How to Learn in Abacus

How to Learn in Abacus

Abacus or abaco refers to calculations, especially the subject of direct calculations, using Hindu numerals without the help of the abacus.

Abacus school is a term applied to any Italian school or tutorial after the 13th century, whose commerce-directed curriculum placed special emphasis on mathematics, such as algebra, among other subjects. 

These schools sprang after the publication of  Fibonacci’s Book of the Abacus an his introduction of  the Hindu-Arabic numeral system. In Fibonacci’s viewpoint, this system, originating in India around 400 BCE. and later adopted by the Arabs, was simpler and more practical than using the existing Roman numeric tradition. Italian merchants and traders quickly adopted the structure as a means of  producing accountants, clerks, and so on, and subsequently abacus schools for students were established.

These were done in many ways: communes could appeal to patrons to support the institution and find masters; religious institutions could finance and oversee the curriculum; independent masters could teach pupils. Unless they were selected 

for teaching occupations that were salaried, most masters taught students who could pay as this was their main source of income.

Abacus schools were significant for a couple of reasons: Firstly, because mathematics was associated with many professions, including trade, there was an increasing need to do away with the old Roman numeral system which produced too many errors.

The number of Roman characters a merchant needed to memorize to carry out financial transactions as opposed to Hindu-numerals made the switch practical. 

Commercialists were first introduced to this new system through Leonardo Fibonacci, who came from a business family and had studied Arabic math. Being convinced of its uses, abacus schools were therefore created and dominated by wealthy  merchants, with some exceptions.

Sons could now be trained by the best and brightest teachers to take over their family business and the fortunate poor had more access to a variety of  vocations. Morality also played a role in determining the school attendance of commoners.

                                     

School system ---

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.

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, 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.