An abacus, called "soroban" in Japanese, is used for arithmetic calculation throughout Asia. In Japan, children study the abacus as part of the third- and fourth-grade mathematics curriculum in elementary schools. They are taught the basics of addition and subtraction, using the abacus. The abacus is also an effective tool in order to acquire a basic conception of number through an elementary arithmetic: it can represent the structure of numbers; it can be manipulable and imaginable mentally by children, in the same way as "TILEs" can (e.g. Toyama, 1972) Recent investigations into the characteristics of abacus and abacus-derived mental calculation skills revealed that abacus operating skills contained a rapid, accurate, and automatic mental system for representing numbers: advanced abacus operators could construct a mental image of the configuration of the beads, and perform mental calculations by moving the "beads" of their mental abacus and reading off the resultant number as they would on a real abacus (Hatano, Miyake, & Binks, 1977; Stigler, 1984). In addition, grand experts of abacusderived mental calculation had an extended and stable mental abacus and used it as a visuo-spatial memory device for digits (Hatano & Osawa, 1983). Furthermore, the digit memory of the mental abacus operators became more and more visuo-spatial in nature as they gained expertise (Hatano, Amaiwa, & Shimizu, 1987). Discussions have also focussed upon whether the visually handicapped could develop an equivalent tactile-spatial mental abacus as they gained expertise; in other words, whether representational changes in digit memory would be observed among the visually handicapped as a function of the extent of expertise in mental abacus operation (Shimizu, 1995). As a whole, these studies suggest that grand experts of mental abacus operating acquire a powerful system of representation of digits and calculation which is formed through routine problem solving, that is a mental abacus, and applied their mental abacus only to digit memory. Therefore, these experts can be called "routine experts" (Hatano, 1982).

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