Abacus

He [Gerebertus] was þe firste þat took abacus of Sarsyns, and ȝaf rules þerynne, þat mowe unneþe be understonde of þe kunnyngeste men of þe craft, þe whiche craftes men beþ cleped abaciste. Marianus. Abacus is a table wiþ þhe whiche schappes be portrayed and i-peynt in powdre, and abacus is a craft of geometrie.

[H]e set fondly and furiously to work upon [Thomas] Simpson's Euclid, [...] The smooth grassy sod answered all the purposes of the abacus, and the cows generously supplied him in a substitute for sand. Spreading and smoothing that substitute with his bear foot, he engraved upon it with his finger the mystic lines and letters; and, with book in hand, proceeded to establish the elementary principles of geometry, [...]

I’ve heard merchants still use an abacus for adding things up in China.

Before leaving the question of early arithmetic I should mention that for practical purposes the almost universal use of the abacus or swan-pan rendered it easy to add or subtract, or even to multiply and divide, without any knowledge of theoretical mathematics. [...] [I]t will be sufficient here to say that they afford a concrete way of representing a number in the decimal scale, and enable the results of addition and subtraction to be obtained by a merely mechanical process.

The computer is but another vehicle to employ in helping people learn, a cousin of books, films, blackboards, chalk, gerbils, abacuses. Like each of these devices, it can be well used or misused.

Take another look at the abacus to see how useful it is. Each row represents a successively higher counting group, or register, by 10 times. Thus, with only 6 rows you can count to one million (actually, up to 999,999, which is 1 short of one million).

Before Pythagoras it was necessary to see the thing before counting it, like children who learn on abacuses, with balls sliding along rods: children learn to add and subtract by sliding stones.

Each rod in the bottom deck of an abacus has 5 beads. The value of each bead depends on which rod it is on. Each bead on the ones rod in the bottom deck equals 1. Each bead on the tens rod in the bottom deck equals 10. Each bead on the hundreds rod in the bottom deck equals 100.