Italian abacus school systems differed more in their establishment than in their curriculum during the
Middle Ages. For example, institutions and appointed educators were set up in a number of ways, either through commune patronage or independent masters' personal funds. Some abbaco teachers tutored privately in homes. All instructors, however, were contractually bound to their agreement which usually meant that they could supplement their
salary with
tuition fees or other rates. Curriculum for Abbaco masters was also universal, in that lessons were directed towards solving commercial problems. Still, these primary and secondary math schools were not to be confused with
university level math subjects.
Establishment Wealthy merchants, because of their substantial influence on public governments and their desire to educate their sons in commercial mathematics, initiated constructions of schools with the support of other parents. Communal governments then proceeded to attract abbaco masters from elsewhere, so as to avoid partiality and inevitable dispute, and to select the best according to qualification, age and salary request. They drew up contracts that specified the number of years an appointed master must work, the number of students he was allowed to teach, and the certain percentage of fees he was to return to the commune. Contracts usually ranged from twenty to thirty ducats or florins, depending on the
currency used, for one to three years. In return, communes, would grant
tax exemptions (full or half), rights to collect fees (tuition fees, textbook and school supply sales), and a
house for personal use over and above the master's annual salary. Independent teachers could also be hired by the commune, but for lower wages. Most times, freelance masters were contracted by a group of parents in a similar fashion to that of communal agreements, thus establishing their own school if the number of students being tutored was significant in size. Abbaco apprentices training to become masters could also tutor household children and pay for their studies simultaneously. Upon graduation, however, apprentices were required to teach elsewhere for fear of stealing the master's students and income.
Curriculum Arithmetic,
geometry, bookkeeping, reading and writing in the vernacular were the basic elementary and secondary subjects in the abbaco syllabus for most institutions, which began in the fall, Mondays through Saturdays. Although Grendler states that the hours students spent in school could be very long and lasting half a year to eight months,
Merry Wiesner-Hanks takes the opposite view: boys and girls only spent half a day for up to four months. Here, Grendler may be considering the wealthy commoners and higher social classes, whereas Wiesner-Hanks may be looking at the working classes. Mathematical problems dealt with the everyday exchange of different types of goods or monies of differing values, whether it was in demand or in good quality, and how much of it was being traded. Other problems dealt with distribution of profits, where each member invested a certain sum and may have later withdrawn a portion of that amount. Labor contracts too, where the
employer agreed to a certain wage over the course of a certain term for a certain type of work that produced a specific amount of goods, but the
employee decided to leave after a while, were brought up. Bookkeeping taught students to note
weight,
length,
size and other quantitative and qualitative information of goods. == See also ==