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 Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

, among other subjects. These schools sprang up after the publication of

Fibonacci Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Wester ...

's '' Book of the Abacus'' and his introduction of the

Hindu–Arabic numeral system The Hindu–Arabic numeral system or Indo-Arabic numeral system Audun HolmeGeometry: Our Cultural Heritage 2000 (also called the Hindu numeral system or Arabic numeral system) is a positional decimal numeral system, and is the most common syste ...

. In Fibonacci's viewpoint, this system, originating in

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area, the List of countries and dependencies by population, second-most populous ...

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 Institutions are humanly devised structures of rules and norms that shape and constrain individual behavior. All definitions of institutions generally entail that there is a level of persistence and continuity. Laws, rules, social conventions a ...

and find masters; religious institutions could finance and oversee the

curriculum In education, a curriculum (; plural, : curricula or curriculums) is broadly defined as the totality of student experiences that occur in the educational process. The term often refers specifically to a planned sequence of instruction, or to ...

; 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. The words ''abacus'' or ''abaco'' refers to calculations, especially the subject of direct calculations, and does not imply the use of an

abacus The abacus (''plural'' abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hi ...

Significance

Abacus schools were significant for a couple of reasons: Firstly, because

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

was associated with many professions, including

trade Trade involves the transfer of goods and services from one person or entity to another, often in exchange for money. Economists refer to a system or network that allows trade as a market. An early form of trade, barter, saw the direct exc ...

,Grendler, 1989, Page 22. 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 A merchant is a person who trades in commodities produced by other people, especially one who trades with foreign countries. Historically, a merchant is anyone who is involved in business or trade. Merchants have operated for as long as indust ...

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 Business is the practice of making one's living or making money by producing or buying and selling products (such as goods and services). It is also "any activity or enterprise entered into for profit." Having a business name does not separ ...

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. Secondly, reading, writing, and some elementary math as job requirements for general occupations meant that

literacy Literacy in its broadest sense describes "particular ways of thinking about and doing reading and writing" with the purpose of understanding or expressing thoughts or ideas in Writing, written form in some specific context of use. In other wo ...

levels rose with the number of ordinary students attending institutions or being tutored at home. Sailors, for example, who wished to climb the social ladder had to present literacy and arithmetic skills on their

résumé A résumé, sometimes spelled resume (or alternatively resumé), also called a curriculum vitae (CV), is a document created and used by a person to present their background, skills, and accomplishments. Résumés can be used for a variety of rea ...

. Aspiring abbaco masters themselves need have studied only elementary, or secondary abbaco in order to teach others.

School system

Italian Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Ita ...

abacus school systems differed more in their establishment than in their curriculum during the

Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...

. 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 A salary is a form of periodic payment from an employer to an employee, which may be specified in an employment contract. It is contrasted with piece wages, where each job, hour or other unit is paid separately, rather than on a periodic basis. F ...

with

tuition Tuition payments, usually known as tuition in American English and as tuition fees in Commonwealth English, are fees charged by education institutions for instruction or other services. Besides public spending (by governments and other public bo ...

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 A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United Stat ...

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 A currency, "in circulation", from la, currens, -entis, literally meaning "running" or "traversing" is a standardization of money in any form, in use or circulation as a medium of exchange, for example banknotes and coins. A more general ...

used, for one to three years. In return, communes, would grant

tax A tax is a compulsory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, or n ...

exemptions (full or half), rights to collect fees (tuition fees, textbook and school supply sales), and a

house A house is a single-unit residential building. It may range in complexity from a rudimentary hut to a complex structure of wood, masonry, concrete or other material, outfitted with plumbing, electrical, and heating, ventilation, and air cond ...

for personal use over and above the masters 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 Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, 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 Employment is a relationship between two parties regulating the provision of paid labour services. Usually based on a contract, one party, the employer, which might be a corporation, a not-for-profit organization, a co-operative, or any o ...

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 Employment is a relationship between two parties regulating the provision of paid labour services. Usually based on a contract, one party, the employer, which might be a corporation, a not-for-profit organization, a co-operative, or any ot ...

decided to leave after a while, were brought up. Bookkeeping taught students to note

weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...

length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Inte ...

size Size in general is the magnitude or dimensions of a thing. More specifically, ''geometrical size'' (or ''spatial size'') can refer to linear dimensions ( length, width, height, diameter, perimeter), area, or volume. Size can also be me ...

and other quantitative and qualitative information of goods. Luis Radford. “On the Epistemological Limits of Language: Mathematical Knowledge and Social Practice During the Renaissance”. Educational Studies in Mathematics. Vol. 52. No. 2. Springer. 2003. Pages 127-129, 131)

Notes

References

* Baron, Hans. "The Social Background of Political Liberty in the Early Italian Renaissance". Comparative Studies in Society and History. Vol. 2. No. 4. Cambridge University Press. July 1960. Page 440. * Fibonacci, Leonardo. "Fibonacci's Liber Abaci: Leonardo Pisano's Book of Calculation". Contributor Laurence Edward Sigler. 202 Springer. 2003. Page 4. * Grendler, Paul F. "Schooling in Renaissance Italy Literacy and Learning, 1300–1600". Baltimore Johns Hopkins University Press. 1989. Pages 2, 5, 19, 12–13, 15–17, 22, 30–31, 33–34, 36, 41, 104. * Michael of Rhodes Project Team, Dibner Institute, and WGBH Interactive
"Michael of Rhodes: A Medieval Mariner and His Manuscript".

Institute and Museum of the History of Science Museo Galileo, the former ''Istituto e Museo di Storia della Scienza'' (Institute and Museum of the History of Science) is located in Florence, Italy, in Piazza dei Giudici, along the River Arno and close to the Uffizi Gallery. The museum, dedicat ...

. 2005. Sunday, March 23, 2008. * Radford, Luis. "On the Epistemological Limits of Language: Mathematical Knowledge and Social Practice During the Renaissance". Educational Studies in Mathematics. Vol. 52. No. 2. Springer. 2003. Pages 127-129, 131. * Wiesner-Hanks, Merry E. "Early Modern Europe, 1450-1789". Cambridge: Cambridge University Press, 2006. Pages 119-124. * Yerkes, Robert M. "The Use of Roman Numerals". Science. New series. Vol. 20. No. 505. American Association for the Advancement of Science. September 2, 1904. Pages 309-310.

External links

* Carson, Stephen W
"Fibonacci and Mises".
Online Posting. Mises Economics Blog.

Ludwig von Mises Institute Ludwig von Mises Institute for Austrian Economics, or Mises Institute, is a libertarian nonprofit think tank headquartered in Auburn, Alabama, United States. It is named after the Austrian School economist Ludwig von Mises (1881–1973). It ...

. May 25, 2006. Sunday, March 23, 2008.
"Mathematical decimal system introduced in 4BC".
Did You Know?. Sunday, March 23, 2008. * Trabia, Carlo.

Best of Sicily Magazine.'' 2006. Sunday, March 23, 2008. {{DEFAULTSORT:Abacus School Medieval European education Medieval European mathematics