First of all I saw the Boethius' image on another book and in the right
hand of the "arithmetic" there is a vertical string with seven little
balls. In another similar German XIII century image arithmetic holds with
both hands a string with approximately twenty little balls.
The trivial answer could be: "it is a rosary" or at least a common
arithmetic tool which appears even in our "rosary".
I remember many years ago old women with their rosaries: fifty balls in
groups of ten with the last one (of every group) greater. It was
substantially the unique arithmetic tool for those women, employed for
many religious rites (to count the right numbers of Aves, PaterNosters and
Creeds even against the Evil Eye).
In addition I raed that the rosary was employed in the Near East even before
its introduction in our religion. Its structure was not very far from other
ancient counting techniques and even abacus was not completely stranger to
this simple technology.
It is not impossible that at the beginning of the Middle Ages, when even the
trade needed no specific arithmetic counting device, something like a rosary
could be the unique arithmetic tool to depict in an icon.
Yours sincerely
Luigi Borzacchini