus used in Europe had a horizontal orientation of rows rather than columns. Later, a ten-bead abacus came into use, particularly in Russia.
In China, the abacus appears in paintings dated in the Song Dynasty, and by the time of the Ming Dynasty, the abacus was the common way of doing arithmetic. During that period, Chinese merchants spread the abacus throughout the Far East. An abacus made of corn kernels strung on strings was also used by the Aztecs around 900 to 1000 AD.
The Chinese abacus featured five beads below the bar and two above. That 5/2 configuration was suited to performing hexadecimal calculations, which was handy because of the base 16 system of weights used in the earlier days. That has now been replaced almost entirely by the 4/1 configuration, which is the most efficient for decimal system arithmetic. The abacus can also be used for the duodecimal or any other number system by simply changing the number of beads in a column.
Aside from its practical value, the abacus offers important benefits as a tool for introducing the concepts of number, counting, and arithmetic operations in early education. Rather than doing the work and simply providing an answer for the student as a calculator does, the abacus makes it easier for them to build up mental computation habits a step at a time. Using an abacus also reinforces the concepts with with multi-sensory visual and physical feedback as students manipulate the beads. Proficient users can sometimes be seen calculating by doing the physical motions without even holding an abacus. Studies have shown that children who learn on the abacus can do mental calculations earlier and faster than students who learn with paper and pencil.